Internal waves Research Papers - Academia.edu (original) (raw)

2000, Nature

The overturning circulation of the ocean plays an important role in modulating the Earth's climate. But whereas the mechanisms for the vertical transport of water into the deep ocean--deep water formation at high latitudes--and horizontal transport in ocean currents have been largely identified, it is not clear how the compensating vertical transport of water from the depths to the surface is accomplished. Turbulent mixing across surfaces of constant density is the only viable mechanism for reducing the density of the water and enabling it to rise. However, measurements of the internal wave field, the main source of energy for mixing, and of turbulent dissipation rates, have typically implied diffusivities across surfaces of equal density of only approximately 0.1 cm2 s(-1), too small to account for the return flow. Here we report measurements of tracer dispersion and turbulent energy dissipation in the Brazil basin that reveal diffusivities of 2-4 cm2 s(-1) at a depth of 500 m ...

2009, Annual Review of Fluid Mechanics

The ocean circulation is a cause and consequence of fluid scale interactions ranging from millimeters to more than 10,000 km. Although the wind field produces a large energy input to the ocean, all but approximately 10% appears to be dissipated within about 100 m of the sea surface, rendering observations of the energy divergence necessary to maintain the full watercolumn flow difficult. Attention thus shifts to the physically different kinetic energy (KE) reservoirs of the circulation and their maintenance, dissipation, and possible influence on the very small scales representing irreversible molecular mixing. Oceanic KE is dominated by the geostrophic eddy field, and depending on the vertical structure (barotropic versus low-mode baroclinic), direct and inverse energy cascades are possible. The pathways toward dissipation of the dominant geostrophic eddy KE depend crucially on the direction of the cascade but are difficult to quantify because of serious observational difficulties for wavelengths shorter than approximately 100-200 km. At high frequencies, KE is dominated by internal waves with near-inertial frequencies (frequencies near the local Coriolis parameter), whose shears appear to be a major source of wave breaking and mixing in the ocean interior. 253 Annu. Rev. Fluid Mech. 2009.41:253-282. Downloaded from arjournals.annualreviews.org by 65.96.167.244 on 01/19/09. For personal use only. Click here for quick links to Annual Reviews content online, including: • Other articles in this volume • Top cited articles • Top downloaded articles • Our comprehensive search Further ANNUAL REVIEWS 254 Ferrari · Wunsch Annu. Rev. Fluid Mech. 2009.41:253-282. Downloaded from arjournals.annualreviews.org by 65.96.167.244 on 01/19/09. For personal use only. www.annualreviews.org • Ocean Circulation Kinetic Energy 256 Ferrari · Wunsch Annu. Rev. Fluid Mech. 2009.41:253-282. Downloaded from arjournals.annualreviews.org by 65.96.167.244 on 01/19/09. For personal use only. 4 Geostrophic eddies are commonly called mesoscale eddies, which is a misnomer (in the atmospheric literature, they are referred to as synoptic scale eddies), but we sometimes use the terminology. www.annualreviews.org • Ocean Circulation Kinetic Energy 257 Annu. Rev. Fluid Mech. 2009.41:253-282. Downloaded from arjournals.annualreviews.org by 65.96.167.244 on 01/19/09. For personal use only. LITERATURE CITED Alford MH. 2003. Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophys. Res. Lett. 30:1424 Alford MH, Whitmont M. 2007. Seasonal and spatial variability of near-inertial kinetic energy from historical moored velocity records. J. Phys. Oceanogr. 37:2022-37 Arbic BK, Flierl GR. 2004. Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom Ekman friction: application to mid-ocean eddies. J. Phys. Oceanogr. 34:2257-73 Arbic B, Flierl GR, Scott RB. 2007. Cascade inequalities for forced-dissipated geostrophic turbulence.

1967, Journal of Fluid Mechanics

A new type of solitary wave motion in incompressible fluids of non-uniform density has been investigated experimentally and theoretically. If a fluid is stratified in such a manner that there are two layers of different density joined by a thin region in which the density varies continuously, this type of wave propagates along the density gradient region without change of shape. In contrast to previously known solitary waves, these disturbances can exist even if the fluid depth is infinite. The waves are described by an approximate solution of the inviscid equations of motion. The analysis, which is based on the assumption that the wavelength of the disturbance is large compared with the thickness, L, of the region in which the density is not constant, indicates that the propagation velocity, U , is characterized by the dimensionless group (gLlU2) In (pl/p2), where g is the gravitational acceleration and p is the density. The value of this group, which is dependent on the wave amplitude and the form of the density gradient, is of the order one. Experimentally determined propagation velocities and wave shapes serve to verify the theoretical model.

2000, Limnology and Oceanography

Basin-scale internal waves provide the driving forces for vertical and horizontal fluxes in a stratified lake below the wind-mixed layer. Thus, correct modeling of lake mixing and transport requires accurate modeling of basinscale internal waves: examining this capability with a hydrostatic, z-coordinate three-dimensional (3D) numerical model at coarse grid resolutions is the focus of this paper. It is demonstrated that capturing the correct thermocline forcing with a 3D mixed-layer model for surface dynamics results in a good representation of low-frequency internal wave dynamics. The 3D estuary and lake computer model ELCOM is applied to modeling Lake Kinneret, Israel, and is compared with field data under summer stratification conditions to identify and illustrate the spatial structure of the lowest-mode basin-scale Kelvin and Poincaré waves that provide the largest two peaks in the internal wave energy spectra. The model solves the unsteady Reynolds-averaged Navier-Stokes equations using a semi-implicit method similar to the momentum solution in the TRIM code with the addition of quadratic Euler-Lagrange discretization, scalar (e.g., temperature) transport using a conservative flux-limited approach, and elimination of vertical diffusion terms in the governing equations. A detailed description is provided of turbulence closure for the vertical Reynolds stress terms and vertical turbulent transport using a 3D mixed-layer model parameterized on wind and shear energy fluxes instead of the convential eddy viscosity/diffusivity assumption. This approach gives a good representation of the depth of the mixed-layer at coarse vertical grid resolutions that allows the internal waves to be energized correctly at the basin scale.

