Non-Planar Beaches: Wave-Induced Setup/Setdown and Longshore Current

Wave-induced setup/setdown and longshore currents are examined theoretically for non-planar, concave-up beaches. A beach profile in which the stillwater-depth is proportional to the horizontal distance offshore raised to the 2/3 power is examined in detail. The total mean-water-depth, which includes the sum of the still-water-depth for this 2/3 power beach profile plus the wave-induced setup/setdown, may be approximated shoreward of the breaker zone in a best least-squares sense by a profile that is proportional to the horizontal distance offshore raised to the 1/2 power. The longshore current profile for this non-planar beach is found to differ significantly from that predicted analytically for a planar beach. The longshore current velocity does not vanish at the shoreline as in the planar beach case and, thus, yields an estimate for the mean longshore swash velocity. In addition, the peak velocities and the total longshore transport of water are found to be less than for the corresponding planar beach cases.