Near-inertial parametric subharmonic instability of internal wave beams in a background mean flow

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

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On the irreversibility of internal-wave dynamics due to wave trapping by mean flow inhomogeneities. Part 1. Local analysis

Journal of Fluid Mechanics ◽

10.1017/s0022112093003325 ◽

1993 ◽

Vol 251 ◽

pp. 21-53 ◽

Cited By ~ 28

Author(s):

Sergei I. Badulin ◽

Victor I. Shrira

Keyword(s):

Shear Flow ◽

Internal Wave ◽

Wave Field ◽

Large Scale ◽

Spatial Scales ◽

Energy Concentration ◽

Local Analysis ◽

Mean Flow ◽

Wave Trapping ◽

Wave Dynamics

The propagation of guided internal waves on non-uniform large-scale flows of arbitrary geometry is studied within the framework of linear inviscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear flow. Attention is focused on the fundamental fact that the generic smooth non-uniformities of the large-scale flow result in specific singularities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential holes acting quite similarly to the ‘black holes’ of astrophysics. It is shown that the particles fall for infinitely long time, each into its own ‘black hole‘. In terms of a particular wave packet this falling implies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-field dynamics this provides a robust mechanism of a very specific conservative and moreover Hamiltonian irreversibility.This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term ‘trapping’ for it was introduced and the basic features were established. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and retains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing and of ‘non-dispersive’ focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hole.These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the presence of large-scale flows and towards considerable wave energy concentration in narrow spatial zones.

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Nonlinear internal wave penetration via parametric subharmonic instability

Physics of Fluids ◽

10.1063/1.4939001 ◽

2016 ◽

Vol 28 (1) ◽

pp. 011703 ◽

Cited By ~ 6

Author(s):

S. J. Ghaemsaidi ◽

S. Joubaud ◽

T. Dauxois ◽

P. Odier ◽

T. Peacock

Keyword(s):

Internal Wave ◽

Nonlinear Internal Wave ◽

Parametric Subharmonic Instability

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Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

Ocean Science Discussions ◽

10.5194/osd-5-545-2008 ◽

2008 ◽

Vol 5 (4) ◽

pp. 545-580

Author(s):

H. Z. Baumert ◽

H. Peters

Keyword(s):

Internal Wave ◽

Internal Waves ◽

Tidal Flow ◽

Wave Turbulence ◽

Mean Flow ◽

Turbulent Length Scale ◽

Turbulent Dissipation ◽

New Model ◽

Turbulence Transition ◽

Ozmidov Scale

Abstract. A new two-equation, closure-like turbulence model for stably stratified flows is introduced which uses the turbulent kinetic energy (K) and the turbulent enstrophy (Ω) as primary variables. It accounts for mean shear – and internal wave-driven mixing in the two limits of mean shear and no waves and waves but no mean shear, respectively. The traditional TKE balance is augmented by an explicit energy transfer from internal waves to turbulence. A modification of the Ω-equation accounts for the effect of the waves on the turbulence time and space scales. The latter is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean-flow shear when turbulence is produced exclusively by internal waves. The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000). At small energy density E of the internal wave field, the turbulent dissipation rate (ε) scales like ε~E2. This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E1. This is observed, for example, in the swift tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.

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Wave Transience in a Compressible Atmosphere. Part I: Transient Internal Wave, Mean-Flow Interaction

Journal of the Atmospheric Sciences ◽

10.1175/1520-0469(1981)038<0281:wtiaca>2.0.co;2 ◽

1981 ◽

Vol 38 (2) ◽

pp. 281-297 ◽

Cited By ~ 45

Author(s):

Timothy J. Dunkerton

Keyword(s):

Internal Wave ◽

Mean Flow ◽

Flow Interaction ◽

Compressible Atmosphere

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A Closure for Internal Wave–Mean Flow Interaction. Part II: Wave Drag

Journal of Physical Oceanography ◽

10.1175/jpo-d-16-0056.1 ◽

2017 ◽

Vol 47 (6) ◽

pp. 1403-1412 ◽

Cited By ~ 10

Author(s):

Carsten Eden ◽

Dirk Olbers

Keyword(s):

Wave Propagation ◽

Internal Wave ◽

Ocean Circulation ◽

Wave Drag ◽

Ocean Model ◽

Vertical Shear ◽

Mean Flow ◽

Flow Interaction ◽

Two Dimensional Flow ◽

Novel Concept

AbstractA novel concept for parameterizing internal wave–mean flow interaction in ocean circulation models is extended to an arbitrary two-dimensional flow with vertical shear. The concept is based on the description of the entire wave field by the wave-energy density in physical and wavenumber space and its prognostic computation by the radiative transfer equation integrated in wavenumber space. Energy compartments result for the horizontal direction of wave propagation as additional prognostic model variables, of which only four are taken here for simplicity. The mean flow is interpreted as residual velocities with respect to the wave activity. The effect of wave drag and energy exchange due to the vertical shear of the residual mean flow is then given simply by a vertical flux of momentum. This flux is related to the asymmetries in upward, downward, alongflow, and counterflow wave propagation described by the energy compartments. A numerical implementation in a realistic eddying ocean model shows that the wave drag effect is a significant sink of kinetic energy in the interior ocean.

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Generation of a mean flow by an internal wave

Physics of Fluids ◽

10.1063/1.4962937 ◽

2016 ◽

Vol 28 (9) ◽

pp. 096601 ◽

Cited By ~ 8

Author(s):

B. Semin ◽

G. Facchini ◽

F. Pétrélis ◽

S. Fauve

Keyword(s):

Internal Wave ◽

Mean Flow

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Internal wave excitation from stratified flow over a thin barrier

Journal of Fluid Mechanics ◽

10.1017/s0022112098003048 ◽

1998 ◽

Vol 377 ◽

pp. 223-252 ◽

Cited By ~ 37

Author(s):

BRUCE R. SUTHERLAND ◽

PAUL F. LINDEN

Keyword(s):

Internal Wave ◽

Numerical Simulations ◽

Internal Waves ◽

Wavelet Transforms ◽

Large Amplitude ◽

Internal Gravity Waves ◽

Wave Excitation ◽

Mean Flow ◽

Propagating Waves ◽

The Waves

We perform laboratory experiments in a recirculating shear flow tank of non-uniform salt-stratified water to examine the excitation of internal gravity waves (IGW) in the wake of a tall, thin vertical barrier. The purpose of this study is to characterize and quantify the coupling between coherent structures shed in the wake and internal waves that radiate from the mixing region into the deep, stationary fluid. In agreement with numerical simulations, large-amplitude internal waves are generated when the mixing region is weakly stratified and the deep fluid is sufficiently strongly stratified. If the mixing region is unstratified, weak but continuous internal wave excitation occurs. In all cases, the tilt of the phase lines of propagating waves lies within a narrow range. Assuming the waves are spanwise uniform, their amplitude in space and time is measured non-intrusively using a recently developed ‘synthetic schlieren’ technique. Using wavelet transforms to measure consistently the width and duration of the observed wavepackets, the Reynolds stress is measured and, in particular, we estimate that when large-amplitude internal wave excitation occurs, approximately 7% of the average momentum across the shear depth and over the extent of the wavepacket is lost due to transport away from the mixing region by the waves.We propose that internal waves may act back upon the mean flow modifying it so that the excitation of waves of that frequency is enhanced. A narrow frequency spectrum of large-amplitude waves is observed because the feedback is largest for waves with phase tilt in a range near 45°. Numerical simulations and analytic theories are presented to further quantify this theory.

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