scholarly journals Experimental study of the nonlinear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence

2019 ◽  
Vol 879 ◽  
pp. 296-326 ◽  
Author(s):  
Thomas Le Reun ◽  
Benjamin Favier ◽  
Michael Le Bars
Keyword(s):  
Rotation Rate ◽  
Resonant Interaction ◽  
Wave Turbulence ◽  
Inertial Waves ◽  
Weakly Nonlinear ◽  
Elliptical Instability ◽  
Inertial Wave ◽  
Geostrophic Turbulence ◽  
Set Up ◽  
Saturation Flow

In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by the parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-metre wide ellipsoid filled with water is brought to solid-body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is injected into the resonant inertial waves only. Depending on the amplitude of the rotation rate modulation, two different saturation states are observed. At large forcing amplitudes, the saturation flow mainly consists of a steady, geostrophic anticyclone. Its amplitude vanishes as the forcing amplitude is decreased while remaining above the threshold of the elliptical instability. Below this secondary transition, the saturation flow is a superposition of inertial waves which are in weakly nonlinear resonant interaction, a state that could asymptotically lead to inertial wave turbulence. In addition to being a first experimental observation of a wave-dominated saturation in unstable rotating flows, the present study is also an experimental confirmation of the model of Le Reun et al. (Phys. Rev. Lett., vol. 119 (3), 2017, 034502) who introduced the possibility of these two turbulent regimes. The transition between these two regimes and their relevance to geophysical applications are finally discussed.

scholarly journals Complete Hamiltonian formalism for inertial waves in rotating fluids

2017 ◽  
Vol 831 ◽  
pp. 128-150 ◽  
Author(s):  
A. A. Gelash ◽  
V. S. L’vov ◽  
V. E. Zakharov
Keyword(s):  
Hamiltonian Formalism ◽  
Wave Interaction ◽  
Wave Theory ◽  
Incompressible Fluids ◽  
Hamiltonian Approach ◽  
Inertial Waves ◽  
Rotating Fluids ◽  
Weakly Nonlinear ◽  
Interaction Processes ◽  
Inertial Wave

A complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluids. Resonance three-wave interaction processes – decay instability and confluence of two waves – are shown to play a key role in the weakly nonlinear dynamics and statistics of inertial waves in the rapid rotation case. Future applications of the Hamiltonian approach to inertial wave theory are investigated and discussed.

Experimental internal gravity wave turbulence

2020 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Sylvain Joubaud ◽  
Timothée Jamin ◽  
Nicolas Mordant ◽  
...  
Keyword(s):  
Internal Wave ◽  
Gravity Waves ◽  
Closed Loop ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Wave Turbulence ◽  
Large Set ◽  
Weakly Nonlinear ◽  
Resonant Interactions ◽  
Set Up

<p>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.</p><p>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.</p>

scholarly journals Inertial Wave Turbulence Driven by Elliptical Instability

2017 ◽  
Vol 119 (3) ◽  
Author(s):  
Thomas Le Reun ◽  
Benjamin Favier ◽  
Adrian J. Barker ◽  
Michael Le Bars
Keyword(s):  
Wave Turbulence ◽  
Elliptical Instability ◽  
Inertial Wave

Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown

1999 ◽  
Vol 396 ◽  
pp. 73-108 ◽  
Author(s):  
D. M. MASON ◽  
R. R. KERSWELL
Keyword(s):  
Finite Amplitude ◽  
Complex Conjugate ◽  
Small Scale ◽  
Conjugate Pair ◽  
Weakly Nonlinear ◽  
Elliptical Instability ◽  
Elliptical Flow ◽  
Complex Conjugate Pair ◽  
Generic Instability ◽  
Secondary Instabilities

A direct numerical simulation is presented of an elliptical instability observed in the laboratory within an elliptically distorted, rapidly rotating, fluid-filled cylinder (Malkus 1989). Generically, the instability manifests itself as the pairwise resonance of two different inertial modes with the underlying elliptical flow. We study in detail the simplest ‘subharmonic’ form of the instability where the waves are a complex conjugate pair and which at weakly supercritical elliptical distortion should ultimately saturate at some finite amplitude (Waleffe 1989; Kerswell 1992). Such states have yet to be experimentally identified since the flow invariably breaks down to small-scale disorder. Evidence is presented here to support the argument that such weakly nonlinear states are never seen because they are either unstable to secondary instabilities at observable amplitudes or neighbouring competitor elliptical instabilities grow to ultimately disrupt them. The former scenario confirms earlier work (Kerswell 1999) which highlights the generic instability of inertial waves even at very small amplitudes. The latter represents a first numerical demonstration of two competing elliptical instabilities co-existing in a bounded system.

