We have studied numerically the development of modulational instability for stationary propogating Stokes waves of a moderate magnitude, (ka=0.15), on a deep water. The spectral code method was applied to exact one-dimensional hydrodynamic equations, which describe the porential flow of an ideal fluid with free surface; this surface was conformlly mapped to the half plane. The equations were solved in a box with periodic boundary conditions containing as much as ten lengths of the leading wave. The total amount of spectral modes were varied between 3ṡ 104 to 1ṡ 106. In the initial moment of time, the exact Stokes wave was modulated by a small long scale perturbation. As a result, we observed an exponential growth of modulation, which was leading to the formation of a single freak wave. The freak wave grew up to the limiting amplitude of (ka ∼ 0.45); then, it demonstrated a tendency to an explosive formation of singularity.
AGU Spring Meeting Abstracts
- Pub Date:
- May 2004
- 4560 Surface waves and tides (1255);
- 4572 Upper ocean processes