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Direct numerical simulations of capillary wave turbulence
Luc Deike1, Daniel Fuster2, Michael Berhanu3
1Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France, EU and Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92093, USA.
Physical Review Letters
|June 28, 2014
Summary
Direct numerical simulations reveal capillary wave turbulence in a two-phase flow. Results confirm weak turbulence theory, showing power-law spectra and validating the Kolmogorov-Zakharov constant.
Area of Science:
- Fluid dynamics
- Wave turbulence
Background:
- Capillary wave turbulence is a complex phenomenon driven by nonlinear interactions.
- Understanding its statistical properties is crucial for various fluid systems.
Purpose of the Study:
- To investigate capillary wave turbulence using direct numerical simulations.
- To validate theoretical models, specifically weak turbulence theory, against simulation data.
Main Methods:
- Solving the full three-dimensional Navier-Stokes equations for a two-phase flow.
- Applying local forcing at large scales to induce turbulence.
- Analyzing the wave height spectrum and energy flux.
Main Results:
- A statistical stationary state was achieved after initial forcing periods.
- Wave number and frequency spectra followed a power law, consistent with weak turbulence theory.
- The estimated Kolmogorov-Zakharov constant matched theoretical predictions.
Conclusions:
- Direct numerical simulations support the weak turbulence approach for capillary waves.
- The study confirms the validity of weak turbulence theory in quantifying out-of-equilibrium wave statistics.
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