Near-inertial waves in the ocean: beyond the ‘traditional approximation’ (original) (raw)

Near-inertial waves in the ocean: beyond the

J Fluid Mech, 2005

The dynamics of linear internal waves in the ocean is analysed without adopting the 'traditional approximation', i.e. the horizontal component of the Earth's rotation is taken into account. It is shown that non-traditional effects profoundly change the dynamics of near-inertial waves in a vertically confined ocean. The partial differential equation describing linear internal-wave propagation can no longer be solved by separation of spatial variables; it was however pointed out earlier in the literature that a reduction to a Sturm-Liouville problem is still possible, a line that is pursued here. In its formal structure the Sturm-Liouville problem is the same as under the traditional approximation, but its eigenfunctions are no longer normal vertical modes of the full problem. The question is addressed of whether the solution found through this reduction is the general one: a set of eigenfunctions to the full problem is constructed, which depend in a non-separable way on the two spatial variables; these functions are orthogonal and form, under mild assumptions, a complete basis.

Near-inertial waves and deep ocean mixing

Physica Scripta, 2013

For the existing pattern of global oceanic circulation to exist, there should be sufficiently strong turbulent mixing in the abyssal ocean, the mechanisms of which are not well understood as yet. The review discusses a plausible mechanism of deep ocean mixing caused by near-inertial waves in the abyssal ocean. It is well known how winds in the atmosphere generate near-inertial waves in the upper ocean, which then propagate downwards losing their energy in the process; only a fraction of the energy at the surface reaches the abyssal ocean. An open question is whether and, if yes, how these weakened inertial motions could cause mixing in the deep. We review the progress in the mathematical description of a mechanism that results in an intense breaking of near-inertial waves near the bottom of the ocean and thus enhances the mixing. We give an overview of the present state of understanding of the problem covering both the published and the unpublished results; we also outline the key open questions. For typical ocean stratification, the account of the horizontal component of the Earth's rotation leads to the existence of near-bottom wide waveguides for near-inertial waves. Due to the β-effect these waveguides are narrowing in the poleward direction. Near-inertial waves propagating poleward get trapped in the waveguides; we describe how in the process these waves are focusing more and more in the vertical direction, while simultaneously their group velocity tends to zero and wave-induced vertical shear significantly increases. This causes the development of shear instability, which is interpreted as wave breaking. Remarkably, this mechanism of local intensification of turbulent mixing in the abyssal ocean can be adequately described within the framework of linear theory. The qualitative picture is similar to wind wave breaking on a beach: the abyssal ocean always acts as a surf zone for near-inertial waves.

Near-inertial motions in the coastal ocean

1995

Internal-inertial waves are frequently observed in the upper ocean and below the thermocline. A three-dimensional general circulation model with turbulence-closure mixed layer is used to study the generation and propagation of near-inertial motion below the mixed layer. In particular, the problem of effect of a coastal wall on the wind induced inertial-internal wave field is re-examined using a fully nonlinear model. Responding to a wind pulse, a sharp wavefront propagates offshore. After the wavefront passage, strong near-inertial internal waves, marked by the tilting velocity isolines and the interface oscillations, are generated. The predicted near-inertial motion is consistent with the wave dispersion relation. Downward energy propagation occurs after the wavefront passage, and both kinetic and potential energy are strongly modified. After several inertial periods, the kinetic energy in the upper layer can be completely removed. The theoretical results, which are supported by observations, indicate that internal-inertial wave are important for mixing in the upper coastal ocean. 0924-7963/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO924-7963(94)00030-l

Propagating and evanescent internal waves in a deep ocean model

Journal of Fluid Mechanics, 2012

We present experimental and computational studies of the propagation of internal waves in a stratified fluid with an exponential density profile that models the deep ocean. The buoyancy frequency profile N(z) (proportional to the square root of the density gradient) varies smoothly by more than an order of magnitude over the fluid depth, as is common in the deep ocean. The non-uniform stratification is characterized by a turning depth z c , where N(z c ) is equal to the wave frequency ω and N(z < z c ) < ω. Internal waves reflect from the turning depth and become evanescent below the turning depth. The energy flux below the turning depth is shown to decay exponentially with a decay constant given by k c , which is the horizontal wavenumber at the turning depth. The viscous decay of the vertical velocity amplitude of the incoming and reflected waves above the turning depth agree within a few per cent with a previously untested theory for a fluid of arbitrary stratification (Kistovich and Chashechkin,

Radiation of Mixed Layer Near-Inertial Oscillations into the Ocean Interior

Journal of Physical Oceanography, 2001

The radiation from the mixed layer into the interior of the ocean of near-inertial oscillations in the presence of the beta effect is reconsidered as an initial-value problem. Making use of the fact that the mixed layer depth is much smaller than the total depth of the ocean, the solution is obtained in the limit of an ocean that is effectively infinitely deep. For a uniform initial condition, analytical results for the velocity, horizontal kinetic energy density, and fluxes are obtained. This is the canonical solution for the radiation of near-inertial oscillations in the vertical, which captures the basic mechanisms due to the beta effect, and leads to the formation of small scales in the vertical. By superposing events, an average vertical wavenumber spectrum is constructed. The predicted decay of near-inertial mixed layer energy in the presence of the beta effect occurs on a timescale similar to that observed.

