Some acoustic wave problems in an inhomogeneous ocean.

Abstract

Some recent studies show that the physical characteristics of the ocean may vary with its depth. Duston, Verma and Wood have used the perturbation method to study acoustic wave problem for such a case assuming the sea bed to be rigid. We consider a more interesting case of a reflecting sea bed and present the corrections to eigenvalues and eigenfunctions due to depth dependent inhomogeneous and present numerical and graphical results based upon our results. Moreover, as observed by experimental studies, the ocean may have piecewise constant physical parameters. To account for this behavior, Boyle has presented a layered model of such an ocean. Introducing homogeneities in his model, we obtain the eigenvalues and eigenfunctions of the depth equation in case of rigid as well as the reflecting sea bed. We use perturbation method to obtain corrections of eigenvalues and eigenfunctions due to the inhomogeneities in the lower layer of a two layer ocean model analytically and present numerical and graphical results based upon our results. We also obtain the WKB solution for the depth equation valid for large wave number.