Experimental internal gravity wave turbulence

Stratified fluids may develop simultaneously turbulence and internal wave turbulence, the latter describing a set of a large number of dispersive and weakly nonlinear interacting waves. The description and understanding of this regime for internal gravity waves (IGW) is really an open subject, in particular due to their very unusual dispersion relation. In this presentation, I will show experimental signatures of a large set of weakly interacting IGW obtained in a 2D trapezoidal tank.Due to the peculiar linear reflexion law of IGW on inclined slopes, this setup - for given excitation frequencies - focuses all the input energy on a closed loop called attractor. If the forcing is large enough, this attractor destabilizes and the system eventually achieves a nonlinear cascade in frequencies and wavevectors via triadic resonant interactions, which results at large forcing amplitudes in a k^-3 spatial energy spectrum. I will also show some results obtained in a much larger set-up -the Coriolis facility in Grenoble- with signature of 3D internal wave turbulence.

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Energy transfer between external and internal gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112064001550 ◽

1964 ◽

Vol 19 (3) ◽

pp. 465-478 ◽

Cited By ~ 71

Author(s):

F. K. Ball

Keyword(s):

Energy Transfer ◽

Internal Wave ◽

Surface Waves ◽

Shallow Water ◽

Gravity Waves ◽

External Surface ◽

Internal Gravity Waves ◽

Liquid System ◽

Resonant Interactions ◽

Non Linear

In a two-layer liquid system non-linear resonant interactions between a pair of external (surface) waves can result in transfer of energy to an internal wave when appropriate resonance conditions are satisfied. This energy transfer is likely to be more powerful than similar transfers between external waves. The shallow water case is discussed in detail.

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On strongly nonlinear gravity waves in a vertically sheared atmosphere

10.5194/egusphere-egu21-4878 ◽

2021 ◽

Author(s):

Georg Sebastian Voelker ◽

Mark Schlutow

Keyword(s):

Gravity Wave ◽

Gravity Waves ◽

Internal Gravity Wave ◽

Internal Gravity Waves ◽

Wave Drag ◽

Mean Flow ◽

Flow Strength ◽

Weakly Nonlinear ◽

Strongly Nonlinear ◽

The Mean

Internal gravity waves are a well-known mechanism of energy redistribution in stratified fluids such as the atmosphere. They may propagate from their generation region, typically in the Troposphere, up to high altitudes. During their lifetime internal waves couple to the atmospheric background through various processes. Among the most important interactions are the exertion of wave drag on the horizontal mean-flow, the heat generation upon wave breaking, or the mixing of atmospheric tracers such as aerosols or greenhouse gases.Many of the known internal gravity wave properties and interactions are covered by linear or weakly nonlinear theories. However, for the consideration of some of the crucial effects, like a reciprocal wave-mean-flow interaction including the exertion of wave drag on the mean-flow, strongly nonlinear systems are required. That is, there is no assumption on the wave amplitude relative to the mean-flow strength such that they may be of the same order.Here, we exploit a strongly nonlinear Boussinesq theory to analyze the stability of a stationary internal gravity wave which is refracted at the vertical edge of a horizontal jet. Thereby we assume that the incident wave is horizontally periodic, non-hydrostatic, and vertically modulated. Performing a linear stability analysis in the vicinity of the jet edge we find necessary and sufficient criteria for instabilities to grow. In particular, the refracted wave becomes unstable if its incident amplitude is large enough and both mean-flow horizontal winds, below and above the edge of the jet, do not exceed particular upper bounds.

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Resonant wave interactions in a stratified shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112088001351 ◽

1988 ◽

Vol 190 ◽

pp. 357-374 ◽

Cited By ~ 11

Author(s):

R. Grimshaw

Keyword(s):

Shear Flow ◽

Gravity Waves ◽

Critical Level ◽

Internal Gravity Waves ◽

Wave Interactions ◽

Resonant Wave ◽

Resonant Interactions ◽

Stratified Shear Flow ◽

Weak Resonance ◽

Background Shear

Resonant interactions between triads of internal gravity waves propagating in a shear flow are considered for the case when the stratification and the background shear flow vary slowly with respect to typical wavelengths. If ωn, kn(n = 1, 2, 3) are the local frequencies and wavenumbers respectively then the resonance conditions are that ω1 + ω2 + ω3 = 0 and k1 + k2 + k3 = 0. If the medium is only weakly inhomogeneous, then there is a strong resonance and to leading order the resonance conditions are satisfied globally. The equations governing the wave amplitudes are then well known, and have been extensively discussed in the literature. However, if the medium is strongly inhomogeneous, then there is a weak resonance and the resonance conditions can only be satisfied locally on certain space-time resonance surfaces. The equations governing the wave amplitudes in this case are derived, and discussed briefly. Then the results are applied to a study of the hierarchy of wave interactions which can occur near a critical level, with the aim of determining to what extent a critical layer can reflect wave energy.

