Noisy spectra, long correlations, and intermittency in wave turbulence
UNSPECIFIED. (2004) Noisy spectra, long correlations, and intermittency in wave turbulence. PHYSICAL REVIEW E, 69 (6 Part 2). -. ISSN 1063-651XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1103/PhysRevE.69.066608
We study the k-space fluctuations of the wave action about its mean spectrum in the turbulence of dispersive waves. We use a minimal model based on the random phase approximation (RPA) and derive evolution equations for the arbitrary-order one-point moments of the wave intensity in the wave-number space. The first equation in this series is the familiar kinetic equation for the mean wave-action spectrum, whereas the second and higher equations describe the fluctuations about this mean spectrum. The fluctuations exhibit a nontrivial dynamics if some long coordinate-space correlations are present in the system, as it is the case in typical numerical and laboratory experiments. Without such long-range correlations, the fluctuations are trivially fixed at their Gaussian values and cannot evolve even if the wave field itself is non-Gaussian in the coordinate space. Unlike the previous approaches based on smooth initial k-space cumulants, the RPA model works even for extreme cases where the k-space fluctuations are absent or very large and intermittent. We show that any initial non-Gaussianity at small amplitudes propagates without change toward the high amplitudes at each fixed wave number. At each fixed amplitude, however, the probability distribution function becomes Gaussian at large time.
|Item Type:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Journal or Publication Title:||PHYSICAL REVIEW E|
|Publisher:||AMERICAN PHYSICAL SOC|
|Official Date:||June 2004|
|Number:||6 Part 2|
|Number of Pages:||6|
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