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Three-Dimensional Response of a Shear Flow to Elevated Heating

Yuh-Lang LinDepartment of Physics and Atmospheric Sciences, Drexel University, Philadelphia, Pennsylvania

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Shiaolin LiDepartment of Physics and Atmospheric Sciences, Drexel University, Philadelphia, Pennsylvania

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Abstract

The three-dimensional response of a shear flow to elevated heating is investigated using linear theory. The basic wind profile is allowed to reverse directions at a certain height. Effects of shear, evaporative cooling, and the stratosphere are investigated. Morphology and spatial scales of the V-shaped features found in this study are consistent with observations and nonlinear numerical modeling results, but are explained by energy propagation associated with the thermally forced gravity wave. The response of a unidirectional shear flow to latent heating at the level of the wind reversal is an axisymmetric pattern of upward vertical motion, which is in direct response to the heating. Away from the level of the wind reversal, V-shaped patterns of upward motion are produced with vertices pointing upwind. The updraft core in the vertical plane in the direction of the storm movement is almost erect for a relatively weak shear flow. In accord with two-dimensional solutions, the critical level plays an important role in producing upward motion at this location since the vertical velocity is directly proportional to the specified heating at the critical level.

For a relatively strong shear flow, the updraft core tilts further downstream. With tilted heating, there exist a CISK-like coincidence of updraft with heating The sloping updraft upstream of the cloud base also strengthens, which may help maintain the existing convection. Based on a group velocity argument, the V-shaped features are explained as a gravity wave phenomenon. The formation of the repeating, damped oscillations of the disturbance at high levels is caused by the nonhydrostatic effect which has a downstream wavelength approximately proportional to Ri−½. In particular, the skewed “V” pattern may be explained by the effects of advection by the multidirectional shear flow. With evaporative cooling, the upward displacement in a reference frame moving with the storm near the heating center at the cloud base strengthens, which tends to help maintain the supercell convection. On the other hand, the downward displacement downstream of the heating produced by the evaporative cooling tends to suppress the growth of new convection downstream of the supercell. With realistically strong stratospheric stability included in the model, the response of the flow in the stratosphere is that the vertical velocity and displacement are weakened. This would reduce the temperature difference across the cold/warm thermal couplet that is a salient stratospheric feature.

Abstract

The three-dimensional response of a shear flow to elevated heating is investigated using linear theory. The basic wind profile is allowed to reverse directions at a certain height. Effects of shear, evaporative cooling, and the stratosphere are investigated. Morphology and spatial scales of the V-shaped features found in this study are consistent with observations and nonlinear numerical modeling results, but are explained by energy propagation associated with the thermally forced gravity wave. The response of a unidirectional shear flow to latent heating at the level of the wind reversal is an axisymmetric pattern of upward vertical motion, which is in direct response to the heating. Away from the level of the wind reversal, V-shaped patterns of upward motion are produced with vertices pointing upwind. The updraft core in the vertical plane in the direction of the storm movement is almost erect for a relatively weak shear flow. In accord with two-dimensional solutions, the critical level plays an important role in producing upward motion at this location since the vertical velocity is directly proportional to the specified heating at the critical level.

For a relatively strong shear flow, the updraft core tilts further downstream. With tilted heating, there exist a CISK-like coincidence of updraft with heating The sloping updraft upstream of the cloud base also strengthens, which may help maintain the existing convection. Based on a group velocity argument, the V-shaped features are explained as a gravity wave phenomenon. The formation of the repeating, damped oscillations of the disturbance at high levels is caused by the nonhydrostatic effect which has a downstream wavelength approximately proportional to Ri−½. In particular, the skewed “V” pattern may be explained by the effects of advection by the multidirectional shear flow. With evaporative cooling, the upward displacement in a reference frame moving with the storm near the heating center at the cloud base strengthens, which tends to help maintain the supercell convection. On the other hand, the downward displacement downstream of the heating produced by the evaporative cooling tends to suppress the growth of new convection downstream of the supercell. With realistically strong stratospheric stability included in the model, the response of the flow in the stratosphere is that the vertical velocity and displacement are weakened. This would reduce the temperature difference across the cold/warm thermal couplet that is a salient stratospheric feature.

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