On Thermally Forced Circulations over Heated Terrain

Abstract

Abstract A combination of analytical and numerical models is used to gain insight into the dynamics of thermally forced circulations over diurnally heated terrain. Solutions are obtained for two-layer flows (representing the boundary layer and the overlying free troposphere) over an isolated mountainlike heat source. A scaling based on the linearized Boussinesq system of equations is developed to quantify the strength of thermally forced updrafts and to identify three flow regimes, each with distinct dynamics and parameter sensitivities. This scaling closely matches corresponding numerical simulations in two of these regimes: the first characterized by a weakly stable boundary layer and significant background winds and the second by a strongly stable boundary layer. In the third regime, characterized by weak winds and weak boundary layer stability, this scaling is outperformed by a fundamentally different scaling based on thermodynamic heat engines. Within this regime, the inability of wind ventilation or static stability to diminish the buoyancy over the heat source leads to intense updrafts that are controlled by nonlinear dynamics. These nonlinearities create a positive feedback loop between the thermal forcing and vorticity that rapidly strengthens the circulation and contracts its central updraft into a narrow core. As the circulation intensifies under daytime heating, the warmest surface-based air is ventilated into the upper boundary layer, where it spreads laterally to occupy a broader area and, ultimately, restrain the circulation strength. The success demonstrated herein of simple theoretical models at predicting key aspects of thermally forced circulations offers hope for improved parameterization of related processes (e.g., convection initiation and aerosol venting) in large-scale models.