The continuity equation for longshore current velocity with breaker angle adjusted for a wave-current interaction

Abstract

The continuity equation for mean longshore current velocity, V = gmT sin 2 θ b, agrees with selected field and laboratory data covering a wide range of conditions. Agreement between continuity equation and data is improved by eliminating those laboratory data which imply deep-water wave crests at angles near or greater than 90 degrees to the shoreline. Agreement between continuity equation and data is further improved by adjusting breaker angles to account for convection of the breaker point by the longshore current. Breaker point convection increases breaker angle by an amount predictable from the analysis developed here. This increase in angle is significant in those laboratory experiments with breaking wave crests at high angles to the shoreline. In the continuity equation, m is bottom slope, T is wave period, and θ b is breaker angle, but breaker height does not appear. According to radiation stress theory, mean velocity does depend on breaker height, but only weakly. Consistency between the two approaches would require a dimensionless velocity, C b/ gT, to be relatively constant, which it is. (The same dimensionless velocity appears in the analyses of breaker point convection.) The continuity equation is functionally independent of friction and mixing, in keeping with its derivation from simple conservation of mass considerations. The equation has no adjustable coefficients. The degress of agreement with data and the internal consistency of the analysis suggests that it is a good predictor of mean velocity in ordinary longshore currents.