2009, Journal of Experimental Marine Biology and Ecology

Mesophotic coral reefs, reefs at depths of 30 m to 150 m, are receiving renewed interest from coral reef scientists and managers because they are linked physically and biologically to their shallow water counterparts, have the potential to be refugia for shallow coral reef taxa such as coral and sponges, and can be a source of larvae that could contribute to the resiliency of shallow water reefs. Here we review what is currently known about how mesophotic reef communities are structured and identify critical areas where new information is needed. The review covers two primary taxa, coral and sponges, where a majority of the ecological work on mesophotic coral reefs has been done, and physical processes (e.g., the attenuation of visible irradiance and internal waves) that exert significant abiotic control on the structure of these deep fore reef communities. Understanding the ecology of mesophotic coral reefs, and the connectivity between them and their shallow water counterparts, should be a primary focus of future reef studies as the worldwide degradation of shallow coral reefs, and the ecosystem services they provide, continues.

2003, Science

The following resources related to this article are available online at

2004, IEEE Journal of Oceanic Engineering

A moored array of current, temperature, conductivity, and pressure sensors was deployed across the Chinese continental shelf and slope in support of the Asian Seas International Acoustics Experiment. The goal of the observations was to quantify the water column variability in order to understand the along-and across-shore low-frequency acoustic propagation in shallow water. The moorings were deployed from April 21-May 19, 2001 and sampled at 1-5 min intervals to capture the full range of temporal variability without aliasing the internal wave field. The dominant oceanographic signal by far was in fact the highly nonlinear internal waves (or solitons) which were generated near the Batan Islands in the Luzon Strait and propagated 485 km across deep water to the observation region. Dubbed trans-basin waves, to distinguish them from other, smaller nonlinear waves generated locally near the shelf break, these waves had amplitudes ranging from 29 to greater than 140 m and were among the largest such waves ever observed in the world's oceans. The waves arrived at the most offshore mooring in two clusters lasting 7-8 days each separated by five days when no waves were observed. Within each cluster, two types of waves arrived which have been named type-a and type-b. The type-a waves had greater amplitude than the type-b waves and arrived with remarkable regularity at the same time each day, 24 h apart. The type-b waves were weaker than the type-a waves, arrived an hour later each day, and generally consisted of a single soliton growing out of the center of the wave packet. Comparison with modeled barotropic tides from the generation region revealed that: 1) The two clusters were generated around the time of the spring tides in the Luzon strait; and 2) The type-a waves were generated on the strong side of the diurnal inequality while the type-b waves were generated on the weaker beat. The position of the Kuroshio intrusion into the Luzon Strait may modulate the strength of the waves being produced. As the waves shoaled, the huge lead solitons first split into two solitons then merged together into a broad region of thermocline depression at depths less than 120 m. Elevation waves sprang up behind them as they continued to propagate onshore. The elevation waves also grew out of regions where the locally-generated internal tide forced the main thermocline down near the bottom. The "critical Manuscript

2000, Annual Review of Fluid Mechanics

▪ We review the dynamics of stably stratified flows in the regime in which the Froude number is considered small and the Rossby number is of order one or greater. In particular we emphasize the nonpropagating component of the flow field, as opposed to the internal wave component. Examples of such flows range from the later stages of decay of turbulent flows to mesoscale meteorological flows. Results from theoretical analyses, laboratory experiments, and numerical simulations are presented. The limiting form of the equations of motion appears to describe the laboratory experiments and numerical simulations rather well. There are similarities with the dynamics of two-dimensional flows, but three-dimensional effects are clearly important. A number of remaining open issues are discussed.

2014, Journal of Physical Oceanography

The authors present inferences of diapycnal diffusivity from a compilation of over 5200 microstructure profiles. As microstructure observations are sparse, these are supplemented with indirect measurements of mixing obtained from (i) Thorpe-scale overturns from moored profilers, a finescale parameterization applied to (ii) shipboard observations of upper-ocean shear, (iii) strain as measured by profiling floats, and (iv) shear and strain from full-depth lowered acoustic Doppler current profilers (LADCP) and CTD profiles. Vertical profiles of the turbulent dissipation rate are bottom enhanced over rough topography and abrupt, isolated ridges. The geography of depth-integrated dissipation rate shows spatial variability related to internal wave generation, suggesting one direct energy pathway to turbulence. The global-averaged diapycnal diffusivity below 1000-m depth is O(10 24 ) m 2 s 21 and above 1000-m depth is O(10 25 ) m 2 s 21 . The compiled microstructure observations sample a wide range of internal wave power inputs and topographic roughness, providing a dataset with which to estimate a representative global-averaged dissipation rate and diffusivity. However, there is strong regional variability in the ratio between local internal wave generation and local dissipation. In some regions, the depthintegrated dissipation rate is comparable to the estimated power input into the local internal wave field. In a few cases, more internal wave power is dissipated than locally generated, suggesting remote internal wave sources. However, at most locations the total power lost through turbulent dissipation is less than the input into the local internal wave field. This suggests dissipation elsewhere, such as continental margins.

2004, IEEE Journal of Oceanic Engineering

A field program to measure acoustic propagation characteristics and physical oceanography was undertaken in April and May 2001 in the northern South China Sea. Fluctuating ocean properties were measured with 21 moorings in water of 350to 71-m depth near the continental slope. The sea floor at the site is gradually sloped at depths less than 90 m, but the deeper area is steppy, having gradual slopes over large areas that are near critical for diurnal internal waves and steep steps between those areas that account for much of the depth change. Large-amplitude nonlinear internal gravity waves incident on the site from the east were observed to change amplitude, horizontal length scale, and energy when shoaling. Beginning as relatively narrow solitary waves of depression, these waves continued onto the shelf much broadened in horizontal scale, where they were trailed by numerous waves of elevation (alternatively described as oscillations) that first appeared in the continental slope region. Internal gravity waves of both diurnal and semidiurnal tidal frequencies (internal tides) were also observed to propagate into shallow water from deeper water, with the diurnal waves dominating. The internal tides were at times sufficiently nonlinear to break down into bores and groups of high-frequency nonlinear internal waves.

