Symmetric flow of a modified Hadley cell model with a free surface

Abstract

Numerical studies are conducted of symmetric flows in an infinite horizontal fluid layer with a constant horizontal temperature gradient. A modified rotating Hadley-cell flow configuration is devised by adopting the free-slip and thermally insulated upper boundary. For this model, an analytic solution is available as the basic slate. A finite volume numerical procedure is utilized to integrate the fully nonlinear Navier-Stokes equations over broad parameter ranges of the thermal Rossby number, Ro, and the Richardson number, Ri. The Ro-Ri diagram illustrates several flow regimes. In the present framework, both the symmetric instability and Benard-type convective instability are found to occur. These are associated respectively with a negative potential vorticity in the interior and a gravitationally unstable vertical temperature gradient in the thermal boundary layer. The detailed flow structures are computed to reveal the characteristic features of these two instabilities. Time dependent responses are analyzed to examine the dominant mechanism for two-dimensional flow developments. The interaction of the symmetric flows with the basic-state flow field is scrutinized.