Waves Generated By A Submerged Body Moving In Stratified Fluids And Vertical Structures Of Internal Waves

This dissertation deals with the internal waves generated by a submerged moving body in stratified fluids, including linear interfacial Kelvin waves, flat internal solitary waves and algebraic solitary waves, by combining theoretical and experimental approaches. Some special structures of those internal waves and their effects on the free surface were elucidated. Scientific evidences were provided for non-acoustic detection of underwater moving bodies based on the principles of dynamics of the internal waves.The novel points and main conclusions of this dissertation are described as follows.1. An approach to velocity potentials obtained by superposing Green's functions of sources and sinks is presented, which is straightforward, intuitive and easy to be extended to complicated cases of multi-objects or asymmetrical bodies with arbitrary shapes moving in stratified fluids. The effects of interacting surface- and internal-wave modes induced by a dipole moving in a two-layer fluid on the surface divergence fieldare investigated for the first time. It is found that as the density ratio y is not close to one, the dipole approaches to the interface and the Froude number Fr tends to the critical value Frn, the equivalent influence of the two wave modes on the divergencefield at the free surface will be generated. A characteristic Froude number Frs corresponding to the situation of exactly the same influence imposed by the two modes on the free surface is found. And a solvability condition for the case of small density difference between the two fluid layers and a uniformly valid second-order asymptoticsolution are also first presented. For the limit case of -1, it is theoretically shownthat there exists no internal-wave mode with infinite amplitude at the interface, and the obtained solution is degenerated to Newman's solution for the single-layer fluid. The above theoretical results are qualitatively consistent with those obtained in our experiments.2. A new theoretical model formulating the interaction of a submerged moving body with the conjugate flow in a three-layer fluid is first presented. A criterion for the existence of weakly-nonlinear weakly-dispersive (WNWD) flat solitary waves is worked out. The numerical results indicate that (a) the conjugate flow due to a two-dimensional body moving at the bottom possesses an apparent behavior with two convex interfaces; (b) the solution satisfying the existence criterion is always unique near the relatively stable state of system. By applying the model to the case of two-layer fluid system with a free surface, some theoretical results are given, agreeing well with those predicted by the fKdV model. In terms of the above modeling idea, a model for treating the interaction of step topography with the conjugate flow in a three-layer fluid is constructed. All these theoretical results are qualitatively confirmed by our experiments.3. An exact solution satisfying the two-dimensional Benjamin-Ono equation is first presented, representing the two-dimensional algebraic solitary wave with shorter wavelength and larger amplitude compared with the one-dimensional one. By means of the ray theory and WKB method, the vertically propagating properties of the weakly nonlinear long waves are attained. It is pointed out that as the density variation becomes drastic, the internal waves of lower-order modes begin to be converted into those of higher-order modes, and that the abrupt inflexion of ray lines of the higher-mode internal waves near the center of pycnocline probably plays an important role in the instability of pycnocline.4. Two special phenomena have been observed in our experiments, which qualitatively verify the related theoretical predictions. One is that as the Froude number Fr for a sphere moving in the lower layer of a two-layer fluid system decreases, the amplitudes of divergent waves in the Kelvin wave system decrease and the amplitudes of transverse waves increase, and then, with the merging of the divergent and transverse waves...