1999

Temperature-gradient microstructure and nutrient profiling were undertaken at both an inshore and an offshore site on Mono Lake, California, to determine whether boundary mixing occurred and the effects on nutrient flux within the lake. Turbulence, as quantified by rates of dissipation of turbulent kinetic energy, was two to three orders of magnitude higher at the inshore site where the pycnocline intersected the bottom than at the same depths at an offshore station. The intense turbulence primarily occurred within 3.5 m of the sediment-water interface. In addition, temperature profiles were more incrementally stepped in the pycnocline inshore than offshore. The Turner angle indicated that double-diffusive processes may have augmented turbulent transport in the upper 10 m, where temperatures were inversely stratified, but not in the main pycnocline. Within the pycnocline, ⑀ exceeded the threshold value for buoyancy flux (⑀ thr ϭ 15N 2 ) in 21% of the turbulent layers inshore but in only 1% of the layers offshore. The coefficient of vertical eddy diffusivity, K z , was two to four orders of magnitude higher within 4 m of the bottom inshore than offshore at the same depths. Spatially averaged values of K z , obtained from the heat-flux method using data obtained from both conductivity-temperature-depth (CTD) profiles and moored thermistor chains, were two orders of magnitude less than those obtained nearshore with microstructure profiling. From the differences in K z , we inferred that most heat flux occurred due to boundary mixing at the base of the pycnocline inshore with the heat redistributed laterally by advection. Boundary mixing was initiated after winds were strong enough for the Lake number to decrease to a value of 2; thermocline compression and steepening of internal waves at the base of the pycnocline occurred, followed by packets of high-frequency internal waves critical for wave breaking. Calculated ammonium fluxes at the inshore site were sufficient to support daily rates of primary productivity in the deep chlorophyll maximum throughout the lake. These results indicate the vertical flux of nutrients across the nutricline in Mono Lake occurs over a limited area during intense mixing events initiated by high winds.

1975, Journal of Geophysical Research

Vertical propagation of near-inertial period waves has been detected in a series of recent velocity profiles by a technique of vector spectral analysis. This method, previously applied to vector series in time, has been used to study the vertical spatial structure of velocity profiles obtained in the Mid-Ocean Dynamics Experiment (MODE). Prior to the use of spectral analysis, however, it is necessary to minimize the influence of vertical variations of the Brunt-Viiisiilii frequency. The procedure was to normalize the current amplitudes and stretch the vertical coordinate according to a WKB scheme. The vector spectral analysis, applied to the normalized and stretched profiles, yielded wave polarization estimates which are related to the sign of the vertical group velocity of internal waves. The analysis of a set of velocity profiles indicates that the net energy flux of the waves near the inertial frequency is downward.

2007, Progress in Oceanography

The present review is focused on the mesoscale physical processes recognized in the Western Iberia Ecosystem, complementing earlier reviews dedicated to larger scales. Recent studies support the idea that the mesoscale processes, superimposed on the larger scale variability, are the major factor controlling the ecosystem functioning in the region. A complex structure of interleaved alongshore slope, shelf and coastal currents that interact with eddies, buoyant plumes, upwelling filaments and fronts, surface layer expressions of the subsurface circulation and internal waves is revealed by the latest research. All of these contribute in different ways to have an effect on the ecosystem. The supposedly less variable winter circulation also exhibits significant mesoscale activity, in the form of eddy shedding from the poleward slope current, intermittent upwelling events and transient nearshore poleward flows. The present incomplete knowledge of this complex system presents a number of challenges and questions that must be addressed if we are to arrive at a satisfactory understanding and predictive capability for the system as a whole.

2005, Science

The Sun's rotation profile and lithium content have been difficult to understand in the context of conventional models of stellar evolution. Classical hydrodynamic models predict that the solar interior must rotate highly differentially, in disagreement with observations. It has recently been shown that internal waves produced by convection in solar-type stars produce an asymmetric, shear layer oscillation, similar to Earth's quasi-biennial oscillation, that leads to efficient angular momentum redistribution from the core to the envelope. We present results of a model that successfully reproduces both the rotation profile and the surface abundance of lithium in solartype stars of various ages.

1982, Journal of Physical Oceanography

1999, Limnology and Oceanography

Internal tidal bore warm fronts were observed during the summer of 1996 off the coast of Southern California. Warm bore fronts had concentrating currents resulting from high-frequency internal motions and from a larger twoway flow; the two-way flow featured surface currents onshore and bottom currents offshore. A sharp thermocline depression and high-frequency, large-amplitude internal motions followed the leading edge of the bore, with downwelling currents on the trailing side of the crest of the nonlinear internal waves and upwelling currents in front of the crest. Warm bores propagated onshore with a propagation speed, c, that ranged from 10.6 to 19.6 cm s Ϫ1 , while time-averaged frontal currents, ū, varied from 11.2 to 17.6 cm s Ϫ1 in the shallowest bin. In one out of three cases ū Ͼ c, which implied that there were faster currents than the rate of advance of the front and which implied that the origin of surface frontal material is behind the front, not in front of it. Three invertebrate larval taxa were found at all sites across fronts, but only two intertidal barnacles, Pollicipes polymerus and Chthamalus spp., were concentrated at the front's surface, while the subtidal bryozoan Membranipora spp. was not. Frontal Pollicipes were more concentrated than were Chthamalus. The frontal downwelling currents observed suggested that concentrated larvae would have to swim upward in order to maintain depth. Pollicipes were abundant on the offshore warm side of the fronts but were absent or rare on the onshore colder side, suggesting that the origin of frontal Pollicipes was behind the front, although an alternative cannot be ruled out conclusively. Chthamalus were more abundant at depth than at the surface at all sites except at the front, where this pattern was reversed. The origin of frontal Chthamalus is uncertain. Membranipora were more abundant on the onshore colder side of the fronts, and abundances were usually higher at depth than at surface. Lack of accumulation in this species may be due to its limited swimming capability.

