ESTIMATION OF CHARACTERISTIC QUANTITIES OF OFFSHORE VORTEX TRAIN

Abstract

A row of two-dimensional vortices forms in an offshore zone when regular surface waves run up a sloping flat bed. This vortex row has been called the offshore vortex train. Its formation region and quantitative properties have been investigated on the basis of experiments for three slopes of the bed. The vortex train is independent of types of wave breaking and forms when the steepness of deep water waves is smaller than 4.2×10-2. The formation region can be expressed universally in the H/L and (1+6.4 tan θ) h/L coordinates system, where H is the wave height, L the wavelength, h the water depth and tan θ the bed slope. The net shoreward velocity near the sloping bed is given by an empirical relation independent of tan θ. The horizontal interval between the vortices is expressed by 1.2×10-2 (tan θ)1/3 (h/L)-1 h. The length of the vortex train is dominated by the wavelength and the water depth at the breaking point. The velocity of the vortex movement is given by 3.6×101 (tan θ)2/3 (h/L) Umax. where Umax is the maximum velocity of steady offshoreward flow induced on a horizontal bed.