Rossby solitary waves excited by the unstable topography in weak shear flow

A new forced KdV equation including topography is derived and the numerical solutions are given. The topographic variable should be related with the temporal and spatial function, which is called unstable topography. The physical features of the solitary waves about the mass and energy are discussed by theoretical analysis. In further studies, the pseudo-spectral numerical methods are used to discuss the evolution of solitary wave generated by the topography when meridional wave number \(m=1\); in a similar way, we analyze the solitary wave when meridional wave number \(m=2\). At last, we make the comparison for the characteristics of waves between \(m=1\) and \(m=2\), the wave of meridional number \(m=1\) plays a leading role.