2004, Journal of Physical Oceanography

Observations of turbulence, internal waves, and subinertial flow were made over a steep, corrugated continental slope off Virginia during May-June 1998. At semidiurnal frequencies, a convergence of low-mode, onshore energy flux is approximately balanced by a divergence of high-wavenumber offshore energy flux. This conversion occurs in a region where the continental slope is nearly critical with respect to the semidiurnal tide. It is suggested that elevated near-bottom mixing (K ϳ 10 Ϫ3 m 2 s Ϫ1 ) observed offshore of the supercritical continental slope arises from the reflection of a remotely generated, low-mode, M 2 internal tide. Based on the observed turbulent kinetic energy dissipation rate ⑀, the high-wavenumber internal tide decays on time scales O(1 day). No evidence for internal lee wave generation by flow over the slope's corrugations or internal tide generation at the shelf break was found at this site.

1997, IEEE Journal of Oceanic Engineering

An overview is given of the July-August 1995 SWARM shallow-water internal wave acoustic scattering experiment. This experiment studied both acoustic propagation through and scattering by the linear and nonlinear internal waves found on the Mid-Atlantic Bight continental shelf, as well as the physical oceanography of the internal wavefield. In order that our goal of explaining the nature of the acoustic scattering should not be hindered by incomplete environmental knowledge, numerous instruments, both ship-deployed and moored, measured the acoustics, geophysics, and oceanography. In this paper, we show some of the results from the first year's analysis of the environmental and acoustic data. The environmental measurements, which are a key input to the analyses of the acoustic data, are given slightly more emphasis at this point in time. Some of the more interesting oceanographic, geophysical, and acoustical results we present here are: evidence for the dominance of the lee-wave mechanism for soliton production, evidence for the "solibore internal tide," the "dnoidal wave" description of solitons, the inversion of chirp sonar data for bottom properties, propagation loss extraction from air-gun data, and the intensity and travel-time fluctuations seen in propagating acoustic normal modes. Directions for future research are outlined.

1996, Journal of …

Proteus mirabilis colonies exhibit striking geometric regularity. Basic microbiological methods and imaging techniques were used to measure periodic macroscopic events in swarm colony morphogenesis. We distin-guished three initial phases... more

1999, Journal of Physical Oceanography

The authors present a field study of estuarine turbulence in which profiles of Reynolds stresses were directly measured using an ADCP throughout a 25-h tidal day. The dataset that is discussed quantifies turbulent mixing for a water column in northern San Francisco Bay that experiences a sequence of states that includes a weak ebb and flood that are stratified, followed

1998, Geophysical Research Letters

We compute solitary wave solutions of a Hamiltonian model for large-amplitude long internal waves in a two-layer stratification. Computations are performed for values of the density and depth ratios close to oceanic conditions, and comparisons are made with solutions of both weakly and fully nonlinear models. It is shown that characteristic features of highly nonlinear solitary waves such as broadening are reproduced well by the present model. To cite this article:

2008, Progress in Oceanography

In this review paper, state-of-the-art observational and numerical modeling methods for small scale turbulence and mixing with applications to coastal oceans are presented in one context. Unresolved dynamics and remaining problems of field observations and numerical simulations are reviewed on the basis of the approach that modern process-oriented studies should be based on both observations and models. First of all, the basic dynamics of surface and bottom boundary layers as well as intermediate stratified regimes including the interaction of turbulence and internal waves are briefly discussed. Then, an overview is given on just established or recently emerging mechanical, acoustic and optical observational techniques. Microstructure shear probes although developed already in the 1970s have only recently become reliable commercial products. Specifically under surface waves turbulence measurements are difficult due to the necessary decomposition of waves and turbulence. The methods to apply Acoustic Doppler Current Profilers (ADCPs) for estimations of Reynolds stresses, turbulence kinetic energy and dissipation rates are under further development. Finally, applications of well-established turbulence resolving particle image velocimetry (PIV) to the dynamics of the bottom boundary layer are presented. As counterpart to the field methods the state-of-the-art in numerical modeling in coastal seas is presented. This includes the 0079-6611/$ -see front matter Ó application of the Large Eddy Simulation (LES) method to shallow water Langmuir Circulation (LC) and to stratified flow over a topographic obstacle. Furthermore, statistical turbulence closure methods as well as empirical turbulence parameterizations and their applicability to coastal ocean turbulence and mixing are discussed. Specific problems related to the combined wave-current bottom boundary layer are discussed. Finally, two coastal modeling sensitivity studies are presented as applications, a two-dimensional study of upwelling and downwelling and a three-dimensional study for a marginal sea scenario (Baltic Sea). It is concluded that the discussed methods need further refinements specifically to account for the complex dynamics associated with the presence of surface and internal waves.

2004, Geophysical Research Letters

1] Evidence for baroclinic tide origin of internal solitary waves (ISWs) in the northeastern South China Sea is presented, based on 116 internal wave packets observed in satellite images from 1995 to 2001. These wave packets can be divided into two types, a single-wave ISW packet containing only one ISW with/without an oscillating tail, and a multiple-wave ISW packet composed of a group of rank-ordered ISWs. All of the 22 single-wave ISW packets occur in the deep water zone. It is suggested that the ISWs, instead of being generated by the lee-wave mechanism, are developed by nonlinear steepening of the baroclinic tides, which are produced by the strong tidal currents flowing over a ridge in Luzon Strait. This suggestion is verified by an ERS-2 SAR image, which records such an evolution process from a baroclinic tide to a single ISW in its spatial domain.

2002, Journal of Fluid Mechanics

Boundary-forced stratified turbulence is studied in the prototypical case of turbulent channel flow subject to stable stratification. The large-eddy simulation approach is used with a mixed subgrid model that involves a dynamic eddy viscosity component and a scale-similarity component. After an initial transient, the flow reaches a new balanced state corresponding to active wall-bounded turbulence with reduced vertical transport which, for the cases in our study with moderate-to-large levels of stratification, coexists with internal wave activity in the core of the channel. A systematic reduction of turbulence levels, density fluctuations and associated vertical transport with increasing stratification is observed. Countergradient buoyancy flux is observed in the outer region for sufficiently high stratification.

