Generation Mechanism Research For The Internal Waves In Uniformly Stratified Fluids

In the recent two decades, with the rapid development of satellite remote sensing technology and image recognition, the detection techniques of the wake and its interference with free-surface have attracted increasing attention around the world. However, few previous studies have made contributions to deepening the understanding of the wake and its formation, meanwhile, the mechanisms and characteristics of the free-surface fluctuations in uniformly stratified fluid, still remainam biguous and difficult to be investigated in both theory and experiment. The studies of the internal waves in density-stratified water andthe free-surface interferences have been regarded as frontier fields of hydrodynamics problems, which need to be paid more attentions.Considerable researches have been done on the Green’s function of internal waves in uniformly stratifiedfluids; unfortunately, theseresults are fragmentary and sometimes contradictory. The previous studies mainly devoted to the Green’s function of infinite fluid, and took no consideration ofthe free surface effect as well asits interference mechanism. Furthermore, when taking the free-surface into consideration, researchers always assume the fluid discontinuously stratified. Obviously, the interfacial waves and the internal waves are two alternative concepts in terms of eithertheory or practice and they behave particularly different in the forms of free-surface fluctuations.As a preliminary step towards this aim, the present paper is devoted to the Green’s function itself. A mathematical model and analysis methods for the internal waves generated by pulsating point sources are theoretically established, for ω2>N2 and ω2<N2 the analytic expressions of the free-surface Green’s function in uniformly density-stratified fluids are derived in the present paper based on the Fourier transformation and contour integration technique. A detailed knowledge of the internal waves generated by pulsating point source could essentially improve our understandings of the internalwave generation, fluctuationand propagation characteristics, which may also facilitate the subsequent studies.