Wave-induced mean flows in vertical rubble mound structures

Waves impinging on rubble mound breakwaters and seawalls induce a mean flow within the breakwater, analogous to the so-called undertow within the surf zone. Here, using a plane wave approximation (kh < 1.5), a second-order pr oblem is solved for an idealized breakwater with a rectangular cross-sectio n to show the origin and the nature of the mean flow within the porous stru cture. The mean flow is expressed in terms of a mean stream function analyt ically derived, obtained based on the mass flux balance between the inciden t, reflected and transmitted waves. Furthermore, the evolution of other sec ond-order magnitudes such as mean water level and mass flux is analyzed und er different incident wave conditions, structure geometry and porous materi al characteristics. Results show that the evolution of the different mean q uantities is controlled mainly by reflection and consequently depends highl y on structure geometry and porous material characteristics. Furthermore, i t is shown that the return flow is stronger with increasing mass flux decay . Some qualitative experiments to show the described mechanism are also pre sented. (C) 1998 Elsevier Science B.V. All rights reserved.