椭圆余弦波的数值计算及其特性研究

STUDY ON THE NUMERICAL SOLUTION OF CNOIDAL WAVE THEORY FOR PRACTICAL APPLICATION

椭圆余弦波能很好地描述浅水区域波浪运动特性,尤其是波浪破碎后形成的击岸波水质点运动规律、波速及波面形态,但按以往的理论,因椭圆积分计算上的繁杂往往给应用带来不便。按本文的方法对椭圆余弦波进行数值求解具有方法简便、正确迅速、便于应用的优点;同时,文中探讨了椭圆余弦波的各种特性,包括相对波峰高度、底面最大流速、波速、波能流及辐射应力和波浪破碎后的平均水面变化值。计算表明,这一方法比较符合试验资料及实际情况。

The cnoidal wave theory is applicable to shallow water area and can fairly descride the kinematic behaviours of waves in nearshore zone, such as water particle velocities, wave celerity and the wave profile. It is known that the solution of the cnoidal wave theory is given in terms of elliptic integrals and Jacobian elliptic functions Due to the complication of calculation of elliptic integrals and Jacobian elliptic functions,the cnoidal wave theory has only a restricted applications. By applying power series to express these quantities a numerical calculation of the cnoidal wave theory is pressented in this paper. It shows that the numerical calculation is quite convenient for practical applications and provides sufficient accurate results.The comparison of numerical computation with the experimental data is shown in Fig. 5 and Figs. 7, 8. It is evident that the values calculated are in good agreement with the experimental data obtained by other researchers The various behaviours of cnoidal wave,including the relative heights of wave crest, the maximum velocity,wave energy flux, radiation stress and the variation of the mean water level after wave breaking, are discussed in this paper.