Field observations were made of wave‐induced nearshore circulations and meandering longshore currents on an undulatory surf‐zone bed, under the action of uniform incident waves. Circulations were associated with normal‐wave incidence; meandering currents were associated with oblique‐wave incidence. The transport in the observed circulations generally agreed with Bowen's (1967) linear theory based on the concept of radiation stress (Longuet‐Higgins and Stewart, 1962, 1964), provided that a friction coefficient C = 0.014 was assumed. The longshore current near the shore line moved from a shoal to a depression as predicted, but this movement was also directed from an area of high waves to one of low waves, which is different from the case of a circulation driven by nonuniform breaker heights on the bar. Spilling breakers over a shoal underwent greater energy dissipation than plunging breakers in the rip current. Observed streamlines were narrow in the outflow and broad in the inflow, a characteristic that was probably associated with a nonlinear mechanism arising from a steep depression in the rip channel, as previously explained by Arthur (1962). These circulations were pulsational, unlike the circulations of a steady‐state solution. Occasional strong outflows at beat frequencies caused water to escape from the circulation. For a given surf‐zone undulation, breaking over the inner bar was essential to the formation of a circulation, and the intensity of breaking, controlled by tide, corresponded with a proportionally stronger circulation. Thus, circulations were generally stronger during low tide than during high tide. Low rip‐current velocities at high tide fluctuated with incoming swells, whereas high velocities at low tide tended to fluctuate at surf beat frequencies. In proportion to increasing rip velocities, the rip pulsation tended toward lower intervals. Mean surface slopes caused by wave set‐up and set‐down agreed with trajectories of neutral‐density balls released in the circulation. Meandering currents associated with oblique‐wave incidence could be explained as a combined effect of circulation cells and parallel longshore flows.
An apparent complex time history of beach geometry can be described as a specific case of first‐order Markov process. Under the assumptions that the profile transition is controlled only by random excitations from waves and that the transition probability is identical for all the possible states of beach profile it is demonstrated that a beach profile time series contains cycles having negative binomial distribution. A simplified case in which the transition probability is taken as 1/2 (i.e., equal probability for either erosional or accretional transition for any profile state) is derived through both numerical simulation and theoretical derivation, the result of which shows reasonable agreement with field observations.
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