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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 Moninâ€“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 Moninâ€“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.

The common statement that the surface pressure in a hydrostatic atmosphere is equal to the weight per unit area of the air aloft is shown to be true only for a Cartesian world. Here the unit area is the surface area of the base of the atmospheric column. For either a cylindrical or a spherical planet the surface pressure is always less than the weight per unit area of the overlying atmosphere. In these curved geometries, lateral pressure forces help support an individual column, thereby reducing the load carried by the surface pressure at the column's base. It is estimated that the surface pressure is a factor of 0.25% less than the weight per unit area of a resting atmosphere similar to that on Earth.

The common statement that the surface pressure in a hydrostatic atmosphere is equal to the weight per unit area of the air aloft is shown to be true only for a Cartesian world. Here the unit area is the surface area of the base of the atmospheric column. For either a cylindrical or a spherical planet the surface pressure is always less than the weight per unit area of the overlying atmosphere. In these curved geometries, lateral pressure forces help support an individual column, thereby reducing the load carried by the surface pressure at the column's base. It is estimated that the surface pressure is a factor of 0.25% less than the weight per unit area of a resting atmosphere similar to that on Earth.

## Abstract

This study explores the diurnal variation in the movement and structure of the dryline using a one-dimensional shallow-water model. The model is adapted to test some common theories of dryline motion including the diurnal variation in surface friction, static stability, inversion erosion, and momentum mixing aloft.

These mechanisms of diurnal variation are first studied individually and then in unison. A diurnal variation in the surface friction produces a model dryline that moves westward during the day (in disagreement with observations) and has a southerly wind maximum near midnight. A diurnal variation in the static stability produces a model dryline that steepens in slope and moves eastward during the day and then surges westward at night with a southerly wind maximum 6 to 9 h after the minimum stability. Inversion erosion during the day produces a nearly vertical model dry front that moves eastward during the day with surface southwesterlies. At sunset the model dryline surges westward with a southerly wind maximum before midnight. A diurnal variation of the momentum mixing aloft has no significant effect on the model dryline. Results show that the combined case with a diurnal variation of surface friction, inversion erosion, and static stability with terrain most accurately describes the observed dryline system. The westward surge depicted in the model is compared to the flow evolution of the corresponding dam-break problem for a rotating fluid.

## Abstract

This study explores the diurnal variation in the movement and structure of the dryline using a one-dimensional shallow-water model. The model is adapted to test some common theories of dryline motion including the diurnal variation in surface friction, static stability, inversion erosion, and momentum mixing aloft.

These mechanisms of diurnal variation are first studied individually and then in unison. A diurnal variation in the surface friction produces a model dryline that moves westward during the day (in disagreement with observations) and has a southerly wind maximum near midnight. A diurnal variation in the static stability produces a model dryline that steepens in slope and moves eastward during the day and then surges westward at night with a southerly wind maximum 6 to 9 h after the minimum stability. Inversion erosion during the day produces a nearly vertical model dry front that moves eastward during the day with surface southwesterlies. At sunset the model dryline surges westward with a southerly wind maximum before midnight. A diurnal variation of the momentum mixing aloft has no significant effect on the model dryline. Results show that the combined case with a diurnal variation of surface friction, inversion erosion, and static stability with terrain most accurately describes the observed dryline system. The westward surge depicted in the model is compared to the flow evolution of the corresponding dam-break problem for a rotating fluid.

## Abstract

Numerical anelastic models solve a diagnostic elliptic equation for the pressure field using derivative boundary conditions. The pressure is therefore determined to within a function proportional to the base-state density field with arbitrary amplitude. This ambiguity is removed by requiring that the total mass be conserved in the model. This approach enables one to determine the correct temperature field that is required for the microphysical calculations. This correct, mass-conserving anelastic model predicts a temperature field that is an accurate approximation to that of a compressible atmosphere that has undergone a hydrostatic adjustment in response to a horizontally homogeneous heating or moistening. The procedure is demonstrated analytically and numerically for a one-dimensional, idealized heat source and moisture sink associated with moist convection. Two-dimensional anelastic simulations compare the effect of the new formulation on the evolution of the flow fields in a simulation of the ascent of a warm bubble in a conditionally unstable model atmosphere.

In the Boussinesq case, the temperature field is determined uniquely from the heat equation despite the fact that the pressure field can only be determined to within an arbitrary constant. Boussinesq air parcels conserve their volume, not their mass.

## Abstract

Numerical anelastic models solve a diagnostic elliptic equation for the pressure field using derivative boundary conditions. The pressure is therefore determined to within a function proportional to the base-state density field with arbitrary amplitude. This ambiguity is removed by requiring that the total mass be conserved in the model. This approach enables one to determine the correct temperature field that is required for the microphysical calculations. This correct, mass-conserving anelastic model predicts a temperature field that is an accurate approximation to that of a compressible atmosphere that has undergone a hydrostatic adjustment in response to a horizontally homogeneous heating or moistening. The procedure is demonstrated analytically and numerically for a one-dimensional, idealized heat source and moisture sink associated with moist convection. Two-dimensional anelastic simulations compare the effect of the new formulation on the evolution of the flow fields in a simulation of the ascent of a warm bubble in a conditionally unstable model atmosphere.

In the Boussinesq case, the temperature field is determined uniquely from the heat equation despite the fact that the pressure field can only be determined to within an arbitrary constant. Boussinesq air parcels conserve their volume, not their mass.