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Dynamic pressure drag on rising buoyant thermals in a neutrally stable environment

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  • 1 aNational Center for Atmospheric Research, Boulder, CO USA
  • | 2 bGeophysical Fluid Dynamics Laboratory, Princeton, NJ, USA
  • | 3 cCNRM, UMR3589 (CNRS), Météo-France, 31057 Toulouse Cedex, France
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Abstract

This study examines dynamic pressure drag on rising dry buoyant thermals. A theoretical expression for drag coefficient Cd as a function of several other non-dimensional parameters governing thermal dynamics is derived based on combining the thermal momentum budget with the similarity theory of Scorer (1957). Using values for these non-dimensional parameters from previous studies, the theory suggests drag on thermals is small relative to that on solid spheres in laminar or turbulent flow. Two sets of numerical simulations of thermals in an unstratified, neutrally stable environment using a LES configuration of the Cloud Model 1 (CM1) are analyzed. One set has a relatively low effective Reynolds number Re and the other has an order of magnitude higher Re; these produce laminar and turbulent resolved-scale flows, respectively. Consistent with the theoretical Cd, the magnitude of drag is small in all simulations. However, whereas the laminar thermals have Cd ≈ 0.01, the turbulent thermals have weakly negative drag (Cd ≈ −0.1). This difference is explained by the laminar thermals having near vertical symmetry but the turbulent thermals exhibiting considerable vertical asymmetry of their azimuthally-averaged flows. In the laminar thermals, buoyancy rapidly becomes concentrated around the main centers of rotation located along the horizontal central axis, leading to expansion of thermals via baroclinic vorticity generation but doing little to break vertical symmetry of the flow. Vertical asymmetry of the azimuthally-averaged flow of turbulent thermals is attributed mainly to small-scale resolved eddies that are concentrated in the upper part of the thermals.

Corresponding author: Hugh Morrison, morrison@ucar.edu

Abstract

This study examines dynamic pressure drag on rising dry buoyant thermals. A theoretical expression for drag coefficient Cd as a function of several other non-dimensional parameters governing thermal dynamics is derived based on combining the thermal momentum budget with the similarity theory of Scorer (1957). Using values for these non-dimensional parameters from previous studies, the theory suggests drag on thermals is small relative to that on solid spheres in laminar or turbulent flow. Two sets of numerical simulations of thermals in an unstratified, neutrally stable environment using a LES configuration of the Cloud Model 1 (CM1) are analyzed. One set has a relatively low effective Reynolds number Re and the other has an order of magnitude higher Re; these produce laminar and turbulent resolved-scale flows, respectively. Consistent with the theoretical Cd, the magnitude of drag is small in all simulations. However, whereas the laminar thermals have Cd ≈ 0.01, the turbulent thermals have weakly negative drag (Cd ≈ −0.1). This difference is explained by the laminar thermals having near vertical symmetry but the turbulent thermals exhibiting considerable vertical asymmetry of their azimuthally-averaged flows. In the laminar thermals, buoyancy rapidly becomes concentrated around the main centers of rotation located along the horizontal central axis, leading to expansion of thermals via baroclinic vorticity generation but doing little to break vertical symmetry of the flow. Vertical asymmetry of the azimuthally-averaged flow of turbulent thermals is attributed mainly to small-scale resolved eddies that are concentrated in the upper part of the thermals.

Corresponding author: Hugh Morrison, morrison@ucar.edu
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