Shear instability, wave and turbulence simulations using the shallow-water equations

Recent numerical simulations of the shear instability, wave and turbulence have led to much progress in understanding the exchange processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts in the atmosphere. A number of numerical simulation examples using the shallow-water equations (SWEs) are presented in this paper to explain how the simulations have helped understanding of the physics, as computational methods are developed to overcome the challenge of numerical instabilities.