2011, Journal of Physical Oceanography

Internal tide generation, propagation, and dissipation are investigated in Luzon Strait, a system of two quasi-parallel ridges situated between Taiwan and the Philippines. Two profiling moorings deployed for about 20 days and a set of nineteen 36-h lowered ADCP–CTD time series stations allowed separate measurement of diurnal and semidiurnal internal tide signals. Measurements were concentrated on a northern line, where the ridge spacing was approximately equal to the mode-1 wavelength for semidiurnal motions, and a southern line, where the spacing was approximately two-thirds that. The authors contrast the two sites to emphasize the potential importance of resonance between generation sites. Throughout Luzon Strait, baroclinic energy, energy fluxes, and turbulent dissipation were some of the strongest ever measured. Peak-to-peak baroclinic velocity and vertical displacements often exceeded 2 m s−1 and 300 m, respectively. Energy fluxes exceeding 60 kW m−1 were measured at spring tid...

1974, Journal of Fluid Mechanics

Internal waves of the fundamental mode propagating into a shoaling region have been studied experimentally in a continuously stratified fluid. The waves divide into three classes depending upon the ratio of the bottom slope γ to the wave-characteristic slope c. For γ/c < 1, the amplitude and wavenumber changes of the waves over the slope are in reasonable accord with a simple inviscid linear theory, prior to wave breakdown near the intersection of the slope and surface. Considerable mixing occurs in this corner region. When γ/c = 1, a striking instability of the bottom boundary layer is observed and the waves are heavily damped. When γ/c > 1, the waves are inhomogeneous and have complex spatial dependence.

2009, Ocean Science

Cross shelf-break exchange is limited by the tendency of geostrophic flow to follow bathymetric contours, not cross them. However, small scale topography, such as canyons, can reduce the local lengthscale of the flow and increase the local Rossby number. These higher Rossby numbers mean the flow is no longer purely geostrophic and significant cross-isobath flow can occur. This cross-isobath flow includes both upwelling and downwelling due to wind-driven shelf currents and the strong cascading flows of dense shelfwater into the ocean. Tidal currents usually run primarily parallel to the shelf-break topography. Canyons cut across these flows and thus are often regions of generation of strong baroclinic tides and internal waves. Canyons can also focus internal waves. Both processes lead to greatly elevated levels of mixing. Thus, through both advection and mixing processes, canyons can enhance Deep Ocean Shelf Exchange. Here we review the state of the science describing the dynamics of the flows and suggest further areas of research, particularly into quantifying fluxes of nutrients and carbon as well as heat and salt through canyons.

2002, Limnology and Oceanography

Vertical and horizontal exchanges in Pilkington Bay, a shallow (9 m) embayment of Lake Victoria, were determined from a surface energy budget, time series measurements of temperature, and quasi synoptic transects of conductivity, temperature, and depth conducted over a 2-d period. The surface energy budget is the first from a tropical lake over a diurnal timescale. Strong stratification developed during morning and early afternoon (Ͼ40 cycles h Ϫ1 ) but was eroded beginning in the afternoon by the combination of wind and heat loss. Surface heat losses contributed Ͼ70% of the energy for surface layer deepening 82% of the time from midafternoon until midmorning. Circulation times of the surface layer were Ͻ2 min as it deepened to 1.5 m in the afternoon and were Ͻ12 min at night even when mixing extended to the lake bottom. Spatial differences in the rates of heating and cooling and in the depth of wind mixing caused fronts to develop on spatial scales of kilometers within the bay. Convergence of these fronts led to downwelling of surface waters and upwelling of deep waters during the stratified period. Horizontal pressure gradients due to differential heating contributed to thermocline downwelling, lateral movement of deep, anoxic waters, and generation of high-frequency internal waves, all of which contribute to vertical and horizontal transports. Although wind and heat loss at one location generally determine the depth of the surface layer and thermocline, the depths of these key features may be strongly influenced by rates of heating and cooling elsewhere in a basin.

2003, Geophysical Research Letters

Tidal energy dissipation is estimated for eight semidiurnal and diurnal constituents using a global inverse solution constrained by TOPEX/Poseidon altimeter data. Very similar spatial patterns are obtained for all semidiurnal... more

1999

A nonlinear model is developed, based on the rotated-modified extended Korteweg-de Vries (reKdV) equation, of the evolution of an initially sinusoidal long wave in the coastal zone, representing an internal tide, into nonlinear waves including internal solitary waves. The coefficients of the basic equation are calculated using observed conditions for the north west shelf (NWS) of Australia. The roles of both quadratic and cubic nonlinearity, the Earth's rotation, and frictional dissipation are discussed. The combined action of nonlinearity and rotation leads to a number of intersting features in the wave form including solitons of both polarities, "thick" solitons, and sharp waves with steep fronts. It is shown that rotation is important for modelling the evolution of the internal tide, even for the relatively low latitude on the NWS of 20øS. Rotation increases the phase speed of the long internal tide, reduces the number of internal solitary waves that form from a long wave, and changes the form of the waves. The effects of nonlinearity on the vertical modal structure of the internal waves are also discussed. Results of numerical simulations are compared with current and temperature observations of the internal wave field on the NWS which show many of the features produced by the generalized KdV model.

