Non-traditional reflection of internal waves from a sloping bottom, and the likelihood of critical reflection

Abstract

The problem of internal inertio-gravity wave reflection from an arbitrarily orientated uniform slope is solved in a linear setting and with Coriolis effects fully included; that is, the horizontal component (f̃) of the Earth rotation vector is taken into account. A new criterion is derived for critical reflection. The presence of f̃ creates a specific anisotropy: the criterion depends on the orientation of the bottom slope in the horizontal geographical plane, while it does not depend on the horizontal orientation of the incident wave. Using an empirical-based bottom-slope distribution, the probability of critical reflection is calculated for diurnal and semi-diurnal internal-tide bands, for a range of latitudes and for various values of stratification. The probability is largest near the inertial latitudes, i.e., when the internal tides are near-inertial. It is explained how the inclusion of f̃ gives significant changes in the probability near these latitudes, especially for weak stratification. Copyright 2006 by the American Geophysical Union.