Trapped rossby waves

The possibility of tidal dynamics at strictly imaginary Lamb parameters has been known for more than three decades. The present paper explores the prevailing physics in this parameter regime. To this end, basic features of the global circulation such as baroclinicity and geostrophy have to be incorporated into tidal dynamics. The tidal equations of the thermal wind are readily obtained in the framework of spherical bishallow water theory. Density surfaces of a circulation with available potential energy alter the spatial inhomogenities of the generic tidal problem. Wave dynamics in an inhomogeneous medium are characterized not only by a dispersion relation but also by a wave guide geography: significant wave amplitudes are trapped in specific regions of frequency-dependent width. As an inherently global issue, evaluation of the Rossby wave guide geography for a given circulation cannot rely on the familiar regional filters of tidal theory. On the global domain, the Rossby wave specification is given by the Margules filter. A thermal wind is stable against nondivergent Rossby wave disturbances. Rossby waves propagating with a geostrophic wind are governed by prolate dynamics (real Lamb parameters) while imaginary Lamb parameters emerge for the oblate dynamics of Rossby waves running against a geostrophic wind. Oblate Rossby wave dynamics include pole-centered wave guides and very low-frequency disturbances propagating eastward against a westward wind.