2005, Limnology and Oceanography

In a laboratory study, we quantified the temporal energy flux associated with the degeneration of basin-scale internal waves in closed basins. The system is two-layer stratified and subjected to a single forcing event creating available potential energy at time zero. A downscale energy transfer was observed from the wind-forced basin-scale motions to the turbulent motions, where energy was lost due to high-frequency internal wave breaking along sloping topography. Under moderate forcing conditions, steepening of nonlinear basin-scale wave components was found to produce a high-frequency solitary wave packet that contained as much as 20% of the available potential energy introduced by the initial condition. The characteristic lengthscale of a particular solitary wave was less than the characteristic slope length, leading to wave breaking along the sloping boundary. The ratio of the steepening timescale required for the evolution of the solitary waves to the travel time until the waves shoaled controlled their development and degeneration within the domain. The energy loss along the slope, the mixing efficiency, and the breaker type were modeled using appropriate forms of an internal Iribarren number, defined as the ratio of the boundary slope to the wave slope (amplitude/wavelength). This parameter allows generalization to the oceanographic context. Analysis of field data shows the portion of the internal wave spectrum for lakes, between motions at the basin and buoyancy scales, to be composed of progressive waves: both weakly nonlinear waves (sinusoidal profile with frequencies near 10 Ϫ4 Hz) and strongly nonlinear waves (hyperbolic-secant-squared profile with frequencies near 10 Ϫ3 Hz). The results suggest that a periodically forced system may sustain a quasi-steady flux of 20% of the potential energy introduced by the surface wind stress to the benthic boundary layer at the depth of the pycnocline.

2003, Limnology and Oceanography

The influence of spatial and temporal variations in wind forcing on the circulation in lakes is investigated using field data and the three-dimensional Estuary and Lake Computer Model (ELCOM) applied to Lake Kinneret. Lake Kinneret field data from six thermistor chains and eight wind anemometers deployed during July 2001 are presented. Internal wave motions are well reproduced by the numerical model when forced with a spatially uniform wind taken from a station near the lake center; however, simulated seiche amplitudes are too large (especially vertical mode 2) and lead observations by 3-10 h (for a 24-h period wave) at different locations around the lake. Consideration of the spatial variation of the wind field improves simulated wave amplitude, and phase error at all stations is reduced to less than 1.5 h. This improvement is attributable to a better representation of the horizontally averaged wind stress and can be reproduced with a spatially uniform wind that has the same horizontally averaged wind stress as the spatially varying wind field. However, a spatially varying wind field is essential for simulating mean surface circulation, which is shown to be predominantly directly forced by the surface-layer-averaged wind stress moment.

1998, Sedimentary Geology

Slope sand deposits have accumulated from at least the Neogene to the Present on the southeastern Brazilian continental margin (Campos Basin area). This region shows sand accumulations concentrated on the upper portion and on the base of the continental slope with a middle to lower slope bypass zone. A synthesis of preliminary results, supported by recent cores, high-resolution geophysical surveys, geotechnical investigations and environmental research, is presented and permits a prelitrdnary analysis of the sedimentological mechanisms operational in this area. These point toward a temporal and spatial multiscale set of phenomena responsible for sand deposits. At any sea-level stand these deposits are dependent on: (1) a suitable sediment source; (2) offshelf transport mechanisms; (3) a morphostructural and hydrodynamic context responsible figr the deposition of these sands in the upper portion of continental slopes. The proposed scenario of depositional processes concerns: (1) a set of hydrological processes such as surface currents and counter-currents, waves, tides and eddies with sufficient energy to form submarine sand dune fields at the outer shelf; (2) the offshelf export of this sediment under a combined action of spillover, internal waves, eddies 'seafloor polishing effect' and gravity processes (turbidity currents); and (3) the slope sand deposits and their distribution controlled by the action of contour currents, mass movements and the morphological context, such as canyons, gullies or scarps.

2011, Reviews of Geophysics

Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability of the deep ocean internal wavefield. The observations are discussed in the context of the universal spectral model proposed by Garrett and Munk. The Garrett and Munk model is a good description of wintertime conditions at Site-D on the continental rise north of the Gulf Stream. Elsewhere and at other times, significant deviations in terms of amplitude, separability of the 2-D vertical wavenumber -frequency spectrum, and departure from the model's functional form are noted.

1996, Arxiv preprint astro-ph/9611189

Abstract. The internal gravity waves of low frequency which are emitted at the base of the solar convection zone are able to extract angular momentum from the radiative interior. We evaluate this transport with some simplify-ing... more

1999, Journal of Fluid Mechanics

Properties of solitary waves propagating in a two-layer fluid are investigated comparing experiments and theory. In the experiments the velocity field induced by the waves, the propagation speed and the wave shape are quite accurately measured using particle tracking velocimetry (PTV) and image analysis. The experiments are calibrated with a layer of fresh water above a layer of brine. The depth of the brine is 4.13 times the depth of the fresh water. Theoretical results are given for this depth ratio, and, in addition, in a few examples for larger ratios, up to 100:1. The wave amplitudes in the experiments range from a small value up to almost maximal amplitude. The thickness of the pycnocline is in the range of approximately 0.13-0.26 times the depth of the thinner layer. Solitary waves are generated by releasing a volume of fresh water trapped behind a gate. By careful adjustment of the length and depth of the initial volume we always generate a single solitary wave, even for very large volumes. The experiments are very repeatable and the recording technique is very accurate. The error in the measured velocities non-dimensionalized by the linear long wave speed is less than about 7-8% in all cases. The experiments are compared with a fully nonlinear interface model and weakly nonlinear Korteweg-de Vries (KdV) theory. The fully nonlinear model compares excellently with the experiments for all quantities measured. This is true for the whole amplitude range, even for a pycnocline which is not very sharp. The KdV theory is relevant for small wave amplitude but exhibit a systematic deviation from the experiments and the fully nonlinear theory for wave amplitudes exceeding about 0.4 times the depth of the thinner layer. In the experiments with the largest waves, rolls develop behind the maximal displacement of the wave due to the Kelvin-Helmholtz instability. The recordings enable evaluation of the local Richardson number due to the flow in the pycnocline. We find that stability or instability of the flow occurs in approximate agreement with the theorem of Miles and Howard.