Scale Separated Approaches to the Interaction of Oceanic Internal Waves, part I: Theory

arXiv (Cornell University), 2022

We report two parallel derivations for transport equations describing the refraction of high frequency internal waves in a sea of random inertial waves. One derivation casts the fields as amplitude modulated waves in an Eulerian format and ultimately results in a Fokker-Planck (generalized diffusion) equation. The second casts the high frequency waves as a frequency modulated system. An ensemble averaged transport equation is obtained here that is characterized by a dispersion of wave-packets about a mean drift in the spectral domain. In this derivation the Fokker-Planck equation contains an advective term. Both transport equations make unrealistic predictions for energy sourced to internal wave breaking. The amplitude modulated system predicts no mixing, the frequency modulated system over predicts by an order of magnitude.

Internal-inertial waves and crossfrontal circulation in the upper ocean

Física de la Tierra, 1991

Se estudia el proceso de ajuste entre des masas de agua de propiedades diferentes y la circulación secundaría asociada, por medio de un modelo oceánico tridimensional de ecuaciones primitivas. En particular, se investiga la recirculación y el movimiento vertical cerca de un ...

Infragravity waves in the deep ocean

Journal of Geophysical Research, 1991

Energetic pressure fluctuations at periods longer than 30 s are a ubiquitous feature of pressure spectra from instruments sited on the deep seafloor in both the Atlantic and the Pacific oceans. We show these pressure fluctuations are caused by freely propagating ocean surface waves. The waves are generated in the near shore region along the entire coastline of an ocean basin through nonlinear transfer of energy from short-period waves. This view contrasts with some earlier work, which described these long-period pressure fluctuations as trapped waves tied to groups of short waves. We have constructed a model based on the average energy in the short (wind driven and swell) wave band along the North Atlantic coast to predict the energy in the long wave band at a site in the Atlantic. Maximum likelihood wave number-frequency spectra calculated on data from an 11 element array in the North Pacific confirm that the long wave energy is confined to wave numbers corresponding to the surface gravity wave dispersion relation. We have used the wave number spectra to isolate particular regions of the Pacific Ocean which are sources of long wave energy. Energetic short-period waves are incident on the coastline in these regions. Long waves are detected at the army which originate in the Gulf of Alaska, the northwestern Pacific, and at the southern tip of South America.

Near-inertial waves on the “nontraditional” β plane

Journal of Geophysical Research, 2005

Propagation of linear near-inertial waves on the b plane is considered, taking into account the horizontal component of the Earth's rotation,f. (Terms, effects etc., due to this component will be referred to as ''nontraditional,'' for brevity.) It is shown that the combined effect of b andf changes the dynamics in a fundamental way. For a vertically unbounded domain, an exact solution shows that near-inertial waves can pass through the inertial latitude, unlike under the traditional approximation. For parameter values typical of the ocean, the subinertial domain extends several hundreds of kilometers poleward of the inertial latitude. The solution undergoes a profound change if a vertically bounded, instead of unbounded, domain is considered. Part of the wave energy then accumulates at the poleward end of the subinertial domain, which involves an evolution toward infinitesimal horizontal and vertical scales. For vertically nonuniform stratification, examined here using the Garrett-Munk exponential profile, one finds a wedge-like waveguide, which becomes increasingly narrow in the poleward direction, and drives subinertial waves into the region of the weakest stratification, i.e., the abyss. For typical parameters, the relative amount of poleward traveling energy that gets trapped is estimated to lie between 10 and 30%; its dependence on latitude and stratification is also outlined. The observational evidence and possible implications for abyssal mixing are discussed.

Intense short-period internal waves in the ocean

Journal of Marine Research, 2005

Trains of quasi-periodic high-frequency internal waves (IWs) of large amplitude are common in the upper thermocline of the ocean. Sources for these waves may be different ones but it is not always possible to experimentally establish them for certain. We analyzed results of many IW experiments carried out in different representative regions of the World Ocean, including continental margins in the Mid-Atlantic Bight, in the northwestern Pacific at Kamchatka, the Seyshelles-Mascarene bottom rise, and some regions of the open ocean where the intense short-period IWs occur. Comparative analysis of the intense IWs observed in the Mid-Atlantic Bight and at Kamchatka revealed similarity and difference in the IW field in these regions differing by their bottom topography. Most of the observed trains in the Mid-Atlantic Bight propagate shoreward from the shelf break in the form of soliton packets or solibores and do not occur seaward from the shelf. The soliton trains in the northwestern Pacific at Kamchatka are common not only at the shelf edge but also in deep water where they propagate in various directions that seem to be related to the supercritical steepness and complicated form of the continental slope. Observation of generation and evolution of the IW trains at the Seyshelles-Mascarene bottom rise where huge internal solitons have been encountered has shown that the undular bore generated at the lee side of the bottom rise gradually evolves in a train of solitons with the trailing linear waves. Large solitons are generated also in deep water as a result of ray propagation of the internal tide emanated from the rise as happens in the Bay of Biscay. Certain consequences of the IW interaction with the background current leading to intensification of the high-frequency waves were observed in several regions of the open ocean. Revealed dependency of the intense wave propagation direction on the current direction, and closeness of the wave frequency to the frequency at which the waveguide steeply tapers may be regarded as clear evidences for the important role which currents play in the IW intensification.