On the applicability of Falkner-Skan boundary layer equations to turbulent thermal convection

Abstract

To approximate main flow characteristics like the velocity or temperature within the boundary layers which appear in turbulent thermal convection at moderate Rayleigh numbers (up to 10^14), one can use the Falkner–Skan boundary layer equations, which are obtained through a generalization of the Prandtl–Blasius ansatz to a non-zero-pressure-gradient case. Within this approach we derive several theoretical estimates with respect to turbulent Rayleigh–Bénard convection and validate them against numerical results obtained in our Direct Numerical Simulations for the operating fluids water and air. In particular it is found that the Falkner–Skan approximation leads to more accurate estimates of the ratio of the thermal and viscous boundary layer thicknesses, compared to the Prandtl–Blasius approach.