海岸碎波拍的计算

A NONLINEAR MODEL OF SURF BEAT 1)

研究了一维碎波拍的计算方法．波浪控制方程由欧拉方程在短波周期上平均而得到．为了考虑低频波浪在海岸上的破碎，采用了ＷＡＦ（ＷｅｉｇｈｔｅｄＡｖｅｒａｇｅＦｌｕｘ）方法求解长波方程．对由辐射应力和海底摩擦力引起的方程非齐次项采用了时间算子分裂法进行了处理，并对由此产生的误差进行了修正．计算了单色波和双色波垂直入射海岸的情况，并与实验结果进行了对比．

A nonlinear, short-wave-averaged model of surf beat, which describes essentially long-period motions associated with the mean free surface,is presented. The numerical techniques used in the solution are based on so-called Weighted-Average Flux (WAF) method, with Time-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modelling breaking long waves. The short wave (or primary-wave) energy equation is solved using a more traditional Lax-Wendroff technique. Although Linear Wave Theory has been used to describe the transformation of short waves in many areas, it seems desirable to make use of a nonlinear theory at least when waves get closer to the shore where nonlinear effects will become important. however, due to the simplicity of the linear theory, a “simplified” nonlinear theory which would combine the advantages of both appears to be most desirable. And the hyperbolic theory of James (1974) is useful in this regard. A set of validity tests is undertaken in this paper, which is based on the monochromatic wave flume data conducted by Stive (1983) (in which the wave flume is of about 55m total length, with a beach slope at one end of 1:40) and the bichromatic wave flume data compiled by Kostense (1984) (in which a wave flume was 55m long, with a 1:20 slope at one end on which to absorb the short waves). The model described in this paper is found to be satisfactory in most respects when compared with the measurements except in modelling the mean free surface very close to the mean shoreline.