A numerical study on statistical characteristics of amplitude fluctuations in a wave turbulence

作者：Tanaka Mitsuhiro^*; Yokoyama Naoto

来源：Physica D: Nonlinear Phenomena , 2011, 240(14-15): 1145-1155.

DOI：10.1016/j.physd.2011.04.005

• Wave turbulence
• Statistics of fluctuation
• Averaging procedure
• PDF

A series of numerical studies has been performed to investigate the statistical characteristics of fluctuations of energy s = vertical bar a(k)vertical bar(2) of each component wave and its time derivative S = d vertical bar a(k)vertical bar(2)/dt in a wave turbulence for a Hamiltonian system with a non-decay type dispersion relation. It has been found that the probability density functions (PDF) of s and S evaluated among independent realizations are almost equivalent to the PDF's evaluated among nearby modes in the k space in a single realization. Therefore, the averaging over the realizations and that over the nearby modes in a single realization are interchangeable. It has also been found that the PDF of s evolves in time toward the chi(2) distribution with two degrees of freedom, while that of. evolves toward the Laplace distribution (or the two-sided exponential distribution) at any wavenumber k, both in the peripheral of the spectrum (large k region) and in the energy-containing range (small k region).

• 出版日期2011-7-15