Lake Aggregate Mesoscale Disturbances. Part I: Linear Analysis

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  • 1 The Pennsylvania State University, University Park, Pennsylvania
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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 that exists over and on both sides of the heating. A flow characterized approximately by 1 ≤ Fr2 < 1 + Er2 + Ex and Pr ≥ 1 yields a purely exponentially damped response that exists only over and downstream of the heating, while a flow characterized approximately by Fr2 > 1 + Er2 + Ex2 and Pr ≥ 1 yields a mixed oscillating-exponentially damped response that exists only over and downstream of the heating. When Pr < 1 and Fr > 1, either of the previous two response types can occur, while when 0 < Fr < 1, a fourth type of response can occur that is mixed oscillating-exponentially damped and exists over and on both sides of the heating.

The model is used to demonstrate the effects that rotation, stability, mean flow speed, and mechanical and thermal dissipation have on the PBL responses that occur over the Great Lakes during wintertime cold air outbreaks. The simulation of heating by the lakes of strong flow within a moderately cold, shallow PBL produces a model response with ascent and implied clouds and precipitation extending well downstream of the lakes, as are typically observed soon after such a response develops. The simulation of heating by the lakes of weak flow within a very cold, deep PBL produces a model response with ascent and implied clouds and precipitation that are collocated with the lakes, as are typically observed just before such a response decays.

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 that exists over and on both sides of the heating. A flow characterized approximately by 1 ≤ Fr2 < 1 + Er2 + Ex and Pr ≥ 1 yields a purely exponentially damped response that exists only over and downstream of the heating, while a flow characterized approximately by Fr2 > 1 + Er2 + Ex2 and Pr ≥ 1 yields a mixed oscillating-exponentially damped response that exists only over and downstream of the heating. When Pr < 1 and Fr > 1, either of the previous two response types can occur, while when 0 < Fr < 1, a fourth type of response can occur that is mixed oscillating-exponentially damped and exists over and on both sides of the heating.

The model is used to demonstrate the effects that rotation, stability, mean flow speed, and mechanical and thermal dissipation have on the PBL responses that occur over the Great Lakes during wintertime cold air outbreaks. The simulation of heating by the lakes of strong flow within a moderately cold, shallow PBL produces a model response with ascent and implied clouds and precipitation extending well downstream of the lakes, as are typically observed soon after such a response develops. The simulation of heating by the lakes of weak flow within a very cold, deep PBL produces a model response with ascent and implied clouds and precipitation that are collocated with the lakes, as are typically observed just before such a response decays.

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