Scattering of Internal Tides by Irregular Bathymetry of Large Extent

Abstract:

We present an analytic theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on the linearized approximation, the idealized case of constant mean sea depth and Brunt-Vaisala
frequency is considered. The depth fluctuation is assumed to be a stationary random function of space characterized by small amplitude and correlation length comparable to the typical wavelength. For both one- and two-dimensional topography the effects of scattering on wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Buhler-& Holmes-Cerfon(2011) computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

In thi talk we shall apply the perturbation technique of multiple scales to treat analytically the random scattering of internal tides by gently sloped bathymetric irregularities.
The basic assumptions are: incompressible fluid, infinitestimal wave amplitudes, constant Brunt-Vaisala frequency, and constant mean depth. In addition, the depth disorder is assumed to be a stationary random function of space with zero mean and small root-mean-square amplitude. The correlation length can be comparable in order of magnitude as the dominant wavelength. Both one- and two-dimensional disorder will be considered. Physical effects of random scattering on the mean wave phase i.e., spatial attenuation and wavenumber shift will be calculated and discussed for one mode of incident wave. For two dimensional topographies, statistically isotropic and anisotropic examples will be presented.