2000, Continental Shelf Research

Synthetic aperture radar (SAR) images from ERS-1 and ERS-2 have been used to study the characteristics of internal waves in the East China Sea. Rank-ordered packets of nonlinear internal waves in the East China Sea are often observed in the SAR images, especially in the northeast of Taiwan. In this region, the internal wave "eld is very complicated, and its generation mechanisms include the in#uence of the tide and the upwelling, which is induced by the intrusion of the Kuroshio across the continental shelf. The internal wave distributions in the East and South China Seas have been compiled based on the SAR observations from satellites. The Kortweg}deVries (KdV) type equation has been used to study the evolution of internal wave packets generated in the upwelling area. Depending on the mixed layer depth, both elevation and depression waves can be generated based on numerical simulations as observed in the SAR images. The merging of two wave packets from nonlinear wave}wave interaction in the Yellow Sea has been observed in the SAR image and is demonstrated by numerical results.

2007, Geophysical Research …

1] An array of instruments air-deployed ahead of Hurricane Frances measured the three-dimensional, time dependent response of the ocean to this strong (60 ms À1 ) storm. Sea surface temperature cooled by up to 2.2°C with the greatest cooling occurring in a 50-km-wide band centered 60 -85 km to the right of the track. The cooling was almost entirely due to vertical mixing, not air-sea heat fluxes. Currents of up to 1.6 ms À1 and thermocline displacements of up to 50 m dispersed as near-inertial internal waves. The heat in excess of 26°C, decreased behind the storm due primarily to horizontal advection of heat away from the storm track, with a small contribution from mixing across the 26°C isotherm. SST cooling under the storm core (0.4°C) produced a 16% decrease in air-sea heat flux implying an approximately 5 ms À1 reduction in peak winds.

2005, Journal of Geophysical Research

A direct computation of the tidal generation of internal waves over the global ocean is presented. It is based on linear wave theory and high-resolution data for the bottom topography. The geographical distribution of the energy flux from tides to internal waves is determined with a spatial resolution of a few kilometers. The total flux over the area with a depth greater than 500 m is found to be 1.2 TW. The greatest uncertainties of the computation are due to unresolved topography and to nonlinear effects caused by supercritical bottom slope.

1988, Deep Sea Research Part A. Oceanographic Research Papers

Almtract-Mudwaves, with wavelengths up to 6 km and heights up to 100 m, are commonly found in the deep sea where steady, sediment-laden currents are present; their internal structure suggests that they have migrated with time. Lee waves appear to be generated in the density gradient above the sinusoidal mudwave topography; the near-bottom flow field associated with the lee waves creates a cross-wave asymmetry in bottom current velocity. A model of bottom flow and sedimentation rate for a transverse mudwave shows that preferential deposition occurs on the upstream flanks and the bed forms migrate upstream. The flow conditions for such lee waves are common in the deep sea; therefore many mudwaves are probably active under present flow conditions. The model suggests that for a given wave, the ratio of downstream-upstream sedimentation rate varies primarily with flow velocity. Thus changes in this ratio, determined by seismic or sampling techniques, might be used to determine past variations in flow velocity.

1997, Nature

Nature © Macmillan Publishers Ltd 1997 ... Leo RM Maas*, Dominique Benielli†, Joe¨l Sommeria† & Frans-Peter A. Lam* * Netherlands Institute for Sea Research, PO Box 59, 1790 AB Texel, The Netherlands † Ecole Normale et Superieure de Lyon,... more

1998, Surveys in Geophysics

Nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed. Attention is focussed upon guided waves long compared to the ocean depth. The effect of rotation on linear processes is reviewed in detail as well as the existing nonlinear models describing weakly and strongly nonlinear dynamics of long waves. The

2006, Geophysical Research Letters

1] We analyze three sets of ADCP measurements taken on the Dongsha plateau, on the shallow continental shelf, and on the steep continental slope in the northern South China Sea (SCS). The data show strong divergences of energy and energy flux of nonlinear internal waves (NLIW) along and across waves' prevailing westward propagation path. The NLIW energy flux is 8.5 kW m À1 on the plateau, only 0.25 kW m À1 on the continental shelf 220 km westward along the propagation path, and only 1 kW m À1 on the continental slope 120 km northward across the propagation path. Along the wave path on the plateau, the average energy flux divergence of NLIW is 0.04WmAˋ2,whichcorrespondstoadissipationrateofO(10Aˋ7Aˋ10Aˋ6)WkgAˋ1.Combiningthepresentwithpreviousobservationsandmodelresults,ascenarioofNLIWenergyfluxintheSCSemerges.NLIWsaregeneratedeastoftheplateau,propagatepredominantlywestwardacrosstheplateaualongabeamof0.04 W m À2 , which corresponds to a dissipation rate of O(10 À7 À10 À6 ) W kg À1 . Combining the present with previous observations and model results, a scenario of NLIW energy flux in the SCS emerges. NLIWs are generated east of the plateau, propagate predominantly westward across the plateau along a beam of 0.04WmAˋ2,whichcorrespondstoadissipationrateofO(10Aˋ7Aˋ10Aˋ6)WkgAˋ1.Combiningthepresentwithpreviousobservationsandmodelresults,ascenarioofNLIWenergyfluxintheSCSemerges.NLIWsaregeneratedeastoftheplateau,propagatepredominantlywestwardacrosstheplateaualongabeamof100 km width that is centered at $21°N, and dissipate nearly all their energy before reaching the continental shelf.

2006, Geophys. Res. Lett

1] Surface signatures associated with non-linear internal waves are often seen in satellite images of the western South China Sea (SCS) slope and shelf. Observation in the deep sea, to the east, are rare. Here we report on the evolution of an energetic packet as it propagated through the deep central basin of the SCS, toward the western slope and shelf. The waves have amplitudes estimated at 170 m, half widths of 3 km, and phase speeds of 2.9 ± 0.1 m/s, faster than the mode-1 linear phase speed of 2.6 m/s. The shape and observed phase speed were consistent with the Korteweg-deVries (KdV) model over the 65-km path that they were tracked. The intrinsic velocity shear of the waves is small compared to pre-existing shears, and the waves exhibit weak turbulence. The KdV fit and a satellite-derived estimate of horizontal wave extent imply a westward energy flux of 4.5 GW for each crest. Citation: Klymak,

