Lake Aggregate Mesoscale Disturbances. Part I: Linear Analysis

Abstract

Abstract The steady boundary-layer responses that occur over the Great Lakes region during wintertime cold air outbreaks are examined using a two-dimensional, linear, analytic model. The planetary boundary layer (PBL) is modeled as an idealized, constantly stratified, viscous, rotating Boussinesq fluid that moves uniformly between two horizontally infinite, rigid, stress-free plates. The heat from the lakes is parameterized in terms of a specified diabatic forcing function. Solution of the governing differential equation yields an integral expression for the vertical motion of the general response. Further assessment of the response is gained by examining closed-form analytic solutions to several limiting cases. Four response types are identified that depend upon the values of the Froude number Fr, the mechanical Ekman number Ex, the thermal Ekman number Ex, and the eddy Prandtl number Pr. Four different flow regimes are found. When 0 ≤ Fr < 1 and Pr ≥ 1, there is a purely exponentially damped response th...