Extension of Homogeneous Fluid Methods to the Calculation of Surface Disturbance Induced by an Object in a Stratified Ocean.

摘要

An extension of homogeneous fluid methods has been developed for calculation of the disturbance induced by a submerged point source in an incompressible, density-stratified fluid with a free surface. The extension comes in the treatment of the inhomogeneous wave equation, which results from linearization and Fourier transformation of the equations of motion. A closely related problem is the solution of the one-dimensional Schrodinger equation, where the negative squared Brunt-Vaisala frequency profile plays the role of the depth-dependent potential. A model potential with known bound state and continuum state eigenfunctions is substituted into the inhomogeneous wave equation, which is solved, subject to the free surface boundary condition, by an eigenfunction expansion method. Surface tension effects are also included. Contour integration techniques assist the evaluation of integrals and enable a clear separation of localized and extended wavelike disturbances. The point-source solutions may be used to calculate fluid disturbance in the near and far fields induced by a submerged body. As an example, the localized surface displacement and rate of strain induced by a surmerged Rankine ovoid are calculated for a square-well density-stratification model. The results are compared to previously calculated far-field internal wave effects induced on the surface by wake collapse behind a submerged body. (Author)