Mass transport under sea waves over a rippled bed

Mass transport under a progressive sea wave propagating over a rippled bed is investigated. Wave amplitudes a of the same order of magnitude as that of the boundary layer thickness delta and of the ripple wavelength l are considered. All the above quantities are assumed to be much smaller than the wavelength L of the sea wave and much larger than the amplitude 2 epsilon of the ripples. The analysis is carried out up to the second order in the wave slope a/L and in the parameter epsilon/delta which is a measure of ripple steepness. Because of these assumptions, the slow damping of wave amplitude in the direction of wave propagation is taken into account. Attention is focused on the bottom boundary layer where an order of the steady velocity components described by Longuet-Higgins (1953) is found. This correction persists at the outer edge of the bottom boundary layer and affects the solution in the entire water column.