A three-dimensional, primitive equation model is applied to the ocean mesoscale eddies and unstable baroclinic waves across a density front in a channel under a very low viscosity environment. Current meanders are well produced. The unstable baroclinic waves are examined for flat, positive (same sense as isopycnal tilt) and negative sloping bottoms. The growth rates with Rat, gentle, medium, and steep slopes and with different wavelengths (wavenumbers) are discussed. A positive slope clearly suppresses the meandering wave growth rate whose maximum slightly shifts to a lower wavenumber compared to the flat bottom. A gentle negative slope, however, favors the wave growth with the maximum shifting toward higher wavenumber. When the negative slope becomes steeper, the growth rate significantly decreases correspondingly. Furthermore, a diagnostic analysis package for the pressure tendency and vertical velocity equations, analogous to the approaches in meteorology (omega equation and Q-vector method), is developed for the first time to reveal the physical processes and mechanisms of the unstable wave propagation in the midlatitude ocean. The weaknesses and strengths of these two diagnostic approaches are evaluated and compared to the model results. The Q-vector method is superior to the quasigeostrophic omega equation for diagnosing the vertical motion associated with the mesoscale dynamics from a hydrographic CTD array because the former has no phase error.
