Mass transport in two-dimensional water waves

Abstract

Mass transport in various kind of two-dimensional water waves is studied. The characteristics of the governing equations for the mass transport depend on the ratio of viscous lengthscale to the amplitude of the free-surface displacement. When this ratio is small, the nonlinearity is important and the mass transport flow acquires a boundary-layer character. Numerical schemes are developed to investigate mass transport in a partially reflected wave and above a hump in the seabed. When the mass transport is periodic in the horizontal direction, a spectral scheme based on a Fourier–Chebyshev expansion, is presented for the solution of the equations. For the ease of a hump on the seabed, the flow domain is divided into three regions. Using the spectral scheme, the mass transport in the uniform-depth regions is calculated first. and the results are used to compute the steady flow in the inhomogeneous flow region which encloses the hump on the seabed.