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Direct numerical simulations of capillary wave turbulence

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Direct numerical simulations of the full two phase Navier-Stokes equations including surface tension in order to investigate capillary wave turbulence are performed for the first time, using the code Gerris [1]. Wave turbulence concerns the study of the statistical properties of a set of numerous nonlinear interacting waves [2]. Waves are observed to follow the linear dispersion relation of capillary waves and a stationary regime is reached. The wave height power spectrum in the wave-number-space or in the frequency-space exhibits power law regimes and shows good agreement with weak turbulence theory [2]. Finally, the scaling of the spectrum with the injected power will be discussed and compared with theoretical and experimental works.

Author(s):

Luc Deike    
Univ Paris Diderot, Sorbonne Paris Cit\'e, MSC, UMR 7057 CNRS, Paris
France

Daniel Fuster    
Institut Jean le Rond d'Alembert, UPMC, UMR 7190 CNRS, Paris
France

Michael Berhanu    
Univ Paris Diderot, Sorbonne Paris Cit\'e, MSC, UMR 7057 CNRS, Paris
France

Eric Falcon    
Univ Paris Diderot, Sorbonne Paris Cit\'e, MSC, UMR 7057 CNRS, Paris
France