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

1993 ◽  
Vol 251 ◽  
pp. 21-53 ◽  
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.

scholarly journals Internal Waves and Mixing near the Kerguelen Plateau

2015 ◽  
Vol 46 (2) ◽  
pp. 417-437 ◽  
Author(s):  
Amelie Meyer ◽  
Kurt L. Polzin ◽  
Bernadette M. Sloyan ◽  
Helen E. Phillips
Keyword(s):  
Internal Wave ◽  
Wave Field ◽  
Internal Waves ◽  
Large Scale ◽  
Polar Front ◽  
Frontal Region ◽  
Small Scale ◽  
Kerguelen Plateau ◽  
Flow Strength ◽  
Internal Wave Field

AbstractIn the stratified ocean, turbulent mixing is primarily attributed to the breaking of internal waves. As such, internal waves provide a link between large-scale forcing and small-scale mixing. The internal wave field north of the Kerguelen Plateau is characterized using 914 high-resolution hydrographic profiles from novel Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. Altogether, 46 coherent features are identified in the EM-APEX velocity profiles and interpreted in terms of internal wave kinematics. The large number of internal waves analyzed provides a quantitative framework for characterizing spatial variations in the internal wave field and for resolving generation versus propagation dynamics. Internal waves observed near the Kerguelen Plateau have a mean vertical wavelength of 200 m, a mean horizontal wavelength of 15 km, a mean period of 16 h, and a mean horizontal group velocity of 3 cm s−1. The internal wave characteristics are dependent on regional dynamics, suggesting that different generation mechanisms of internal waves dominate in different dynamical zones. The wave fields in the Subantarctic/Subtropical Front and the Polar Front Zone are influenced by the local small-scale topography and flow strength. The eddy-wave field is influenced by the large-scale flow structure, while the internal wave field in the Subantarctic Zone is controlled by atmospheric forcing. More importantly, the local generation of internal waves not only drives large-scale dissipation in the frontal region but also downstream from the plateau. Some internal waves in the frontal region are advected away from the plateau, contributing to mixing and stratification budgets elsewhere.

scholarly journals Mesoscale Eddy–Internal Wave Coupling. Part I: Symmetry, Wave Capture, and Results from the Mid-Ocean Dynamics Experiment

2008 ◽  
Vol 38 (11) ◽  
pp. 2556-2574 ◽  
Author(s):  
Kurt L. Polzin
Keyword(s):  
Internal Wave ◽  
Wave Field ◽  
Mesoscale Eddy ◽  
Horizontal Velocity ◽  
Ocean Dynamics ◽  
Energy Propagation ◽  
Wave Trapping ◽  
Inertial Wave ◽  
Parallel Shear Flow ◽  
Field Wave

Abstract Vertical profiles of horizontal velocity obtained during the Mid-Ocean Dynamics Experiment (MODE) provided the first published estimates of the high vertical wavenumber structure of horizontal velocity. The data were interpreted as being representative of the background internal wave field, and thus, despite some evidence of excess downward energy propagation associated with coherent near-inertial features that was interpreted in terms of atmospheric generation, these data provided the basis for a revision to the Garrett and Munk spectral model. These data are reinterpreted through the lens of 30 years of research. Rather than representing the background wave field, atmospheric generation, or even near-inertial wave trapping, the coherent high wavenumber features are characteristic of internal wave capture in a mesoscale strain field. Wave capture represents a generalization of critical layer events for flows lacking the spatial symmetry inherent in a parallel shear flow or isolated vortex.

scholarly journals Spontaneous inertia-gravity-wave generation by surface-intensified turbulence

2012 ◽  
Vol 699 ◽  
pp. 153-173 ◽  
Author(s):  
E. Danioux ◽  
J. Vanneste ◽  
P. Klein ◽  
H. Sasaki
Keyword(s):  
Wave Field ◽  
Large Scale ◽  
Spatial Scales ◽  
Baroclinic Instability ◽  
Small Scale ◽  
Random Wave ◽  
Spontaneous Generation ◽  
Thin Filaments ◽  
Random Wave Field ◽  
Omega Equation

