Adiabatic behavior of strongly nonlinear internal solitary waves in slope-shelf areas (original) (raw)
Related papers
Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves
Journal of Physical Oceanography, 2004
Due to the horizontal variability of oceanic hydrology (density and current stratification) and the variable depth over the continental shelf, internal solitary waves transform as they propagate shorewards into the coastal zone. If the background variability is smooth enough, a solitary wave possesses a soliton-like form with varying amplitude and phase. This stage is studied in detail in the framework of the variable-coefficient extended Korteweg-de Vries equation where the variation of the solitary wave parameters can be described analytically through an asymptotic description a slowly-varying solitary wave. Direct numerical simulation of the variablecoefficient extended Korteweg-de Vries equation is performed for several oceanic shelves (North-west Shelf of Australia, Malin Shelf Edge, Arctic Shelf) to demonstrate the applicability of the asymptotic theory. It is shown that the solitary wave may maintain its soliton-like form for large distances (up to 100 km), and this confirms why internal solitons are observed widely in the world's oceans. In some cases the background stratification contains critical points (when the coefficients of the nonlinear terms in the extended Korteweg-de Vries equation change sign), or does not vary sufficiently smoothly; in such cases the solitary wave deforms a group of secondary waves. This stage is studied numerically.
Modelling Internal Solitary Waves in the Coastal Ocean
Surveys in Geophysics, 2007
In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, horizontally propagating internal solitary waves. These waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modeling of these waves by nonlinear evolution equations of the Korteweg-de Vries type with variable coefficients, and we describe how these models to describe the shoaling of internal solitary waves over the continental shelf and slope. The theories are compared with various numerical simulations.
Large Internal Solitary Waves in Shallow Waters
2018
The propagation of finite amplitude internal waves over an uneven bottom is considered. One of the specific features of the large amplitude internal waves is the ability of the waves to carry fluid in the “trapped core” for a long distance. The velocity of particles in the “trapped core” is very close and, even, exceeds the wave speed. Such waves are detected in different parts of seas and oceans as internal waves of depression and elevation as well as short intrusions at interfaces. Laboratory experiments on the generation, interaction and decay of solitary waves in a two-layer fluid are discussed. Analytical and numerical solutions describing the evolution of internal waves in a shelf zone are constructed by the three-layer shallow water model. Laboratory investigations of the different types of internal waves (bottom, subsurface and interlayer waves) are demonstrating, that the model can be effectively applied to the numerical solution of unsteady wave motions, and the traveling ...
Nonlinear Processes in Geophysics, 2013
An interaction of internal solitary waves with the shelf edge in the time periods related to the presence of a pronounced seasonal pycnocline in the Red Sea and in the Alboran Sea is analysed via satellite photos and SAR images. Laboratory data on transformation of a solitary wave of depression while passing along the transverse bottom step were obtained in a tank with a two-layer stratified fluid. The certain difference between two characteristic types of hydrophysical phenomena was revealed both in the field observations and in experiments. The hydrological conditions for these two processes were named the "deep" and the "shallow" shelf respectively. The first one provides the generation of the secondary periodic short internal waves -"runaway" edge waves -due to change in the polarity of a part of a soliton approaching the shelf normally. Another one causes a periodic shear flow in the upper quasi-homogeneous water layer with the period of incident solitary wave. The strength of the revealed mechanisms depends on the thickness of the water layer between the pycnocline and the shelf bottom as well as on the amplitude of the incident solitary wave.
Structure of Large-Amplitude Internal Solitary Waves
Journal of Physical Oceanography, 2000
The horizontal and vertical structure of large-amplitude internal solitary waves propagating in stratified waters on a continental shelf is investigated by analyzing the results of numerical simulations and in situ measurements. Numerical simulations aimed at obtaining stationary, solitary wave solutions of different amplitudes were carried out using a nonstationary model based on the incompressible two-dimensional Euler equations in the frame of the Boussinesq approximation. The numerical solutions, which refer to different density stratifications typical for midlatitude continental shelves, were obtained by letting an initial disturbance evolve according to the numerical model. Several intriguing characteristics of the structure of the simulated large-amplitude internal solitary waves like, for example, wavelength-amplitude and phase speed-amplitude relationship as well as form of the locus of zero horizontal velocity emerge, consistent with those obtained previously using stationary Euler models. The authors' approach, which tends to exclude unstable oceanic internal solitary waves as they are filtered out during the evolution process, was also employed to perform a detailed comparison between model results and characteristics of large-amplitude internal solitary waves found in high-resolution in situ data acquired north and south of the Strait of Messina, in the Mediterranean Sea. From this comparison the importance of using higher-order theoretical models for a detailed description of large-amplitude internal solitary waves observed in the real ocean emerge. Implications of the results showing the complexity related to a possible inversion of sea surface manifestations of oceanic internal solitary waves into characteristics of the interior ocean dynamics are finally discussed.
