Wave turbulence

Abstract

Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence -Kolmogorov-Zakharov (KZ) spectra.

Finescale parameterizations of turbulent dissipation

“…The first source is a general paradigm of weakly interacting dispersive waves in continuous media referred to as wave turbulence [ Zakharov et al ., ; Nazarenko , ]. One of the corner stones of wave turbulence is the development of kinetic equations quantifying the spectral energy transfer associated with resonant wave interactions for statistically homogeneous systems.…”

Wave condensation with weak disorder versus beam self-cleaning in multimode fibers

“…This phenomenon has been observed in a variety of quantum systems, such as ultracold atoms and molecules [1], exciton polaritons [2] and photons [3] (also see [4]). On the other hand, several studies on wave turbulence predicted that completely classical waves can undergo a condensation process [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The picture the reader may have in mind is the following.…”

“…This phenomenon refers to wave condensation. It originates in the natural thermalization of the wave system toward the thermodynamic Rayleigh-Jeans equilibrium distribution, whose divergence is responsible for the macroscopic occupation of the fundamental mode of the system [6,7,10,13,14,17,20,[24][25][26][27]. We recall that this self-organization process takes place in a conservative (Hamiltonian) and formally reversible system: The ('condensate') remains immersed in a sea of small-scale fluctuations ('uncondensed particles'), which store the information for time reversal.…”

“…We pursue the work initiated in Ref. [41] along different lines: (i) On the basis of the wave turbulence theory [6,7,20,24] and related developments on finite size effects [55][56][57][58][59][60][61][62][63][64][65][66], we derive kinetic equations describing the nonequilibrium evolution of random waves in the regime where disorder effects dominate nonlinear effects. Considering the dominant contribution of polarization random fluctuations (weak disorder) [45], the theory shows that a conservative disorder introduces an effective dissipation in the evolution of the moments equations.…”

Complementary remarks to properties of the energy spectrum in Leith's model of turbulence

“…These results are in the line with recent studies of analogous problems in the theory of wave turbulence and may point to a generic phenomenon observed in the dynamics of flux spectra of Kolmogorov type. Examples also include MHD wave turbulence and weak turbulence with local interactions . The main feature of such self‐similarity is that the scaling exponents cannot be deduced for a conservation law or dimensional analysis, and for determination of which one has to solve a nonlinear eigenvalue problem is of the second type.…”