A Model for Investigating Eddy Viscosity Effects on Mesoscale Cellular Convection

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Abstract
A mathematical model consisting of a complete set of the Boussinesq equations governing Rayleigh convection in the atmosphere has been solved for the marginal stability case in order to study the geometry and circulation patterns of mesoscale cellular convection. The significant new feature of the model is the inclusion of eddy viscosity variation with height through the convecting layer. Results obtained show that the direction of convection circulations are controlled by the sign of the vertical gradient of eddy viscosity. It is also concluded that variable convective depth has a significant but small effect on the geometry of the convection, with the degree of cell flatness being principally controlled by the degree of anisotropy. Using an assumed periodic form of the perturbation solutions, the problem reduced to solving a sixth-order differential stability equation with variable coefficients and accompanying boundary conditions. By applying the two-variable, small-perturbation technique, the... Abstract A mathematical model consisting of a complete set of the Boussinesq equations governing Rayleigh convection in the atmosphere has been solved for the marginal stability case in order to study the geometry and circulation patterns of mesoscale cellular convection. The significant new feature of the model is the inclusion of eddy viscosity variation with height through the convecting layer. Results obtained show that the direction of convection circulations are controlled by the sign of the vertical gradient of eddy viscosity. It is also concluded that variable convective depth has a significant but small effect on the geometry of the convection, with the degree of cell flatness being principally controlled by the degree of anisotropy. Using an assumed periodic form of the perturbation solutions, the problem reduced to solving a sixth-order differential stability equation with variable coefficients and accompanying boundary conditions. By applying the two-variable, small-perturbation technique, the...

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