Shallow-Water Models with the Weak Coriolis and Underlying Shear Flow Effects (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we are committed to deriving shallow-water modelequations from the governing equations in the two-dimensional incompressiblefluid with the effects of weak Coriolis force and underlying shear flow. Theseapproximate models are established by working within a weakly nonlinearregime, introducing suitable far-field or near-field variables, and truncatingthe asymptotic expansions of the unknowns to an appropriate order. Theobtained models generalize the classical KdV and Boussinesq equations, aswell as KdV and Boussinesq equations with the Coriolis or shear flow effects.