On the wave turbulence theory for stratified flows in the ocean

Gamba, Irene M.; Smith, Leslie; Tran, Minh-Binh

doi:10.1142/s0218202520500037

Cited by 24 publications

(21 citation statements)

References 70 publications

(82 reference statements)

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“…In addition, our local approach provides an efficient way to numerically investigate the detailed and possibly universal properties of weakly forced internal wave turbulence in low dissipation regimes. Despite recent experimental ) and theoretical ([Gamba et al, 2017]) advances, this particular state of stratified turbulence remains challenging and difficult to be compared to the classical theory of wave turbulence ( [Zakharov et al, 1992, Nazarenko, 2011). As in rotating turbulence, this is essentially due to the anisotropy of the dispersion relation (see for instance the discussion in ), the role played by nearresonant interactions and the non-linear interaction with non-propagative modes ( [Cambon, 2001, Galtier, 2003, Smith and Lee, 2005, Bellet et al, 2006, Scott, 2014, Gelash et al, 2017, Gamba et al, 2017).…”

Section: Resultsmentioning

confidence: 99%

Parametric instability and wave turbulence driven by tidal excitation of internal waves

2018

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We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically stretched and sheared by the tidal base flow. While keeping the key physical ingredients only, such a model is efficient to simulate planetary regimes where tidal amplitudes and dissipation are small. With this model, we prove that tidal flows are able to drive parametric subharmonic resonances of internal waves, in a way reminiscent of the elliptical instability in rotating fluids. The growth rates computed via Direct Numerical Simulations (DNS) are in very good agreement with WKB analysis and Floquet theory. We also investigate the turbulence driven by this instability mechanism. With spatio-temporal analysis, we show that it is a weak internal wave turbulence occurring at small Froude and buoyancy Reynolds numbers. When the gap between the excitation and the Brunt-Väisälä frequencies is increased, the frequency spectrum of this wave turbulence displays a -2 power law reminiscent of the highfrequency branch of the Garett and Munk spectrum ([Garrett and Munk, 1979]) which has been measured in the oceans. In addition, we find that the mixing efficiency is altered compared to what is computed in the context of DNS of stratified turbulence excited at small Froude and large buoyancy Reynolds numbers and is consistent with a superposition of waves.

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Section: Resultsmentioning

confidence: 99%

Parametric instability and wave turbulence driven by tidal excitation of internal waves

2018

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“…where the integral is defined in the sense of (33). Observe that ξ in the integral is taken within the interval [p 1 , p 1 + p 2 ], then 1…”

Section: Let Us Now Estimatementioning

confidence: 99%

On the Energy Cascade of 3-Wave Kinetic Equations: Beyond Kolmogorov–Zakharov Solutions

Soffer

Tran

2019

Commun. Math. Phys.

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In weak turbulence theory, the Kolmogorov-Zakharov spectra is a class of time-independent solutions to the kinetic wave equations. In this paper, we construct a new class of time-dependent isotropic solutions to the decaying turbulence problems (whose solutions are energy conserved), with general initial conditions. These solutions exhibit the interesting property that the energy is cascaded from small wavenumbers to large wavenumbers. We can prove that starting with a regular initial condition whose energy at the infinity wave number |p| = ∞ is 0, as time evolves, the energy is gradually accumulated at {|p| = ∞}. Finally, all the energy of the system is concentrated at {|p| = ∞} and the energy function becomes a Dirac function at infinity Eδ {|p|=∞} , where E is the total energy. The existence of this class of solutions is, in some sense, the first complete rigorous mathematical proof based on the kinetic description for the energy cascade phenomenon for waves with quadratic nonlinearities. We only represent in this paper the analysis of the statistical description of acoustic waves (and equivalently capillary waves). However, our analysis works for other cases as well.

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“…Besides the 4-wave kinetic equation, the 3-wave kinetic equation also plays an important role in the theory of weak turbulence, and has been studied in [16,2,23,11,15] for the phonon interactions in anharmonic crystal lattices, in [23] for stratified flows in the ocean, and in [48] for capillary waves.…”

Section: Rigorous Results On the Isotropic 4-wave Kinetic Equation Anmentioning

confidence: 99%

Optimal local well-posedness theory for the kinetic wave equation

Germain

Ionescu²,

Tran

2020

Journal of Functional Analysis

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On the wave turbulence theory for stratified flows in the ocean

Cited by 24 publications

References 70 publications

Parametric instability and wave turbulence driven by tidal excitation of internal waves

Parametric instability and wave turbulence driven by tidal excitation of internal waves

On the Energy Cascade of 3-Wave Kinetic Equations: Beyond Kolmogorov–Zakharov Solutions

Optimal local well-posedness theory for the kinetic wave equation

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