Several effects of a baroclinic current on the cross?stream propagation of inertial?internal waves†

Abstract

Several effects of a baroclinic current on inertial‐internal waves at constant frequency are investigated, primarily through use of the method of characteristics. The special case of waves propagating transverse to a baroclinic current is considered. When the slope of an isopycnal is of the same order of magnitude as the slope of the characteristics, appreciable asymmetries are induced in the characteristics, the phase and group velocities, and the solution itself. These asymmetric effects are especially significant for waves at the low frequency end of the passband for free waves. Also, modifications occur to the passband, resulting in anomalously high and low frequency bands. The effective local inertial frequency, σ_f = [f(f+v_x )]^1/2, separates the normal and anomalously low frequency bands. Hence, the low frequency limit of the normal frequency band increases or decreases depending upon whether the horizontal shear in the mean flow is cyclonic or anticyclonic. In the anomalous frequency bands, the slopes of both characteristics have the same sign, causing various refraction and reflection phenomena. If the absolute value of the slope, s, of an isopycnal exceeds its critical value, s_c = effective local inertial frequency/Väisälä‐Brunt frequency, the anomalously low frequency band extends to imaginary frequencies. If s ? 0, the reflection of waves from a boundary is modified, the effective wavelength is increased, and the lines of constant phase are tilted from the vertical. For the general solution, discontinuities in the first‐order partial derivatives of the velocity field occur across certain characteristics. The nonseparable normal modes do not exhibit these discontinuous derivatives, but they only satisfy one of the two pairs of kinematic boundary conditions in rectangular regions.