Methods for analysis of internal-tide propagation variability

Abstract:

The strong variability of internal tidal phase with respect to tidal phase has been recently documented. The slowness of internal tidal propagation through evolving uncertain environmental conditions offers a simple descriptive explanation for this effect. Here, a method for analyzing the propagation of internal tides through the random medium is presented. The equations of motion for internal waves are recast into vertical and horizontal equations. The vertical equation is a generalization of the internal-wave modal equation and the Taylor-Goldstein equation. This equation takes into account the effects of two-dimensionally sheared currents into the normal mode wavelength and speed. The horizontal equation is the Helmholtz equation with an azimuthally variable (anisotropic) phase speed. Ray tracing methods for this anisotropic speed scenario are presented. Tehniques for solving the equations and some example results are shown. The method differs from other internal tide propagation analysis methods that use the long wave approximation normal modes and include current effects in the horizontal equations. The figure shows, at the right, phase speed as a function of azimuth for three M2-frequency internal-wave modes for the shear flow and stratification conditions shown at the left.