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Lifting by Convergence Lines

N. Andrew CrookNational Center for Atmospheric Research, Boulder, Colorado

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Joseph B. KlempNational Center for Atmospheric Research, Boulder, Colorado

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Abstract

The lifting depth of a convergence line in an unstratified boundary layer beneath a stably stratified atmosphere is examined with both analytical and numerical models. Cases are considered with and without flow in the layer above the convergence line. Three different stability profiles above the boundary layer are also considered: an inversion, continuous stratification, and a combination of the two.

For the case in which there is no flow above the convergence line, analytical solutions are obtained for the lifting depth for the three different stability profiles. Simulations of the flow with a nonlinear, nonhydrostatic model show good agreement with these analytical predictions.

The presence of flow in the upper layer increases the complexity of the problem due to the presence of gravity waves in the steady-state solution. For an atmosphere with just an inversion, the analytical model predicts that, for hydrostatic flow, the depth of lifting is independent of the upper-level flow; while for nonhydrostatic conditions the lifting first increases as the upper-level flow increases, but then reaches a maximum and subsequently decreases. For an atmosphere with continuous stratification in the upper layer, the depth of lifting decreases with increasing upper-level flow for both hydrostatic and nonhydrostatic conditions. For the case of both an inversion and continuous stratification, a condition is found when the damping effect of the continuous stratification approximately balances the amplifying nonhydrostatic effects. The numerical simulations show reasonable agreement for an atmosphere containing only an inversion; however, for the case of continuous stratification, shearing instabilities develop along the interface at the top of the boundary layer that make it difficult to compare with the analytical predictions. These instabilities are reduced by the presence of an inversion at the top of the convergence line, and in the combined case of continuous stratification and an inversion, there is again reasonable agreement with the analytical predictions.

Corresponding author address: Dr. N. Andrew Crook, NCAR/MMM, P.O. Box 3000, Boulder, CO 80307-3000.

Email: crook@ucar.edu

Abstract

The lifting depth of a convergence line in an unstratified boundary layer beneath a stably stratified atmosphere is examined with both analytical and numerical models. Cases are considered with and without flow in the layer above the convergence line. Three different stability profiles above the boundary layer are also considered: an inversion, continuous stratification, and a combination of the two.

For the case in which there is no flow above the convergence line, analytical solutions are obtained for the lifting depth for the three different stability profiles. Simulations of the flow with a nonlinear, nonhydrostatic model show good agreement with these analytical predictions.

The presence of flow in the upper layer increases the complexity of the problem due to the presence of gravity waves in the steady-state solution. For an atmosphere with just an inversion, the analytical model predicts that, for hydrostatic flow, the depth of lifting is independent of the upper-level flow; while for nonhydrostatic conditions the lifting first increases as the upper-level flow increases, but then reaches a maximum and subsequently decreases. For an atmosphere with continuous stratification in the upper layer, the depth of lifting decreases with increasing upper-level flow for both hydrostatic and nonhydrostatic conditions. For the case of both an inversion and continuous stratification, a condition is found when the damping effect of the continuous stratification approximately balances the amplifying nonhydrostatic effects. The numerical simulations show reasonable agreement for an atmosphere containing only an inversion; however, for the case of continuous stratification, shearing instabilities develop along the interface at the top of the boundary layer that make it difficult to compare with the analytical predictions. These instabilities are reduced by the presence of an inversion at the top of the convergence line, and in the combined case of continuous stratification and an inversion, there is again reasonable agreement with the analytical predictions.

Corresponding author address: Dr. N. Andrew Crook, NCAR/MMM, P.O. Box 3000, Boulder, CO 80307-3000.

Email: crook@ucar.edu

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