Free-Surface Green’s Function of Internal Waves in Uniformly Stratified Fluid

Abstract

Abstract:

Abstract： A mathematical model and analysis methods for the internal waves generated by pulsating point sources were theoretically established, and the analytic expression of the free-surface Green’s function for ω2>N2 in uniformly density-stratified fluids was derived based on the Fourier transformation and contour integration technique, where N is the buoyancy (or Brunt-V-is-l) frequency. Compared with the previous Green’s function of internal waves, this paper laid emphasis on the consideration of the free surface. A complete description of the properties of solution and the free-surface fluctuation characteristics were discussed in detail. In fact, the pulsating sources do not produce the real internal waves when ω2>N2. The analytical solution corresponds to the influence of density uniformly stratified upon the commonly used Green’s function, which is extremely intuitive on the radiation term.

Key words: uniformly density-stratified fluids, freesurface Green’s function, Fourier transformation, contour integration, pulsating point source

CLC Number:

U 661.3

GAO Yang1,ZHU Renchuan1,MIAO Guoping1,YAO Zhicong2. Free-Surface Green’s Function of Internal Waves in Uniformly Stratified Fluid[J]. Journal of Shanghai Jiaotong University, 2014, 48(12): 1788-1794.

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