High-frequency instabilities of Stokes waves

Euler's equations govern the behavior of gravity waves on surface an incompressible, inviscid, and irrotational fluid arbitrary depth. We investigate spectral stability sufficiently small-amplitude, one-dimensional Stokes waves, i.e., periodic permanent form constant velocity, in both finite infinite Using a nonlocal formulation developed by Ablowitz et al. (2006), we develop perturbation method to describe first few high-frequency instabilities away from origin, present spectrum linearization about small-amplitude waves. Asymptotic numerical computations these are compared for time excellent agreement.