Representation of Water Particle Velocity of Breaking Waves on Beaches by Dean's Stream Function

Abstract

Experimental values of water particle velocity of breaking waves on uniformly sloping beaches differ considerably from the theoretical values of Stokes waves of the third order and cnoidal waves of the second approximation. In this paper, Dean's stream functions are calculated by giving simultaneously measured time variations of the water level of the breaking waves. Vertical distributions of horizontal water particle velocity at the crest phase, calculated by using these stream functions, are compared with experimental distributions in order to discuss the applicability of Dean's stream function method. These theoretical distributions can explain the experimental results well, although this stream function method assumes permanent waves in uniform depth. Dean's stream function can express an asymmetric wave profile as that of breaking waves on sloping beaches, while the Stokes wave theory has a symmetric wave profile. It is suggested that the breaking wave profile dominates the water particle velocity field of breaking waves.