含强水流高阶Boussinesq水波方程
Higher-order Boussinesq equations with strong currents
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摘要: 采用摄动法并利用已建立的纯波情况下高阶Boussinesq方程,建立了可以考虑强水流与波浪相互作用的高阶Boussinesq方程.水流速度与波浪群速具有相同量级,且随时间和空间的变化尺度远大于波浪周期和波长.方程色散性近似到[4/4]阶Pade展开,对浅水情况方程可以是完全非线性的,可适用于波流相互作用的强非线性问题.通过将水流存在时波长和波幅的结果与一阶斯托克斯波结果对比,讨论了具有不同近似程度的3种含波流相互作用的Boussinesq方程的适用性.Abstract: The higher-order Boussinesq equations for the case of strong current are developed by a perturbation method under the assumption that the current velocity is of the same magnitude as the wave group velocity, and its time and space scales of variation are much greater than the wave period and length respectively.The frequency dispension of the equations is accurate to [4/4] Pade's expansion and the equations are applicable to fully nonlinear case of wave and current interactions for very shallow water.The discussion is also made for the validations of the Boussinesq equations with different frequency dispersion.
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Key words:
- Water wave /
- current /
- wave-current interactions
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Pergrine D H. Interaction of water waves and currents. Adv Appl Mech, 1976, 16:10～117 Brevik I, Aas B. Flume experiments on wave and current. I. Rippled bed. Coastal Engineering, 1980, 3:149～177 Yoon S B, Liu P L F. Interaction of currents and weakly nonlinear water waves in shallow water. J Fluid Mech, 1989, 205:397～419 Priiser H H, Zielke W. Irregular wave on a current. In:Proc 22nd Int Conf Coastal Eng, Delft, The Netherlands, Vol. 1. New York:ASCE, 1990, 1 088～1 101 Chen Q, Madsen P A, Schaffer H A, et al. Wave-current interaction bassed on an enhanced Boussinesq approach. Coastal Eng, 1998, 33:11～39 Madsen P A, Schaffer H A, Chen Q. et al. Boussineaq type equations with high accuracy in dispersion and nonlinearity. In:Proc 25th Int Conf Coastal Eng, Vol 1. Orlando:ASCE, 1996. 95～108 邹志利.高阶Boussinesq水波方程.中国科学(E辑),1997,27(5):460～473 邹志利.高阶Boussinesq水波方程的改进.中国科学(E辑),1998,28(5):1～10 -
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