AbstractThe spontaneous generation of inertia-gravity waves (IGWs) by surface-intensified, nearly balanced motion is examined using a high-resolution simulation of the primitive equations in an idealized oceanic configuration. At large scale and mesoscale, the dynamics, which is driven by baroclinic instability near the surface, is balanced and qualitatively well described by the surface quasi-geostrophic model. This however predicts an increase of the Rossby number with decreasing spatial scales and, hence, a breakdown of balance at small scale; the generation of IGWs is a consequence of this breakdown. The wave field is analysed away from the surface, at depths where the associated vertical velocities are of the same order as those associated with the balanced motion. Quasi-geostrophic relations, the omega equation in particular, prove sufficient to separate the IGWs from the balanced contribution to the motion. A spectral analysis indicates that the wave energy is localized around dispersion relation for free IGWs, and decays only slowly as the frequency and horizontal wavenumber increase. The IGW generation is highly intermittent in time and space: localized wavepackets are emitted when thin filaments in the surface density are formed by straining, leading to large vertical vorticity and correspondingly large Rossby numbers. At depth, the IGW field is the result of a number of generation events; away from the generation sites it takes the form of a relatively homogeneous, apparently random wave field. The energy of the IGW field generated spontaneously is estimated and found to be several orders of magnitude smaller than the typical IGW energy in the ocean.

scholarly journals On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars

2021 ◽  
Author(s):  
Caroline Terquem
Keyword(s):  
Shear Flow ◽  
Convective Flow ◽  
Large Scale ◽  
Dissipation Factor ◽  
Giant Planets ◽  
Small Scale ◽  
Late Type ◽  
Mean Flow ◽  
Tidal Dissipation ◽  
Tidal Period

Abstract All the studies of the interaction between tides and a convective flow assume that the large scale tides can be described as a mean shear flow which is damped by small scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover timescale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late–type binaries or the tidal dissipation factor of giant planets. Here, we argue that the above description is inconsistent, because fluctuations and mean flow should be identified based on the timescale, not on the spatial scale, on which they vary. Therefore, the standard picture should be reversed, with the fluctuations being the tidal oscillations and the mean shear flow provided by the largest convective eddies. We assume that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal Q factor of Jupiter and Saturn and for the circularization periods of PMS binaries in good agreement with observations. The timescales obtained with the equilibrium tide approximation are however still 40 times too large to account for the circularization periods of late–type binaries. For these systems, shear in the tachocline or at the base of the convective zone may be the main cause of tidal dissipation.

On the interactions between large-scale structure and finegrained turbulence in a free shear flow II. The development of spatial interactions in the mean

1978 ◽  
Vol 359 (1699) ◽  
pp. 497-523 ◽  
Keyword(s):  
Shear Flow ◽  
Shear Layer ◽  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Free Shear Layer ◽  
Mean Flow ◽  
The Mean

Organized structures in turbulent shear flow have been observed both in the laboratory and in the atmosphere and ocean. Recent work on modelling such structures in a temporally developing, horizontally homogeneous turbulent free shear layer (Liu & Merkine 19766) has been extended to the spatially developing mixing layer, there being no available rational transformation between the two nonlinear problems. We consider the kinetic energy development of the mean flow, large-scale structure and finegrained turbulence with a conditional average, supplementing the usual time average, to separate the non-random from the random part of the fluctuations. The integrated form of the energy equations and the accompanying shape assumptions are used to derive ‘ amplitude ’ equations for the mean flow, characterized by the shear layer thickness, the non-random and the random components of flow (which are characterized by their respective energy densities). The closure problem was overcome by the shape assumptions which entered into the interaction integrals: the instability-wavelike large-scale structure was taken to be two-dimensional and the local vertical distribution function was obtained by solving the Rayleigh equation for various local frequencies; the vertical shape of the mean stresses of the fine-grained turbulence was estimated by making use of experimental results; the vertical shapes of the wave-induced stresses were calculated locally from their corresponding equations.

scholarly journals An asymptotic model for the propagation of oceanic internal tides through quasi-geostrophic flow

2017 ◽  
Vol 828 ◽  
pp. 779-811 ◽  
Author(s):  
G. L. Wagner ◽  
G. Ferrando ◽  
W. R. Young
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Large Scale ◽  
Spatial Scales ◽  
Coupled Model ◽  
Boussinesq Equations ◽  
Internal Tides ◽  
Numerical Comparison ◽  
Asymptotic Model ◽  
Geostrophic Flow

We derive a time-averaged ‘hydrostatic wave equation’ from the hydrostatic Boussinesq equations that describes the propagation of inertia–gravity internal waves through quasi-geostrophic flow. The derivation uses a multiple-scale asymptotic method to isolate wave field evolution over intervals much longer than a wave period, assumes the wave field has a well-defined non-inertial frequency such as that of the mid-latitude semi-diurnal lunar tide, assumes that the wave field and quasi-geostrophic flow have comparable spatial scales and neglects nonlinear wave–wave dynamics. As a result the hydrostatic wave equation is a reduced model applicable to the propagation of large-scale internal tides through the inhomogeneous and moving ocean. A numerical comparison with the linearized and hydrostatic Boussinesq equations demonstrates the validity of the hydrostatic wave equation model and illustrates how the model fails when the quasi-geostrophic flow is too strong and the wave frequency is too close to inertial. The hydrostatic wave equation provides a first step toward a coupled model for energy transfer between oceanic internal tides and quasi-geostrophic eddies and currents.

