The propagation of tides near the critical latitude

The propagation of tides in the vicinity of the critical latitude, defined here as the latitude where the tidal frequency ω equals the Coriolis parameter f, is investigated using a barotropic, depth-averaged, divergent and frictionless analytical model using the standard β-plane approximation f = ω + βy. Standard techniques of ray theory are used to deduce the energy propagation path, which temporarily crosses the critical latitude in a parabolic path when — β/k<0, where k is the eastward component of wavenumber. An expression for eccentricity and sense of rotation of the velocity vector in the horizontal current ellipse shows a complicated dependence on the wavenumber k and on the dimensionless parameter γ = gHβ 2/(2ω)4, where H is the ocean depth and g is the gravitational acceleration.