Nonlinear evolution of shear instabilities of the longshore current

Surface gravity waves breaking in the nearshore region force a longshore surf zone current. This current can be unstable to longshore periodic perturbations. The objective of this study is to analyze the finite amplitude behavior of instabilities of the longshore current utilizing numerical experiments.;For this purpose a solution method of the governing equations is developed. Spatial derivatives are computed using spectral collocation methods. A high-order time integration scheme is used to compute the time evolution of the velocities and water surface elevation. The model domain extends from the shoreline to a distance offshore and is periodic in the longshore direction. A curvilinear moving boundary is incorporated at the shoreline. An absorbing-generating boundary is incorporated offshore. The boundary treatments are tested. The model is then applied to the prediction of stability boundaries and equilibrium amplitudes of subharmonic edge waves. Numerical results are compared to theory and are found to reproduce it well.;Instabilities of an analytic longshore current profile over a plane beach are simulated. The instabilities are observed to equilibrate at amplitudes up to 50% of the original peak longshore current. For long domains in the longshore direction the long time behavior is observed to be dominated by subharmonic transitions that result in a reduction of the number of waves in the domain. The resulting longshore periodic flow structures exhibit strong offshore directed velocities and propagate in the longshore direction at a fraction of the peak current speed. Details of the subharmonic transitions and the effect of nonlinearity on the flow structures are analyzed.;Next, the shear instability climate during the S scUPERDUCK field experiment is simulated. Due to uncertainties in the friction and lateral mixing coefficients, numerical simulations are carried out for a realistic range of values. The resulting flow structures can be characterized as unsteady vortices propagating in the longshore direction. These vortices interact, merge and are shed offshore. During the shedding process, locally strong offshore directed currents are generated. Lateral mixing induced by the finite amplitude shear instabilities is analyzed and found to be of comparable magnitude to other mixing processes in the surf zone.