Sea waves and mass transport on a sloping beach

The steady streaming induced by a sea wave shoaling on a sloping beach and partly reflected at the coastline is determined in the region seaward of the breaker line. Shallow waters and waves of small amplitude are considered. Moreover, the Reynolds number is assumed to be large but still within the laminar regime and the flow domain is split into a bottom boundary layer and a core region. For an incoming wave which is fully absorbed at the coast the solution shows that close to the bottom the steady streaming is onshore directed even though the depth-averaged value represents an offshore directed flow. Moreover, the vertical velocity distribution depends on the ratio between the wave amplitude alpha* and the thickness delta* of the bottom boundary layer. For a fully reflected wave, steady recirculation cells are induced, the form and strength of which depend on the ratio alpha*/delta*. A complex flow is generated for reflection coefficients falling between 0 and 1.