Numerical Experiments on the Breaking of Solitary Internal Wavesover a Slope–Shelf Topography
Journal of Physical Oceanography, 2002
A theoretical study of the transformation of large amplitude internal solitary waves (ISW) of permanent form over a slope-shelf topography is considered using as basis the Reynolds equations. The vertical fluid stratification, amplitudes of the propagating ISWs, and the bottom parameters were taken close to those observed in the Andaman and Sulu Seas. The problem was solved numerically. It was found that, when an intense ISW of depression propagates from a deep part of a basin onto the shelf with water depth H s , a breaking event will arise whenever the wave amplitude a m is larger than 0.4(H s Ϫ H m), where H m is the undisturbed depth of the isopycnal of maximum depression. The cumulative effect of nonlinearity in a propagating ISW leads to a steepening and overturning of a rear wave face over the inclined bottom. Immediately before breaking the horizontal orbital velocity at the site of instability exceeds the phase speed of the ISW. So, the strong breaking is caused by a kinematic instability of the propagating wave. At the latest stages of the evolution the overturned hydraulic jump transforms into a horizontal density intrusion (turbulent pulsating wall jet) propagating onto the shelf. The breaking criterion of the ISW over the slope was found. Over the range of examined parameters (0.52Њ Ͻ ␥ Ͻ 21.8Њ, where ␥ is the slope angle) the breaking event arises at the position with depth H b , when the nondimensional wave amplitude ϭ a m /(H b Ϫ H m) satisfies the condition ഡ 0.8Њ/␥ ϩ 0.4. If the water depth a a H s on a shelf is less than H b , a solitary wave breaks down before it penetrates into a shallow water zone; otherwise (at H s Ͼ H b) it passes as a dispersive wave tail onto the shelf without breaking.
Modeling Internal Solitary Waves in the Coastal Ocean
2000
In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, hori- zontally propagating internal solitary waves. These waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modeling of these waves by nonlinear evolution equations of the Korteweg-de Vries type with variable co- ecients,
Deep-water internal solitary waves near critical density ratio
Physica D: Nonlinear Phenomena, 2007
Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the supercritical bifurcation changes to the subcritical one. As the solitary wave velocity approaches the minimum phase velocity of linear interfacial waves (the bifurcation point), the solitary wave solutions transform into envelope solitons. In order to describe their behavior and bifurcations, a generalized nonlinear Schrödinger equation describing the behavior of solitons and their bifurcations is derived. In comparison with the classical NLS equation this equation takes into account three additional nonlinear terms: the so-called Lifshitz term responsible for pulse steepening, a nonlocal term analogous to that first found by Dysthe for gravity waves and the six-wave interaction term. We study both analytically and numerically two solitary wave families of this equation for values of the density ratio ρ that are both above and below the critical density ratio ρcr. For ρ > ρcr, the soliton solution can be found explicitly at the bifurcation point. The maximum amplitude of such a soliton is proportional to √ ρ − ρcr, and at large distances the soliton amplitude decays algebraically. A stability analysis shows that solitons below the critical ratio are stable in the Lyapunov sense in the wide range of soliton parameters. Above the critical density ratio solitons are shown to be unstable with respect to finite perturbations.
Internal solitary waves of elevation advancing on a shoaling shelf
2003
1] A sequence of three internal solitary waves of elevation were observed propagating shoreward along a near-bottom density interface over Oregon's continental shelf. These waves are highly turbulent and coincide with enhanced optical backscatter, consistent with increased suspended sediments in the bottom boundary layer. Nonlinear solitary wave solutions are employed to estimate wave speeds and energy. The waves are rank ordered in amplitude, phase speed, and energy, and inversely ordered in width. Wave kinetic energy is roughly twice the potential energy. The observed turbulence is not sufficiently large to dissipate the waves' energy before the waves reach the shore. Because of high wave velocities at the sea bed, bottom stress is inferred to be an important source of wave energy loss, unlike near-surface solitary waves. The wave solution suggests that the lead wave has a trapped core, implying enhanced cross-shelf transport of fluid and biology. INDEX TERMS: 4544 Oceanography: Physical: Internal and inertial waves; 4219 Oceanography: General: Continental shelf processes; 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; 4524 Oceanography: Physical: Fine structure and microstructure; 4558 Oceanography: Physical: Sediment transport. Citation: Klymak, J. M., and J. N. Moum, Internal solitary waves of elevation advancing on a shoaling shelf, Geophys.
Internal solitary waves: propagation, deformation and disintegration
Nonlinear Processes in Geophysics, 2010
In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate largeamplitude, horizontally propagating internal solitary waves. Typically these waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of the Kortewegde Vries type with variable coefficients. We shall review how these models are used to describe the propagation, deformation and disintegration of internal solitary waves as they propagate over the continental shelf and slope.