The cubic vortical Whitham equation

The cubic vortical Whitham equation is a model for wave motion on vertically sheared current of constant vorticity in shallow inviscid fluid. It generalizes the classical by allowing and adding nonlinear term. inclusion this extra term allows to admit periodic, traveling-wave solutions with larger amplitude than equation. Increasing leads as well. stability these examined numerically. All moderate- large-amplitude solutions, regardless wavelength, are found be unstable. A formula cutoff function wavelength small-amplitude presented. In case zero vorticity, unstable respect modulational instability if kh>1.252, where k wavenumber h mean fluid depth.