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A laboratory experiment on alongshore currents was conducted for two plane beaches, with gradients 1:40 and 1:100, to investigate the instability of alongshore currents. Complicated and strongly unstable alongshore current motions were observed. In order to clearly examine the spatial and temporal variations of the shear instability of the currents, digital images from a charge-coupled device (CCD) recorded the deformations of dye batches released in the surf zone. Some essential characteristics of the shear instability were obtained from analyses of images showing the temporal variation of the dye patches. A high-resolution spectral analysis technique (the maximum entropy method, or MEM) was used to analyze the dominant frequency of the observed oscillation, along with the trigonometric regression method for determining the variations of the oscillation strength in the cross-shore direction. The propagation speed of the dye patch was obtained by tracking the movement over time of fixed locations in the dye patch, such as its peak, in the longshore direction. This data was then fitted linearly. Alongshore and cross-shore velocity time series acquired from sensors showed clearly that large-amplitude, long-period (about 50 s or 100 s) oscillations were present for all sensors deployed in the cross-shore direction under regular and irregular wave conditions. The analysis found that the maximum shear wave amplitude was approximately one-sixth of the maximum for the mean alongshore current, and occurred approximately at the position of the maximum of the mean alongshore current for irregular waves. The spatial structure of the shear waves was studied by analyzing collected images of the dye patches. The phase velocity of the meandering movements was obtained by measuring the magnitude of the oscillations of the dye patches in the alongshore direction with respect to time. The results suggest that the propagation speed of the shear instability was approximately one-half to three-quarters of the maximum mean longshore current for both regular and irregular waves. Linear instability analysis theory was applied to the characteristics of alongshore current instability, which suggested that there are two instability modes related to the observed oscillations: the frontshear mode observed for the 1:100 slope, and the backshear mode observed for the 1:40 slope. Theoretical analyses agreed with the experimental results in both cases. The velocity profile of the mean longshore current was found to affect the instability mode significantly, leading to further investigations on the influence of the velocity profiles and to provide support for the above conclusions.

Themildslopeequationisusedtodescribewavepropagatinginthenearshoreregion.Inthispaper,thefinitedifferencemethod isusedtodiscretizethegoverningellipticequationandthediscretizedlinearequationissolvedusingGPBiCG(m,n)method.Two cases of wave propagating are used to test the model, and reasonable agreements have been achieved. It is shown that the present algorithm: GPBiCG(m,n)withaflexibleanddiverseform,hasafastandrelativelyrobust convergencerate,andcanbeefficiently and economically run in either the linear or nonlinear wave model and easily used to a complicated region. D 2004 Elsevier B.V. All rights reserved.