适合中等水流的Boussinesq方程

基金项目: 国家重点基础研究专项经费资助项目(59979002,59839330);教育部科学技术重点资助项目(99147);博士学科专项基金资助项目

Boussinesq equation with moderate current

摘要: 推导了含量阶为O(ε^1/2)的瞬变非均匀流的Boussinesq水波方程,讨论了该量阶水流对流场速度和压力分布的影响,采用了Crank-Nicolson格式的预估-校正有限差分法对该方程进行了数值求解.把数值结果与无水流情况的实验结果进行了对比,验证了该方程和数值计算方法的有效性,与经典的Boussinesq方程和含量阶为O(1)的瞬变非均匀流的Boussinesq水波方程的计算结果进行了比较,考察了该方程的适用范围.
- 波浪 /
- 水流 /
- Boussinesq方程
Abstract: The Boussinesq equations with the transient and non-uniform current of O(ε^1/2) are derived.The effects of currents on the distributions of velocities and pressure are discussed.The prediction-correction method of finite difference scheme is employed to solve the equat ions numerically.The numerical results are compared with the experimental data for the case of currents being equal to 0 and the agreements are good,which demonstrates the accuracy of the equations and the efficiency of the numerical methods.The numerical results are also compared with the numerical results of the classic Boussinesq equations and the Boussinesq equations with strong currents of O(1),and the application range of the equations is also investigated.
- waves /
- current /
- Boussinesq equation

UNNA P J. Wave and tidal streams[J].Nature,1942,149:219-220.

LONGUET-HIGGINS M S,STEWART R W. Changes in form of short gravity waves on long waves and tidal current[J].J Fluid Mech,1960,6:565-583.

李玉成.波浪谱在斜向流作用下的折射[J].海洋学报,1985,7(5):611-620.

YOON S B,LIU P L F. Interaction of currents and weakly nonlinear water waves in shallow water[J].J Fluid Mech,1989,204:397-419.

CHEN Qin,MADSEN P A,SCHAFFER H A,et al. Wave-current interaction based on an enhanced Boussinesq equation approach[J].Coastal Eng,1998,33:11-39.

邹志利.含强水流的高阶Boussinesq方程[J].海洋学报,2000,22(4):41-50.

ZOU Zhi-li,XU Ben-he. Numerical model for solving Boussinesq-type equations[J].Acta Oceanologica Sinica,1998,17(3):375-386.