The diffraction of Kelvin waves and bores at coastal bends

Abstract

Bends in coastal mountain ranges may diffract propagating atmospheric Kelvin waves and trapped coastal currents. Analytic solutions exist for the diffraction of both linear Kelvin waves and linear nonrotating gravity waves. Within the context of the single-layer shallow-water equations, we examine the diffraction of nonlinear gravity waves and bores in a nonrotating reference frame and nonlinear Kelvin waves and coastally trapped bores in a rotating reference frame. The diffraction process can significantly decrease the amplitude of linear and nonlinear waves and bores in the nonrotating reference frame. Unlike for their linear counterpart, however, the diffraction-related amplitude decay for the nonrotating nonlinear waves takes place entirely within the region of the bend and does not produce a continuous decay after the bend. Moreover, theory predicts a critical bend angle at which bore amplitudes will be zero at the wall after propagation around the bend, but shallow-water model simulations do not confirm the existence of the critical angle. For Kelvin waves and trapped bores in the rotating reference frame, we find robust wave and bore propagation around coastal bends in all cases. No critical angles exist for the waves and bores in the rotating reference frame.