Stratified Fluid Rankine Ovoid Generated Internal Waves

A problem on internal waves generated by moving Rankine ovoid in stably arbitrary stratified flow and in the stably stratified ocean is studied in present thesis. Based on wide prospects in applied research, it attracts hydrodynamists' and oceanographers' great notice. So called stably arbitrary stratification means that the density profiles are not restricted in condition of stably stratification. Therefore theory and computational methods presented in the present thesis can be employed into two-layer flow, flows in strong pycnocline and in other continuous stratifications. Rankine ovoid is a fluid body enclosed by a zero-stream surface, which is generated by a pair of source and sink moving at a given velocity in the stratified flow, the fluid body is an approximation of a kind of moving body in stratified ocean.First of all, the basic governing equations described this kind of the forced internal waves were discussed and they were classified into two sorts: the simplified hydrodynamic equations and corresponding spectrum equations. The Sturm-Liouville eigenvalue problem and nonlinear equations of first order are derived under condition of Boussinesq' s approximation, static pressure hypothesis, non-Earth rotation, lip-rigid approximation and horizontal bottom, and the equations were transformed into the spectrum ones. Because the S-L equation is resulted from the zero-order linear system, hence once it could be solved, all the other properties will be obtained. The forced SturnrLiouville eigenvalue problem is found in terms of the Green delayed potential and Green advancing potential, then contributions from all the residuals in partial fraction expansions are calculated and summed, and a spectrum solution is found. Finally, an expected solution in physical space is obtained by using theinvert Fourier transformation.This method used in this thesis is theoretical one, and the computational calculation is only a kind of operation with respect to Fourier integration in terms of quick FFT, an advantage of this method is that the wave factors generated by the moving body in the stratified ocean can be obtained rapidly. Therefore this method can be used in REA widely.In order to examine the theoretical results obtained in this thesis, a preliminary experimental study on the internal waves generated by Rankine ovoid is carried out in Key Laboratory of Physical Oceanography, Ocean University of China. This tank system includes an independent producing system of the stratified water and the apparatus measuring density profile. The model used in the experiments is a Rankine ovoid which is similar to that used in theoretical study in geometrical shape. From the comparison between experimental and theoretical results, it is shown that they are basically in agreement.The results from theory and experiments also show that this kind of internal waves generated by moving Rankine ovoid in the stratified flow have the following features:(1) the amplitude of the internal waves generated by moving Rankine ovoid doesn' t increase along with the increase of model' s velocity. And the amplitude has a maximum value at a particular velocity which is different in condition of different stratification.(2) The internal Kelvin angle decreases with the increasing of velocity of model.(3) The depth of the model will influence on the amplitude. In general, under condition of similar stratification the amplitude is higher as the model is in upper layer than those in middle and lower layer.(4) In situation of low velocity, the internal wave field is transverse wave system, and with the increasing of moving velocity the divergence wavesystem becomes stronger and the transverse wave system becomes weaker. In situation of the high velocity, the wave system is dominantly the divergence wave system.