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The Impact of Effective Buoyancy and Dynamic Pressure Forcing on Vertical Velocities within Two-Dimensional Updrafts

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
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Abstract

This research develops simple diagnostic expressions for vertical acceleration dw/dt and vertical velocity w within updrafts that account for effective buoyancy and the dynamic pressure gradient force. Effective buoyancy is the statically forced component of the vertical gradient in the nonhydrostatic pressure field. The diagnostic expressions derived herein show that the effective buoyancy of an updraft is dependent on the magnitude of the temperature perturbation within an updraft relative to the air along the updraft’s immediate periphery (rather than relative to an arbitrary base state as in ), the updraft’s height-to-width aspect ratio, and the updraft’s slant relative to the vertical.

The diagnostic expressions are significantly improved over parcel theory (where pressure forces are ignored) in their portrayal of the vertical profile of w through updrafts from a cloud model simulation and accurately diagnosed the maximum vertical velocity wmax within updrafts. The largest improvements to the diagnostic expressions over parcel theory resulted from their dependence on rather than . Whereas the actual wmax within simulated updrafts was located approximately two-thirds to three-fourths of the distance between the updraft base and the updraft top, wmax within profiles diagnosed by expressions was portrayed at the updraft top when the dynamic pressure force was ignored. A rudimentary theoretical representation of the dynamic pressure force in the diagnostic expressions improved their portrayal of the simulated w profile. These results augment the conceptual understanding of convective updrafts and provide avenues for improving the representation of vertical mass flux in cumulus parameterizations.

Corresponding author address: John M. Peters, Colorado State University, Department of Atmospheric Science, 1371 Campus Delivery, Fort Collins, CO 80523-1371. E-mail: jpeters3@atmos.colostate.edu

Abstract

This research develops simple diagnostic expressions for vertical acceleration dw/dt and vertical velocity w within updrafts that account for effective buoyancy and the dynamic pressure gradient force. Effective buoyancy is the statically forced component of the vertical gradient in the nonhydrostatic pressure field. The diagnostic expressions derived herein show that the effective buoyancy of an updraft is dependent on the magnitude of the temperature perturbation within an updraft relative to the air along the updraft’s immediate periphery (rather than relative to an arbitrary base state as in ), the updraft’s height-to-width aspect ratio, and the updraft’s slant relative to the vertical.

The diagnostic expressions are significantly improved over parcel theory (where pressure forces are ignored) in their portrayal of the vertical profile of w through updrafts from a cloud model simulation and accurately diagnosed the maximum vertical velocity wmax within updrafts. The largest improvements to the diagnostic expressions over parcel theory resulted from their dependence on rather than . Whereas the actual wmax within simulated updrafts was located approximately two-thirds to three-fourths of the distance between the updraft base and the updraft top, wmax within profiles diagnosed by expressions was portrayed at the updraft top when the dynamic pressure force was ignored. A rudimentary theoretical representation of the dynamic pressure force in the diagnostic expressions improved their portrayal of the simulated w profile. These results augment the conceptual understanding of convective updrafts and provide avenues for improving the representation of vertical mass flux in cumulus parameterizations.

Corresponding author address: John M. Peters, Colorado State University, Department of Atmospheric Science, 1371 Campus Delivery, Fort Collins, CO 80523-1371. E-mail: jpeters3@atmos.colostate.edu
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