海洋波群的弱非线性演化及仿真

摘要

Aiming at the complicated relationships between the weak nonlinear and the dispersion in the wave group evolvement, we analyzed the extended KdV equation and discussed the effect of weakly nonlinear and dispersion. The computation procedure of eKdV equation was presented using one step time-four data space central finite-difference method. Slowly modulated gauss-amplitude sine wave was simulated. The results show that the wave group is focused when the weakly nonlinear terra is dominated, and the wave group is defocused when the dispersion term is dominated.%针对波群时间演化过程中出现的聚焦和散焦现象,采用扩展的KdV方程进行分析,研究了扩展的KdV方程中的弱非线性项和色散项在波群时间演化过程中所起的不同作用.在此基础上,提出了时间一步---空间四点的中心有限差分法来计算扩展KdV方程.通过对具有高斯幅度缓慢调制的正弦波进行仿真,仿真结果表明,当弱非线性项占主导地位时,波群会出现聚焦现象;当色散项占主导地位时,波群会出现散焦现象.所提的方法和仿真结果对研究波群空间演化过程也具有参考价值.