Free-surface breakdown in a rapidly rotating liquid

1978 ◽  
Vol 86 (3) ◽  
pp. 457-463 ◽  
Author(s):  
W. E. Scott
Keyword(s):  
Free Surface ◽  
Capillary Waves ◽  
Mode Frequency ◽  
Wave Form ◽  
Inertial Waves ◽  
Rotating Liquid ◽  
Surface Breakdown ◽  
Beat Phenomenon ◽  
Inertial Wave ◽  
Wave Modes

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.

scholarly journals Energy intensity of inertial waves in a sphere

1983 ◽  
Vol 25 (2) ◽  
pp. 145-160
Author(s):  
W. W. Wood
Keyword(s):  
Energy Density ◽  
General Theory ◽  
Energy Intensity ◽  
Initial Disturbance ◽  
Inertial Waves ◽  
Inertial Wave

AbstractThe decay at large wavenumbers of the energy density in an inertial wave generated in a sphere by an arbitrary initial disturbance is determined as a first step to a comparison with the general theory of Phillips [17] for a statistically steady field of random inertial waves in an arbitrary cavity.

scholarly journals Comparison Between Experiments and a Multibody Weakly Nonlinear Potential Flow Approach for Modeling of Marine Operations

2018 ◽  
Author(s):  
Pierre-Yves Wuillaume ◽  
Pierre Ferrant ◽  
Aurélien Babarit ◽  
François Rongère ◽  
Mattias Lynch ◽  
...  
Keyword(s):  
Potential Flow ◽  
Wave Structure ◽  
Body Motion ◽  
Dynamics Modeling ◽  
Flow Solver ◽  
Weakly Nonlinear ◽  
Validation Test ◽  
Nonlinear Potential ◽  
Set Up ◽  
Validation Tests

This paper presents validation tests for a new numerical tool for the numerical simulation of marine operations. It involves multibody dynamics modeling, wave-structure interactions with large amplitude body motion and cable’s dynamic modeling. Hydrodynamic loads are computed using the WS_CN weakly nonlinear potential flow solver, based on the weak-scatterer hypothesis. Large deformation of the wetted body surfaces can be taken into account. Firstly the ECN’s WS_CN solver capabilities are extended to multibody simulations. A first validation test is performed by comparing numerical results to the experimental data of [1]. Then, a second validation test is proposed. It consists in the ballasting operation of a spar. The experimental set-up is described.

scholarly journals Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers

2007 ◽  
Vol 585 ◽  
pp. 323-342 ◽  
Author(s):  
M. LE BARS ◽  
S. LE DIZÈS ◽  
P. LE GAL
Keyword(s):  
Growth Rates ◽  
Close Agreement ◽  
Unstable Mode ◽  
Quantitative Agreement ◽  
Fixed Rate ◽  
Elliptical Instability ◽  
Normal Mode Theory ◽  
Set Up ◽  
First Time ◽  
Selection Of

The effects of the Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers placed on a table rotating at a fixed rate $\tilde{\Omega}^G$. For a given set-up, changing the ratio ΩG of global rotation $\tilde{\Omega}^G$ to flow rotation $\tilde{\Omega}^F$ leads to the selection of various unstable modes due to the presence of resonance bands, in close agreement with the normal-mode theory. No instability occurs when ΩG varies between −3/2 and −1/2 typically. On decreasing ΩG toward −1/2, resonance bands are first discretized for ΩG<0 and progressively overlap for −1/2 ≪ ΩG < 0. Simultaneously, the growth rates and wavenumbers of the prevalent stationary unstable mode significantly increase, in quantitative agreement with the viscous short-wavelength analysis. New complex resonances have been observed for the first time for the sphere, in addition to the standard spin-over. We argue that these results have significant implications in geo- and astrophysical contexts.

scholarly journals Quantitative Experimental Observation of Weak Inertial-Wave Turbulence

2020 ◽  
Vol 125 (25) ◽  
Author(s):  
Eduardo Monsalve ◽  
Maxime Brunet ◽  
Basile Gallet ◽  
Pierre-Philippe Cortet
Keyword(s):  
Experimental Observation ◽  
Wave Turbulence ◽  
Inertial Wave
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