Finite-amplitude, neutral baroclinic eddies and mean flows in an internally heated, rotating fluid: 2. Effects of spatially varying N

The analytical model of finite-amplitude, quasi-geostrophic ‘free mode’ baroclinic eddies and mean zonal flows in a Cartesian channel, presented recently by Read, is extended to take account of vertical variations in the buoyancy frequency N. A series of exact solutions is presented to illustrate the effect of monotonically varying static stability on the structure and properties of the flow. The analytical solutions are then compared with a corresponding series of numerical simulations of steady wave flows in a rotating fluid annulus subject to internal heating and sidewall cooling. By suitable choices of internal heating distributions and boundary conditions, several different forms of N² profile could be obtained in the simulated flows, in which N² was concentrated to a greater or lesser extent towards the upper boundary. The resulting steady flows exhibited strong qualitative similarities in their structure and dependence upon the form of N²(z) to that of the analytical solutions when realistic profiles of N² were included in the latter, especially when an equivalent-barotropic component was included, although the latter component is unable to satisfy the simplest (internal jet) form of horizontal boundary condition as usually applied to Rossby waves.The relatively weak, though crucially important, forcing and dissipation processes in the annulus are examined using approximate quasi-geostrophic diagnostics of the major terms in the budget of potential enstrophy for the numerical simulations. Internal heating is found to be the major source of potential enstrophy for the mean zonal flow, solely by virtue of the variation of N² with height, but has only a minor direct effect upon the eddy flow component. Because of the presence of critical layers in the flow, all non-linear terms (including the third-order potential enstrophy flux divergence) are found to be significant in certain regions. Some implications for the value and applicability of EP flux diagnostics are discussed. Potential enstrophy budgets for horizontal regions enclosed by geostrophic streamlines are used to shed further insight into the maintenance of the flow against ‘friction’, and on the form of the potential vorticity-streamfunction relationship. Some implications of the results for other systems of geophysical interest are also discussed.