On boundary-layer convection in a rotating fluid layer

The asymptotic solutions of second-order accuracy taking account of the velocity boundary conditions imposed on the sidewalls are derived for wall-localized boundary-layer convection in a rotating fluid layer in the presence of stress-free or no-slip vertical sidewalls. The second-order asymptotic solutions give a satisfactory quantitative agreement with the fully numerical solutions obtained in a rotating channel with either stress-free or no-slip sidewalls. Furthermore, we show, through fully three-dimensional numerical simulations, that the structure of the boundary-layer convection is highly robust in strongly nonlinear regimes.