A Study On Fission Laws Of Initial Internal Solitary Waves On The Continental Shelf/Slope

In recent years, the fission processes of initial internal solitary waves and solitary internal tides are paid a considerable attention by oceanographers. From the SAR imageries of internal waves, it is known that the internal soliton wave-train (packet) and undular bore propagated on the continental shelf are dominant forms of internal waves in shallow continental shelf water region. In order to study the generation and fission mechanism of nonlinear internal waves on the shelf, a theoretical and numerical study related to these mechanisms is carried out in present paper.First, a one-dimensional variable-cofficient KdV equation of two-layer stratified flow with bottom topography and a two-dimensional variable-cofficient KdV equation of any stable stratified fluid with bottom topography are derived in present paper. Secondly, the fission laws of initial internal solitary waves are also studied in terms of the KdV equations as derived above. Finally, numerical calculations on the fission laws and the topography eigenvalue problem are also carried out by means of the finite difference and shutting methods.From the theoretical results, it is shown that in the weakly stratified fluid, the odd modes all have similar eigen-depths, but for all even modes there not exist the fission phenomena. The results from the numerical calculations shows (1) The larger the amplitudes of initial solitary waves, the longer the their widths, the shallower the water depths on the shelf are, the more fission number N are. (2) The fission process is a dominant mechanism of generation of internal soliton wave-train on the shelf /slope and is independent on the shapes of the initialinternal solitary waves. (3) The internal soliton with large width and small amplitude in an internal soliton wave-train on the shelf appears first, after then the soliton with less width and larger amplitude appears ,finally the soliton with the highest amplitude appears. (4) At the eigendepths of zero nonlinearity points on the slope, the polarity overturning will occur and the initial internal solitary waves will also fission.