Boundary layer associated with the Darcy–Brinkman–Boussinesq model for convection in porous media

We study the asymptotic behavior of the infinite Darcy–Prandtl number Darcy–Brinkman–Boussinesq system for convection in porous media at a small Brinkman–Darcy number. The existence of a boundary layer with thickness proportional to the square root of the Brinkman–Darcy number for the velocity field is established in both the L ∞ ( H 1 ) norm (in 2 and 3 d) and the L ∞ ( L ∞ ) norm (in 2d). This improves in several respects an earlier result of Payne and Straughan (1998) [60] where the vanishing Brinkman–Darcy number limit is studied without resolving the boundary layer.