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Topographic Generation of Mesoscale Vortices in Mixed-Layer Models

David P. DempseyNational Center for Atmospheric Research, Boulder, Colorado

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Richard RotunnoNational Center for Atmospheric Research, Boulder, Colorado

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Abstract

The fundamental assumptions underlying mesoscale mixed-layer models of the atmospheric boundary layer are that 1) the flow is hydrostatic, and 2) the Reynolds-averaged potential temperature and horizontal velocity are vertically well mixed. These assumptions determine completely the Reynolds-stress profile, which to a good approximation is a quadratic function of height, and has curvature proportional to the horizontal buoyancy gradient. The only significant source of the vertical component of vorticity in mesoscale mixed-layer models is the curl of the divergence of the Reynolds stress, which can generate quasi-stationary vortices downstream of three-dimensional topography in flow containing buoyancy gradients. We provide quantitative guidance about conditions sufficient for these vortices to form under the mixed-layer modeling assumptions.

We caution that observations do not appear to support strongly the assumption that velocity is vertically well mixed in baroclinic, convective boundary layers. We also caution that, while sufficient conditions exist under the mixed-layer modeling assumptions for quasi-stationary vortices to form, these conditions are not necessary. Sufficient conditions for such vortices to form also exist under other, completely independent modeling assumptions. Hence, the mechanism by which vorticity is generated in mixed-layer models has uncertain relevance to the atmosphere.

Abstract

The fundamental assumptions underlying mesoscale mixed-layer models of the atmospheric boundary layer are that 1) the flow is hydrostatic, and 2) the Reynolds-averaged potential temperature and horizontal velocity are vertically well mixed. These assumptions determine completely the Reynolds-stress profile, which to a good approximation is a quadratic function of height, and has curvature proportional to the horizontal buoyancy gradient. The only significant source of the vertical component of vorticity in mesoscale mixed-layer models is the curl of the divergence of the Reynolds stress, which can generate quasi-stationary vortices downstream of three-dimensional topography in flow containing buoyancy gradients. We provide quantitative guidance about conditions sufficient for these vortices to form under the mixed-layer modeling assumptions.

We caution that observations do not appear to support strongly the assumption that velocity is vertically well mixed in baroclinic, convective boundary layers. We also caution that, while sufficient conditions exist under the mixed-layer modeling assumptions for quasi-stationary vortices to form, these conditions are not necessary. Sufficient conditions for such vortices to form also exist under other, completely independent modeling assumptions. Hence, the mechanism by which vorticity is generated in mixed-layer models has uncertain relevance to the atmosphere.

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