Turbulence structure in a boundary layer with two-dimensional roughness

2009 ◽  
Vol 635 ◽  
pp. 75-101 ◽  
Author(s):  
R. J. VOLINO ◽  
M. P. SCHULTZ ◽  
K. A. FLACK
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Outer Flow ◽  
Dominant Feature

Turbulence measurements for a zero pressure gradient boundary layer over a two-dimensional roughness are presented and compared to previous results for a smooth wall and a three-dimensional roughness (Volino, Schultz & Flack, J. Fluid Mech., vol. 592, 2007, p. 263). The present experiments were made on transverse square bars in the fully rough flow regime. The turbulence structure was documented through the fluctuating velocity components, two-point correlations of the fluctuating velocity and swirl strength and linear stochastic estimation conditioned on the swirl and Reynolds shear stress. The two-dimensional bars lead to significant changes in the turbulence in the outer flow. Reynolds stresses, particularly $\overline {{v'}^2} ^ +$ and $ - \overline {{u}'{v}'} ^ + $, increase, although the mean flow is not as significantly affected. Large-scale turbulent motions originating at the wall lead to increased spatial scales in the outer flow. The dominant feature of the outer flow, however, remains hairpin vortex packets which have similar inclination angles for all wall conditions. The differences between boundary layers over two-dimensional and three-dimensional roughness are attributable to the scales of the motion induced by each type of roughness. This study has shown three-dimensional roughness produces turbulence scales of the order of the roughness height k while the motions generated by two-dimensional roughness may be much larger due to the width of the roughness elements. It is also noted that there are fundamental differences in the response of internal and external flows to strong wall perturbations, with internal flows being less sensitive to roughness effects.

scholarly journals Dynamic soliton–mean flow interaction with non-convex flux

2021 ◽  
Vol 928 ◽  
Author(s):  
Kiera van der Sande ◽  
Gennady A. El ◽  
Mark A. Hoefer
Keyword(s):  
Wave Propagation ◽  
Large Scale ◽  
Fluid Dynamic ◽  
Internal Gravity Wave ◽  
Mkdv Equation ◽  
Stratified Fluids ◽  
Mathematical Framework ◽  
Mean Flow ◽  
Wave Trapping ◽  
Flow Interaction

The interaction of localised solitary waves with large-scale, time-varying dispersive mean flows subject to non-convex flux is studied in the framework of the modified Korteweg–de Vries (mKdV) equation, a canonical model for internal gravity wave propagation and potential vorticity fronts in stratified fluids. The effect of large amplitude, dynamically evolving mean flows on the propagation of localised waves – essentially ‘soliton steering’ by the mean flow – is considered. A recent theoretical and experimental study of this new type of dynamic soliton–mean flow interaction for convex flux has revealed two scenarios where the soliton either transmits through the varying mean flow or remains trapped inside it. In this paper, it is demonstrated that the presence of a non-convex cubic hydrodynamic flux introduces significant modifications to the scenarios for transmission and trapping. A reduced set of Whitham modulation equations is used to formulate a general mathematical framework for soliton–mean flow interaction with non-convex flux. Solitary wave trapping is stated in terms of crossing modulation characteristics. Non-convexity and positive dispersion – common for stratified fluids – imply the existence of localised, sharp transition fronts (kinks). Kinks play dual roles as a mean flow and a wave, imparting polarity reversal to solitons and dispersive mean flows, respectively. Numerical simulations of the mKdV equation agree with modulation theory predictions. The mathematical framework developed is general, not restricted to completely integrable equations like mKdV, enabling application beyond the mKdV setting to other fluid dynamic contexts subject to non-convex flux such as strongly nonlinear internal wave propagation that is prevalent in the ocean.

Numerical Studies of Internal Wave Dynamics

1997 ◽  
Author(s):  
George F. Carnevale ◽  
M. C. Hendershott
Keyword(s):  
Internal Wave ◽  
Wave Dynamics ◽  
Numerical Studies
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