2011/12/06 by Benjamin Miquel, Nicolas Mordant · 29 citations
Earth and Planetary Sciences · Physics and Astronomy · #Classical mechanics #Dissipative system #Energy cascade #K-epsilon turbulence model #K-omega turbulence model #Mechanics #Nonlinear system #Ocean Waves and Remote Sensing #Physics #Quantum mechanics #Random lasers and scattering media #Seismic Waves and Analysis #Statistical physics #Turbulence #Wave turbulence #nlin.CD #physics.class-ph
paper · pdf · doi:10.1103/physreve.84.066607
published in Physical Review E 84(6), 066607 (American Physical Society) · accepted for publication in Physical Review E
arxiv created 2011/12/06 · openalex publication_date 2011/12/20 · arxiv updated 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Kolmogorov-Zakharov spectrum predicted by the weak turbulence theory remains elusive for wave turbulence of flexural waves at the surface of a thin elastic plate. We report a direct measurement of the nonlinear time scale T(NL) 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 (T(d) >> T(NL) >> T). 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.