The nonlinear, time-dependent dynamics of rip currents in the surf zone are studied using numerical experiments involving finite-difference solutions to the shallow water equations for idealized, forced, dissipative, initial value problems. Beach topography with along-shore variability that includes rip channels through a shore parallel sand bar is used with periodic boundary conditions in the along-shore direction. The physical domain has dimensions of approximately one square kilometer. Forcing effects from breaking surface waves are parameterized with a two-dimensional submodel that is coupled to the beach bathymetry and provides gradients of the full radiation stress tensor. Dissipative effects are modeled by linear bottom friction. The solutions depend on the dimensionless parameter Q, which is the ratio of an advective to a frictional time scale. Initial experiments involve steady forcing from normally incident surface waves. For large Q, steady offshore rip currents are formed in the rip channels with weak onshore flow elsewhere. For small Q, the flow remains time-dependent and instabilities develop in the offshore rip currents. These instabilities can lead to extensive vortex generation and the development of an energetic eddy field offshore of the bar. Rip currents extending over 400 m offshore with peak mean velocities of approximately 0.5 m/s can be formed for moderate values of wave field and beach conditions. The initial response is often characterized by the formation of a vortex pair at the offshore front of the developing rip currents. This can be followed by the growth, advection offshore, and subsequent detachment of eddies in a regular or irregular manner. The behavior of the rip currents are found to depend on the form of the beach topography, including the width, depth, and spacing between the rip channels. Rip currents generated by incident waves fields oriented at relatively small angles away from the shore-normal direction may turn along-shore after they pass through the rip channels in the sand bar or may collapse into recirculating cells accompanied by a strong net along-shore transport depending on Q, the beach topography, and the angle of wave incidence. The dependence of the flow dynamics on Q, on the wave height, and on the angle of wave incidence is studied and is illustrated by flow visualization.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics