Momentum and heat transport scalings in laminar vertical convection.
We derive the dependence of the Reynolds number Re and the Nusselt number Nu on the Rayleigh number Ra and the Prandtl number Pr in laminar vertical convection (VC), where a fluid is confined between two differently heated isothermal vertical walls. The boundary layer equations in laminar VC yield two limiting scaling regimes: Nu∼Pr^{1/4}Ra^{1/4}, Re∼Pr^{-1/2}Ra^{1/2} for Pr≪1 and Nu∼Pr^{0}Ra^{1/4}, Re∼Pr^{-1}Ra^{1/2} for Pr≫1. These theoretical results are in excellent agreement with direct numerical simulations for Ra from 10^{5} to 10^{10} and Pr from 10^{-2} to 30. The transition between the regimes takes place for Pr around 10^{-1}.
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
Olga
O
Shishkina