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Linear and Nonlinear Propagation of Supercell Storms

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  • 1 NOAA/National Severe Storms Laboratory, Norman, Oklahoma
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Abstract

A nonlinear formula for updraft motion in supercell storms is derived from Petterssen's formula for the motion of systems and the vertical equation of motion, and tested on form-preserving disturbances. At each level, continuous propagation of an updraft maximum is determined largely by the horizontal gradient of the nonhydrostatic vertical pressure-gradient force (NHVPGF) at the updraft center. The NHVPGF is deduced from the formal solution of the Poisson equation for nonhydrostatic pressure in anelastic flow subject to homogeneous Neumann boundary conditions at the ground and top boundary. Recourse also is made to published fields of partitioned vertical pressure-gradient force. Updraft motion is partitioned into parts forced by horizontal gradients of hydrostatic pressure, linear interaction between the environmental shear and updraft, and nonlinear dynamical effects.

The dynamics of supercell storms for nearly straight and highly curved hodographs are found to be different. Nonlinear rotationally induced propagation is important during storm splitting in fairly unidirectional shear where the vortex pair, formed at midlevels by lifting of environmental vortex tubes, straddles the initial updraft. After the initial storm splits into severe right-moving (SR) and left-moving (SL) supercells, anomalous motion is maintained by the distribution of the NHVPGF. For the SR storm, the NHVPGF is upward below the cyclonic vortex on the right side of the updraft and downward on the left side. The anticyclonic vortex on the left side of this storm migrates to the downdraft and so does not affect updraft propagation. For a storm in shear that turns markedly clockwise with height, the cyclonic vortex is nearly coincident with the updraft, while the anticyclonic vortex is located in the downdraft so that the horizontal gradient of nonlinear NHVPGF at the updraft center associated with rotationally induced propagation is relatively small. Linear shear-induced propagation now becomes the dominant mechanism. At each level, propagation off the hodograph to the concave side increases with updraft width. Once the propagation has been deduced, tilting of storm-relative environmental streamwise vorticity explains the origins of overall updraft rotation in all cases.

Corresponding author address: Dr. Robert Davies-Jones, National Severe Storms Laboratory, NOAA, 1313 Halley Circle, Norman, OK 73069-8493. Email: bobdj@nssl.noaa.gov

Abstract

A nonlinear formula for updraft motion in supercell storms is derived from Petterssen's formula for the motion of systems and the vertical equation of motion, and tested on form-preserving disturbances. At each level, continuous propagation of an updraft maximum is determined largely by the horizontal gradient of the nonhydrostatic vertical pressure-gradient force (NHVPGF) at the updraft center. The NHVPGF is deduced from the formal solution of the Poisson equation for nonhydrostatic pressure in anelastic flow subject to homogeneous Neumann boundary conditions at the ground and top boundary. Recourse also is made to published fields of partitioned vertical pressure-gradient force. Updraft motion is partitioned into parts forced by horizontal gradients of hydrostatic pressure, linear interaction between the environmental shear and updraft, and nonlinear dynamical effects.

The dynamics of supercell storms for nearly straight and highly curved hodographs are found to be different. Nonlinear rotationally induced propagation is important during storm splitting in fairly unidirectional shear where the vortex pair, formed at midlevels by lifting of environmental vortex tubes, straddles the initial updraft. After the initial storm splits into severe right-moving (SR) and left-moving (SL) supercells, anomalous motion is maintained by the distribution of the NHVPGF. For the SR storm, the NHVPGF is upward below the cyclonic vortex on the right side of the updraft and downward on the left side. The anticyclonic vortex on the left side of this storm migrates to the downdraft and so does not affect updraft propagation. For a storm in shear that turns markedly clockwise with height, the cyclonic vortex is nearly coincident with the updraft, while the anticyclonic vortex is located in the downdraft so that the horizontal gradient of nonlinear NHVPGF at the updraft center associated with rotationally induced propagation is relatively small. Linear shear-induced propagation now becomes the dominant mechanism. At each level, propagation off the hodograph to the concave side increases with updraft width. Once the propagation has been deduced, tilting of storm-relative environmental streamwise vorticity explains the origins of overall updraft rotation in all cases.

Corresponding author address: Dr. Robert Davies-Jones, National Severe Storms Laboratory, NOAA, 1313 Halley Circle, Norman, OK 73069-8493. Email: bobdj@nssl.noaa.gov

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