2,613 research outputs found
Nonlinear dynamics of flexural wave turbulence
The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory
remains elusive for wave turbulence of flexural waves at the surface of an thin
elastic plate. We report a direct measurement of the nonlinear timescale
related to energy transfer between waves. This time scale is extracted
from the space-time measurement of the deformation of the plate by studying the
temporal dynamics of wavelet coefficients of the turbulent field. The central
hypothesis of the theory is the time scale separation between dissipative time
scale, nonlinear time scale and the period of the wave (). We
observe that this scale separation is valid in our system. The discrete modes
due to the finite size effects are responsible for the disagreement between
observations and theory. A crossover from continuous weak turbulence and
discrete turbulence is observed when the nonlinear time scale is of the same
order of magnitude as the frequency separation of the discrete modes. The
Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen
before reaching the dissipative regime expected in the theory.Comment: accepted for publication in Physical Review
A weak turbulence theory for incompressible magnetohydrodynamics
We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B0ĂȘ[parallel R: parallel]. Numerically and analytically, we find energy spectra E± [similar] kn±[bot bottom], such that n+ + nâ = â4, where E± are the spectra of the ElsĂ€sser variables z± = v ± b in the two-dimensional case (k[parallel R: parallel] = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made
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