Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
Abstract
We study the longtime evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in moderately small wave numbers. We numerically implemented the primitive Euler equations for the potential flow of an ideal fluid with free surface written in Hamiltonian canonical variables, using the expansion of the Hamiltonian in powers of nonlinearity of terms up to fourth order. We show that because of nonlinear interaction processes a stationary Fourier spectrum of a surface elevation close to <η_{k}^{2}>∼k^{7/2} is formed. The observed spectrum can be interpreted as a weakturbulent Kolmogorov spectrum for a direct cascade of energy.
 Publication:

Physical Review Letters
 Pub Date:
 April 2004
 DOI:
 10.1103/PhysRevLett.92.134501
 arXiv:
 arXiv:physics/0308099
 Bibcode:
 2004PhRvL..92m4501D
 Keywords:

 47.27.Eq;
 05.45.a;
 47.11.+j;
 47.35.+i;
 Nonlinear dynamics and chaos;
 Physics  Fluid Dynamics;
 Physics  Atmospheric and Oceanic Physics;
 Physics  Computational Physics;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 4 pages, 5 figures