Boundary layer theory for turbulent Rayleigh-Benard convection: Approximation of a self-organized turbulent wind

We have derived a system of the boundary layer equations for turbulent Rayleigh-Benard convection (RBC), where we consider a quasi-two-dimensional fluid flow along a semi-infinite horizontal heated plate with the requirement that the horizontal velocity vanishes far away from the plate. This boundary condition, which reflects the fact that the time-averaged horizontal component of the wind in RBC achieves its maximum value at a certain distance from the plate but vanishes in the core part of the cell, is different from what is considered in the Prandtl-Blasius or Falkner-Skan approximations. In this talk, we focus on the development of the velocity boundary layer equation. The turbulent fluctuations in the equation are taken into account by an eddy viscosity, which, based on Prandtl's mixing length ideas, is related to the dimensionless stream function.