Mass Transport Velocity in Shallow-Water Waves Reflected in a Rotating Ocean with a Coastal Boundary

Abstract

AbstractThe mass transport velocity in shallow-water waves reflected at right angles from an infinite and straight coast is studied theoretically in a Lagrangian reference frame. The waves are weakly nonlinear and monochromatic, and propagate in a homogenous, viscous, and rotating ocean. Unlike the traditional approach where the domain is divided into thin boundary layers and a core region, the uniform solution is obtained here without constraints on the thickness of the bottom wave boundary layer. It is shown that the mass transport velocity is not only sensitive to topography, but depends heavily on the interplay between the vertical length scales. Similarities and differences between the cases of a constant depth, a linearly sloping bottom, and a wavy and linearly sloping bottom are discussed. The mass transport velocity can be divided into two main categories—that induced by waves with a frequency close to the inertial frequency, and that induced by waves with a much larger frequency. For waves significantly affected by rotation to first order, the cross-shore mass transport velocity is very small relative to the alongshore mass transport velocity, and the direction of the mass transport velocity is reversed relative to that in waves of much higher frequencies.