Aspects of the Baroclinic Boundary Layer

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  • 1 Department of Meteorology, The Pennsylvania State University, University Park Pennsylvania
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Abstract

The Ekman-Taylor boundary layer model is solved for the case of a linear variation of the geosptophic wind with height. The two-layer model couples a Monin–Obukhov similarity layer to an Ekman layer with a vertically constant eddy diffusivity. The presence of the thermal wind contributes both an along-isotherm and a cross-isotherm component to the boundary layer flow. The along-isotherm flow is supergeostrophic and results from the net downward transport of geostrophic momentum by the eddies. The cross-isotherm flow is toward the warm air and results from the Coriolis deflection of the geostrophic momentum-rich air aloft that has been mixed downward. The effect of the baroclinity (i.e., the thermal wind shear) on the wind field is conveniently summarized geometrically.

The model predicts that the surface vorticity increases in regions of cyclonic thermal vorticity (i.e., the vorticity of the thermal wind). However, anticyclonic thermal vorticity produces convergence of the low-level warmward flow and rising motion. Thus, a warm core cyclone experiences increased boundary layer convergence.

The effects of horizontal gradients in the turbulent momentum mixing on the surface vorticity, convergence, and rising motion are ascertained. For example, there is convergence of the Ekman mass transport and an upward contribution to the boundary layer pumping for mixing gradients directed downstream or to the right of the surface geostrophic wind and directed upstream or to the left of the surface thermal wind. The mixing gradients appear most sensitive to variations in the surface stability (i.e., the air - surface temperature difference).

A case study estimates the influence of these processes on the surface vorticity in a frontal zone. The surface vorticity is shown to be displaced behind (i.e., coldward of) its geostrophic location, in agreement with observations.

An appendix provides justification for the generalized Prandtl boundary layer approximation that, to lowest order, the pressure and thermal fields (and their vertical variations) in the boundary layer are those associated with the large-scale interior flow.

Abstract

The Ekman-Taylor boundary layer model is solved for the case of a linear variation of the geosptophic wind with height. The two-layer model couples a Monin–Obukhov similarity layer to an Ekman layer with a vertically constant eddy diffusivity. The presence of the thermal wind contributes both an along-isotherm and a cross-isotherm component to the boundary layer flow. The along-isotherm flow is supergeostrophic and results from the net downward transport of geostrophic momentum by the eddies. The cross-isotherm flow is toward the warm air and results from the Coriolis deflection of the geostrophic momentum-rich air aloft that has been mixed downward. The effect of the baroclinity (i.e., the thermal wind shear) on the wind field is conveniently summarized geometrically.

The model predicts that the surface vorticity increases in regions of cyclonic thermal vorticity (i.e., the vorticity of the thermal wind). However, anticyclonic thermal vorticity produces convergence of the low-level warmward flow and rising motion. Thus, a warm core cyclone experiences increased boundary layer convergence.

The effects of horizontal gradients in the turbulent momentum mixing on the surface vorticity, convergence, and rising motion are ascertained. For example, there is convergence of the Ekman mass transport and an upward contribution to the boundary layer pumping for mixing gradients directed downstream or to the right of the surface geostrophic wind and directed upstream or to the left of the surface thermal wind. The mixing gradients appear most sensitive to variations in the surface stability (i.e., the air - surface temperature difference).

A case study estimates the influence of these processes on the surface vorticity in a frontal zone. The surface vorticity is shown to be displaced behind (i.e., coldward of) its geostrophic location, in agreement with observations.

An appendix provides justification for the generalized Prandtl boundary layer approximation that, to lowest order, the pressure and thermal fields (and their vertical variations) in the boundary layer are those associated with the large-scale interior flow.

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