1993, Journal of Geophysical Research

During the winter of 1988-1989 five acoustic Doppler current profilers (ADCPs) were moored in the central Greenland Sea to measure vertical currents that might occur in conjunction with deep mixing and convection. Two ADCPs were looking up from about 300 m and combined with thermistor strings in the depth range 60-260 m, two were looking downward from 200 m, and one was looking upward from 1400 m. First maxima of vertical velocity variance occurred at two events of strong cold winds in October and November when cooling and turbulence in the shallow mixed layer generated internal waves in the thermocline. Beginning in late November the marginal ice zone expanded eastward over the central Greenland Sea, reaching its maximum extent in late December. In mid-January a bay of ice-free water opened over the central Greenland Sea, leaving a wedge of ice, the "is odden," curled around it along the axis of the Jan Mayen Current and then northeastward and existing well into April 1989. Below the ice a mixed layer at freezing temperatures developed that increased in thickness from 60 to 120 m during the period of ice cover, corresponding to an average heat loss of about 40 W m -2.

2000, Limnology and Oceanography

The response of the water column to varying conditions of stratification and wind forcing was investigated in Lake Kinneret (Israel) using data collected from thermistor chains and acoustic Doppler current profilers during 1997 and 1998. The strong daily sea breeze was found to generate a vertical mode 1 internal Kelvin wave and basin-scale internal Poincaré waves of vertical modes 1, 2, and 3. The Kelvin wave, the dominant component of the internal wave field, was responsible for alongshore velocities in the nearshore regions. In the upwind nearshore regions, velocities were dominated by the forced response to the wind and were cross-shore in nature. In the lake interior, the Kelvin wave effect on the horizontal velocity field was minor compared to the higher vertical mode Poincaré waves. The Kelvin wave is shown to exist in resonant and nonforced states with the wind, whereas the vertical mode 1 Poincaré wave energy remained relatively constant, despite large variability in the forcing conditions. The energy in the higher mode Poincaré waves varied greatly, both on daily and seasonal timescales. The results demonstrate that the wind energy forces multiple basin-scale internal wave modes and that prior motion in the water column must be considered when determining the subsequent internal wave response in periodically forced systems.

2010, Journal of Physical …

In the South China Sea (SCS), 14 nonlinear internal waves are detected as they transit a synchronous array of 10 moorings spanning the waves' generation site at Luzon Strait, through the deep basin, and onto the upper continental slope 560 km to the west. Their arrival time, speed, width, energy, amplitude, and number of trailing waves are monitored. Waves occur twice daily in a particular pattern where larger, narrower ''A'' waves alternate with wider, smaller ''B'' waves. Waves begin as broad internal tides close to Luzon Strait's two ridges, steepening to O(3-10 km) wide in the deep basin and O(200-300 m) on the upper slope. Nearly all waves eventually develop wave trains, with larger-steeper waves developing them earlier and in greater numbers. The B waves in the deep basin begin at a mean speed of '5% greater than the linear mode-1 phase speed for semidiurnal internal waves (computed using climatological and in situ stratification). The A waves travel '5%-10% faster than B waves until they reach the continental slope, presumably because of their greater amplitude. On the upper continental slope, all waves speed up relative to linear values, but B waves now travel 8%-12% faster than A waves, in spite of being smaller. Solutions of the Taylor-Goldstein equation with observed currents demonstrate that the B waves' faster speed is a result of modulation of the background currents by an energetic diurnal internal tide on the upper slope. Attempts to ascertain the phase of the barotropic tide at which the waves were generated yielded inconsistent results, possibly partly because of contamination at the easternmost mooring by eastward signals generated at Luzon Strait's western ridge. These results present a coherent picture of the transbasin evolution of the waves but underscore the need to better understand their generation, the nature of their nonlinearity, and propagation through a time-variable background flow, which includes the internal tides.

2005, Astronomy and Astrophysics

In this paper, we develop a formalism in order to incorporate the contribution of internal gravity waves to the transport of angular momentum and chemicals over long time-scales in stars. We show that the development of a double peaked shear layer acts as a filter for waves, and how the asymmetry of this filter produces momentum extraction from the core when it is rotating faster than the surface. Using only this filtered flux, it is possible to follow the contribution of internal waves over long (evolutionary) time-scales. We then present the evolution of the internal rotation profile using this formalism for stars which are spun down via magnetic torquing. We show that waves tend to slow down the core, creating a "slow" front that may then propagate from the core to the surface. Further spin down of the surface leads to the formation of a new front. Finally we show how this momentum transport reduces rotational mixing in a 1.2 M ⊙ , Z = 0.02 model, leading to a surface lithium abundance in agreement with observations in the Hyades.

2003, Limnology and Oceanography

Observations are presented from Lake Biwa and Lake Kinneret showing the ubiquitous and often periodic nature of high-frequency internal waves in large stratified lakes. In both lakes, high-frequency wave events were observed within two distinct categories: (1) Vertical mode 1 solitary waves near a steepened Kelvin wave front and vertical mode 2 solitary waves at the head of an intrusive thermocline jet were found to have wavelengths ϳ64-670 m and ϳ13-65 m, respectively, and were observed to excite a spectral energy peak near 10 Ϫ3 Hz. (2) Sinusoidal vertical mode 1 waves on the crests of Kelvin waves (vertically coherent in both phase and frequency) and bordering the thermocline jets in the high shear region trailing the vertical mode 2 solitary waves (vertically incoherent in both phase and frequency) were found to have wavelengths between 28-37 and 9-35 m, respectively, and excited a spectral energy peak just below the local maximum buoyancy frequency near 10 Ϫ2 Hz. The waves in wave event categories 1 and 2 were reasonably described by nonlinear wave and linear stability models, respectively. Analysis of the energetics of these waves suggests that the waves associated with shear instability will dissipate their energy rapidly within the lake interior and are thus responsible for patchy turbulent events that have been observed within the metalimnion. Conversely, the finite-amplitude solitary waves, which each contain as much as 1% of the basinscale Kelvin wave energy, will propagate to the lake perimeter where they can shoal, thus contributing to the maintenance of the benthic boundary layer.