有限深两层流体中内孤立波造波实验及其理论模型

Wave-making experiments and theoretical models for internal solitary waves in a two-layer fluid of finite depth

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推,以基于Miyata-Choi-Camassa(MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度,发展了一种振幅可控的双推板内孤立波实验室造波方法.在此基础上,针对有限深两层流体中定态内孤立波Korteweg-deVries(KdV),扩展KdV(eKdV),MCC和修改的KdV(mKdV)理论的适用性条件等问题,开展了系列实验研究.结果表明,对以水深为基准定义的非线性参数ε和色散参数μ,存在一个临界色散参数μ0,当μ<μ0时,KdV理论适用于ε≤μ的情况,eKdV理论适用于μ<ε^(1/2)μ的情况,而MCC理论适用于ε>μ^(1/2)的情况,而且当μ≥μ0时MCC理论也是适用的.结果进一步表明,当上下层流体深度比并不接近其临界值时,mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况,但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件,为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据.

A laboratory wave-making method is developed for the internal solitary wave under the condition of giving its amplitude produced by oppositely and horizontally pushing two vertical plates placed separately in the upper- and lower-layer fluids of a large-scale density stratified tank where based on the Miyata-Choi-Camassa （MCC） theoretical model, the layer-mean velocities of the upper- and lower- layer fluids induced by the internal solitary, wave are used as the velocities of the two plates. On this basis, a series of experiments is conducted to explore the applicability conditions for internal solitary wave theories with stationary solutions which are Korteweg-de Vries （KdV）, extended KdV （eKdV）, MCC and modified KdV （mKdV） models in a two-layer fluid of finite depth respectively. It is shown that for the nonlinear parameter e and the dispersion parameter μ defined by the total water depth, there exists a critical dispersion parameterμ0, in the case of μ ≤μ0, the KdV model is applicable for e ≤2, the eKdV model is applicable forμ 〈 ε ≤ √μ, as well as the MCC model is applicable forμ〈ε√μ. However, in the case of μ≥μ0, the MCC model is still applicable for a wide range of e. Furthermore, for the case where the ratio of depth between the upper- and lower-layer fluids is not close to its critical value, the mKdV model is mainly applicable for the case where the amplitude of the internal solitary wave is close to its theoretical limiting amplitude, however, the MCC model is also applicable for such a case. The investigation quantitatively characterizes the applicability conditions for four classes of internal solitary wave theories, and provides an important theoretical foundation For what kinds of theories can be chosen to model internal solitary waves in the ocean.