MASS-TRANSPORT UNDER SEA WAVES PROPAGATING 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 magnitud e as that of the boundary layer thickness delta and of the ripple wav elength l are considered. All the above quantities are assumed to be much smaller than the wavelength L of the sea wave and much larger th an the amplitude 2 epsilon of the ripples. The analysis is carried ou t 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 the se assumptions, the slow damping of wave amplitude in the direction of wave propagation is taken into account. Attention is focused on the b ottom boundary layer where an order (epsilon/delta*)(2) correction of the steady velocity components described by Longuet-Higgins (1953) is found. This correction persists at the outer edge of the bottom bound ary layer and affects the solution in the entire water column.