The Modulation of Convection by a Lateral Shear

J. E. Hart Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

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Abstract

Several aspects of thermal convection in the presence of a lateral shear associated with either a shear line [with velocity V(x)] or a circular vortex [with azimuthal velocity V(r)] are considered. Parameter settings that favor suppression of convection near the axis of the shear flow or near the center of a cyclonic vortex are determined by looking at the structure of the linear neutral modes at the onset of convection, or at the modes that have the largest growth rates at highly supercritical Rayleigh numbers where the motions are nearly inviscid. Both parallel [or axisymmetric (2D longitudinal)] and wavy [or nonaxisymmetric (3D)] disturbances are considered, although the analysis focuses on the former. A weakly nonlinear amplitude equation shows that the bifurcation is supercritical, but even in the presence of vertical asymmetry in the applied thermal mean gradient, there is not a significant preference for upwelling or downwelling at the axis. Within the context of the linear model of convection in lateral shear, it is suggested that strong atmospheric vortices may suppress thermal convection in their cores, a mechanism possibly associated with vortex “eyes.” A simple laboratory demonstration of the main result is included.

Corresponding author address: Dr. John Hart, PAOS, Campus Box 311, University of Colorado, Boulder, CO 80309.

Email: hart@tack.colorado.edu

Abstract

Several aspects of thermal convection in the presence of a lateral shear associated with either a shear line [with velocity V(x)] or a circular vortex [with azimuthal velocity V(r)] are considered. Parameter settings that favor suppression of convection near the axis of the shear flow or near the center of a cyclonic vortex are determined by looking at the structure of the linear neutral modes at the onset of convection, or at the modes that have the largest growth rates at highly supercritical Rayleigh numbers where the motions are nearly inviscid. Both parallel [or axisymmetric (2D longitudinal)] and wavy [or nonaxisymmetric (3D)] disturbances are considered, although the analysis focuses on the former. A weakly nonlinear amplitude equation shows that the bifurcation is supercritical, but even in the presence of vertical asymmetry in the applied thermal mean gradient, there is not a significant preference for upwelling or downwelling at the axis. Within the context of the linear model of convection in lateral shear, it is suggested that strong atmospheric vortices may suppress thermal convection in their cores, a mechanism possibly associated with vortex “eyes.” A simple laboratory demonstration of the main result is included.

Corresponding author address: Dr. John Hart, PAOS, Campus Box 311, University of Colorado, Boulder, CO 80309.

Email: hart@tack.colorado.edu

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