Vertically varying Eulerian mean currents induced by internal coastal Kelvin waves

Abstract

The lost momentum in spatially damped internal Kelvin waves reappears as Eulerian mean currents through the action of the nonlinear wave-wave interaction terms. A novel expression is derived for the steady balance between the frictional force on the coastally trapped horizontal Eulerian mean flow, and the forcing from the wave field in terms of the mean wave Reynolds stresses and the horizontal divergence of the Stokes drift. The forcing can be expressed in terms of orthogonal eigenfunctions for internal waves, yielding the vertical variation of the Eulerian mean flow. For arbitrary values of the Brunt-Vaisala frequency N, it is shown that the wave forcing on the Eulerian mean is always negative, yielding a Poiseuille type flow. Therefore, unlike the Stokes drift velocity in internal Kelvin waves which exhibits a backward drift for the first mode in the region of maximum N, the wave-induced horizontal Eulerian mean current is always in the direction of the waves. The results are illustrated by an example from Van Mijenfjorden in Svalbard, which is an arctic sill fjord where internal waves are generated by the action of the barotropic semi-diurnal tide. This article is protected by copyright. All rights reserved.