Direct numerical simulations of capillary wave turbulence

L. Deike1, 2, D. Fuster3, M. Berhanu1 & E. Falcon1
1 Univ Paris Diderot, Sorbonne Cité, MSC, CNRS, UMR 7057, F-75 013 Paris, France, EU
2 Scripps Institution of Oceanography, University of California San Diego, La Jolla, California
3 Institut Jean le Rond d'Alembert, Universit\'e Pierre et Marie Curie, UMR 7190, Paris, France, EU

Reference: Physical Review Letters 112, 234501 (2014)



This work presents Direct Numerical Simulations of capillary wave turbulence solving the full 3D Navier Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency in good agreement with weak turbulence theory. By estimating the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction and dissipative times is also observed. These numerical results confirm the validity of weak turbulence approach to quantify out-of equilibrium wave statistics.

Keywords : direct numerical simulation, capillary wave turbulence

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See also press items from

- CNRS logo  CNRS Research News, 28 August 2014 "Comment interagissent les vagues à la surface de l'océan?" (in french)
here for an approximative english "google" translation)

- 18, September 2014  « Comment interagissent les vagues à la surface des océans ? » (in french)
Synthèse de Presse CNRS du 19 Septembre 2014
(in french)

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