On thermally forced circulations over heated terrain

Although thermally forced circulations driven by elevated surface heating are often responsible for important meteorological phenomena (e.g., convection initiation and aerosol venting), they remain poorly understood due to their physical complexity. This understanding must be improved to inform large-scale models that are unable to resolve such mesoscale circulations. Recent studies have used linear and nonlinear theory to quantitatively describe these circulations, with varying success. The present study advances the linear theory by extending it to three-dimensional, diurnally varying, two-layer flows with a mean background wind and varying boundary-layer stability. To avoid nonlinearities introduced by a complex lower boundary condition, the elevated heating is represented by a localized heat source over flat terrain, which is valid in the linear approximation. This theory is used to develop a scaling for boundary-layer vertical velocity, to separate flows into three distinct regimes based on environmental and terrain-related parameters, and to determine the bounds of quasi-linear dynamics for each regime. The theoretical analysis is complemented by high-resolution idealized numerical simulations, which accurately represent the flow dynamics within both the linear and nonlinear regimes. Comparison of boundary-layer updraft velocity between the simulations, the linear scaling, and a steady-state nonlinear scaling (derived by analogy with thermodynamic heat engines) reveals impressive scaling performance, in mutually exclusive regions of parameter space: the linear scaling is accurate only within the quasi-linear regime, while the nonlinear scaling is accurate only outside that regime. The interactions between mechanical and thermal orographic forcing are also interpreted through detailed analysis of the nonlinear numerical simulations.