Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

Details Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

2003-08-27

arxiv.org/abs/physics/0308099v2

Phys. Rev. Lett., vol. 92, issue 13, 134501 (2004)

Physics

Fluid Dynamics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.92.134501

We study the long-time evolution of gravity waves on deep water exited by the stochastic external force concentrated in moderately small wave numbers. We numerically implement the primitive Euler equations for the potential flow of an ideal fluid with free surface written in canonical variables, using expansion of the Hamiltonian in powers of nonlinearity of up to fourth order terms. We show that due to nonlinear interaction processes a stationary energy spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.

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