Stability of periodic progressive gravity wave solutions of the Whitham equation in the presence of vorticity

Publication date: Available online 15 October 2019Source: Physics Letters AAuthor(s): C. Kharif, M. Abid, J.D. Carter, H. KalischAbstractThe modulational instability of two-dimensional nonlinear traveling-wave solutions of the Whitham equation in the presence of constant vorticity is considered. It is shown that vorticity has a significant effect on the growth rate of the perturbations and on the range of unstable wavenumbers. Waves with kh greater than a critical value, where k is the wavenumber of the solution and h is the fluid depth, are modulationally unstable. This critical value decreases as the vorticity increases. Additionally, it is found that waves with large enough amplitude are always unstable, regardless of wavelength, fluid depth, and strength of vorticity. Furthermore, these new results are in qualitative agreement with those obtained by considering fully nonlinear solutions of the water-wave equations.

Source: Physics Letters A - October 16, 2019 Category: Physics Source Type: research