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A conservation law for internal gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112076002401 ◽

1976 ◽

Vol 78 (2) ◽

pp. 209-216 ◽

Cited By ~ 4

Author(s):

Michael Milder

Keyword(s):

Internal Wave ◽

Group Velocity ◽

Internal Waves ◽

Gravity Waves ◽

Conservation Law ◽

Short Wavelength ◽

Internal Gravity Waves ◽

Volume Integral ◽

Weak Density ◽

Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

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On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

Journal of Fluid Mechanics ◽

10.1017/s0022112079002123 ◽

1979 ◽

Vol 90 (1) ◽

pp. 161-178 ◽

Cited By ~ 11

Author(s):

R. H. J. Grimshaw

Keyword(s):

Velocity Profile ◽

Gravity Waves ◽

Second Harmonic ◽

Phase Speed ◽

Internal Gravity Waves ◽

Finite Amplitude ◽

Weakly Nonlinear ◽

Velocity Discontinuity ◽

Interface Displacement ◽

Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

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Nonlinear interactions among standing surface and internal gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112074002205 ◽

1974 ◽

Vol 63 (4) ◽

pp. 801-825 ◽

Cited By ~ 17

Author(s):

Terrence M. Joyce

Keyword(s):

Energy Transfer ◽

Steady State ◽

Internal Wave ◽

Surface Waves ◽

Viscous Dissipation ◽

Growth Rates ◽

Internal Gravity Wave ◽

Internal Gravity Waves ◽

Resonant Interaction ◽

Initial Growth

A laboratory study has been undertaken to measure the energy transfer from two surface waves to one internal gravity wave in a nonlinear, resonant interaction. The interacting waves form triads for which \[ \sigma_{1s} - \sigma_{2s} \pm\sigma_1 = 0\quad {\rm and}\quad \kappa_{1s} - \kappa_2s} \pm \kappa_I = 0; \] σj and κj being the frequency and wavenumber of the jth wave. Unlike previously published results involving single triplets of interacting waves, all waves here considered are standing waves. For both a diffuse, two-layer density field and a linearly increasing density with depth, the growth to steady state of a resonant internal wave is observed while two deep water surface eigen-modes are simultaneously forced by a paddle. Internal-wave amplitudes, phases and initial growth rates are compared with theoretical results derived assuming an arbitrary Boussinesq stratification, viscous dissipation and slight detuning of the internal wave. Inclusion of viscous dissipation and slight detuning permit predictions of steady-state amplitudes and phases as well as initial growth rates. Satisfactory agreement is found between predicted and measured amplitudes and phases. Results also suggest that the internal wave in a resonant triad can act as a catalyst, permitting appreciable energy transfer among surface waves.

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Interaction Features of Internal Wave Breathers in a Stratified Ocean

Fluids ◽

10.3390/fluids5040205 ◽

2020 ◽

Vol 5 (4) ◽

pp. 205

Author(s):

Ekaterina Didenkulova ◽

Efim Pelinovsky

Keyword(s):

Internal Wave ◽

Internal Waves ◽

Gravity Waves ◽

Fourth Order ◽

Numerical Experiments ◽

Vries Equation ◽

Internal Gravity Waves ◽

Wave Fields ◽

Tidal Waves ◽

Stratified Ocean

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.

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Observations of Near-Inertial Internal Gravity Waves Radiating from a Frontal Jet

Journal of Physical Oceanography ◽

10.1175/jpo-d-12-0146.1 ◽

2013 ◽

Vol 43 (6) ◽

pp. 1225-1239 ◽

Cited By ~ 27

Author(s):

Matthew H. Alford ◽

Andrey Y. Shcherbina ◽

Michael C. Gregg

Keyword(s):

Gravity Waves ◽

Three Dimensional ◽

Internal Gravity Wave ◽

Internal Gravity Waves ◽

Shear Layers ◽

Adjustment Process ◽

Vertical Wavelength ◽

The North ◽

Inertial Wave ◽

The North Pacific

Abstract Shipboard ADCP and towed CTD measurements are presented of a near-inertial internal gravity wave radiating away from a zonal jet associated with the Subtropical Front in the North Pacific. Three-dimensional spatial surveys indicate persistent alternating shear layers sloping downward and equatorward from the front. As a result, depth-integrated ageostrophic shear increases sharply equatorward of the front. The layers have a vertical wavelength of about 250 m and a slope consistent with a wave of frequency 1.01f. They extend at least 100 km south of the front. Time series confirm that the shear is associated with a downward-propagating near-inertial wave with frequency within 20% of f. A slab mixed layer model forced with shipboard and NCEP reanalysis winds suggests that wind forcing was too weak to generate the wave. Likewise, trapping of the near-inertial motions at the low-vorticity edge of the front can be ruled out because of the extension of the features well south of it. Instead, the authors suggest that the wave arises from an adjustment process of the frontal flow, which has a Rossby number about 0.2–0.3.

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Trapped internal gravity waves in a geostrophic boundary current

Journal of Fluid Mechanics ◽

10.1017/s0022112093000448 ◽

1993 ◽

Vol 247 ◽

pp. 205-229

Author(s):

Hong Ma

Keyword(s):

Gravity Waves ◽

Internal Gravity Wave ◽

Internal Gravity Waves ◽

Combined Effects ◽

Kelvin Wave ◽

Boundary Current ◽

Trapping Mechanism ◽

Rossby Radius Of Deformation ◽

Wave Guides ◽

Internal Kelvin Wave

The effect of a geostrophic boundary current on internal gravity waves is studied with a reduced-gravity model. We found that the boundary current not only modifies the coastal Kelvin wave, but also forms wave guides for short internal gravity waves. The combined effects of current shear, the boundary, and the slope of the interface create the trapping mechanism. These trapped internal gravity waves appear as groups of discrete zonal modes. They have wavelengths comparable to or shorter than the internal Rossby radius of deformation. Their phase speeds are close to that of the internal Kelvin wave. However, they can propagate both in, or opposite to, the direction of the Kelvin wave. The results of the present work suggest the possibility of finding an energetic internal gravity wave phenomenon with near-inertial frequency in a broad geostrophic boundary current.

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