Shallow-Water Models with the Weak Coriolis and Underlying Shear Flow Effects

Abstract

In this paper, we are committed to deriving shallow-water model equations from the governing equations in the two-dimensional incompressible fluid with the effects of weak Coriolis force and underlying shear flow. These approximate models are established by working within a weakly nonlinear regime, introducing suitable far-field or near-field variables, and truncating the asymptotic expansions of the unknowns to an appropriate order. The obtained models generalize the classical KdV and Boussinesq equations, as well as KdV and Boussinesq equations with the Coriolis or shear flow effects.