On Cellular Cloud Patterns. Part 3: Applicability of the Mathematical and Laboratory Models

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Abstract
A nonlinear mathematical model of an unstably stratified layer of fluid with an imposed uniform vertical mass flux γ through porous boundaries has shown that, for Rayleigh number R near its critical value Rc for | γ | ≤ 1, and for Prandtl number Pr > 1.1, open cells are the only stable flow if γ < 0; closed cells are the only stable flow if γ > 0; and roll convection is the only stable flow if γ = 0. Laboratory experiments have verified these results and have shown that their range of validity can be extended to | γ | ≈ 2, and R several times Rc. Here these results are applied to the region of sinking air behind cold fronts of mid-latitude cyclones over the oceans. The quasi-geostrophic omega equation is used to compute vertical velocities. An equivalent potential temperature gradient is determined from upper air soundings. Good agreement is found between regions of large-scale descending motion and occurrence of open cells, and between regions of large-scale ascending motion and occurrence of cl... Abstract A nonlinear mathematical model of an unstably stratified layer of fluid with an imposed uniform vertical mass flux γ through porous boundaries has shown that, for Rayleigh number R near its critical value Rc for | γ | ≤ 1, and for Prandtl number Pr > 1.1, open cells are the only stable flow if γ < 0; closed cells are the only stable flow if γ > 0; and roll convection is the only stable flow if γ = 0. Laboratory experiments have verified these results and have shown that their range of validity can be extended to | γ | ≈ 2, and R several times Rc. Here these results are applied to the region of sinking air behind cold fronts of mid-latitude cyclones over the oceans. The quasi-geostrophic omega equation is used to compute vertical velocities. An equivalent potential temperature gradient is determined from upper air soundings. Good agreement is found between regions of large-scale descending motion and occurrence of open cells, and between regions of large-scale ascending motion and occurrence of cl...

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