Stability of gravity-capillary waves generated by a moving pressure disturbance in water of finite depth

In previous work, we investigated two-dimensional steady gravity-capillary waves generated by a localized pressure distribution moving with a constant speed U in water of finite depth h. Localized solitary waves can only exist in subcritical flows where the Froude number F=U/(gh)(1/2)<1, and were found using a combination of numerical simulations of the fully nonlinear inviscid, irrotational equations, and analytically from a weakly nonlinear long-wave model, the steady forced Korteweg-de Vries equation. The solution branches depended on three parameters, the Froude number, F<1, the Bond number, tau->1/3, and the magnitude and sign of the pressure distribution, epsilon. In this paper, we examine the two-dimensional stability of these waves using numerical simulations of the fully nonlinear unsteady equations. The results are favorably compared to analogous numerical solutions of the unsteady forced Korteweg-de Vries equation. We find that for epsilon>0, the small-amplitude steady depression wave is stable whereas the large-amplitude steady depression wave is unstable. The depression wave with a dimple at its crest, which occurs only when epsilon<0 is unstable, but the small-amplitude elevation wave with epsilon<0 is stable. (C) 2009 American Institute Of Physics. [DOI: 10.1063/1.3207024]