A theory on the drag increment of internal waves with a spheroid moving horizontally at a high velocity （or for large internal Froude number） in uniformly vertically stratified fluid （or ocean） is presented in the present paper. A surface source distribution is employed to model a hydrodynamic interaction between the spheroid and the stratified fluid. From theoretical results, it is shown that there exists an asymptote of zero-drag increment in supercritical regimes, where internal Froude numbers are larger than the critical internal Froude numbers. When the spheroid reduces to a sphere, the results in this paper is in good agreement with the previous theoretical and experimental results of the sphere.
Several ray-type 1D and 2D KdV equations for two-layer stratified ocean with topographic effect are derived in detail in the present study. A simplified version of these equations, ray type 1D KdV equation, is used to calculate numerically the disintegration of initial interface soliton from the deep sea to the continental shelf. At the same time, a laboratory experiment is carried out in a 2D stratified flow and internal wave tank to examine the numerical results. A comparison of the numerical results with the experimental results shows that they are in good agreement. The numerical results also show that the ray-type KdV equation has high accuracy in describing the evolution of initial interface waves in shelf/slope regions. Form these results, it can be concluded that the fission process is a dominant generating mechanism of interface soliton packets on the continental shelf.
A linear theory on the internal waves generated in the stratified fluid with a pycnocline is presented in this paper. The internal wave fields such as the velocity fields in the stratified fluid and velocity gradient fields at the free surface are also investigated by means of the theoretical and numerical method. From the numerical results, it is shown that the internal wave generated by horizontally moving Rankine ovoid is a sort of trapped wave which propagates in a wave guide, and its waveform is a kind of Mach front-type internal wave in the pycnocline. Influence of the internal wave on the flow fields at the free surface is represented by the velocity gradient fields resulted from the internal waves generated by motion of the Rankine ovoid. At the same time, it is also shown that under the hypothesis of inviscid fluid, the synchronism between the surface velocity gradient fields at the free surface and the internal wave fields in the fluid is retained. This theory opens a possibility to study further the modulated spectrum of the Bragg waves at the free surface.
Based on a nonhydrostatic numerical ocean model developed by one of the authors, the interaction of an intemal solitary wave with a step-type topography was investigated. Over the step topography, the flow pattern could be classified into three categories： 1） the propagation and spatial structure of the internal solitary wave was little influenced by the bottom topography, 2） the internal solitary wave was significantly distorted by the blocking effect of the topography without the occurrence of wave breaking and 3） the internal solitary wave was broken as it encountered and passed over the bottom topography. A detailed description of the processes leading to wave breaking is given in this paper together with energy budget analysis. The results revealed that the maximum of the energy dissipation rate is no more than 40%, which is consistent with available experimental data.
