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Article Type:
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Nonmodal Development of Baroclinic Waves Undergoing Horizontal Shear Deformation

A. BarcilonGeophysical Fluid Dynamics Institute and Department of Meteorology, The Florida State University, Tallahassee, Florida

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C. H. BishopDepartment of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Print Publication:
01 Dec 1998
DOI:
https://doi.org/10.1175/1520-0469(1998)055<3583:NDOBWU>2.0.CO;2
Page(s):
3583–3597
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Abstract

The evolution of waves in a basic state containing a constant vertical shear and a smaller constant horizontal shear is considered. The “PV-thinking” associated with counterpropagating Rossby potential vorticity (PV) edge waves found at the horizontal boundaries is used to interpret the evolution of the waves.

The presence of the barotropic shear introduces a time-dependent y wavenumber, which, in turn, makes the total horizontal wavenumber a function of time. For properly configured initial (x, y) wavenumbers, the horizontal wavenumber decreases at first. This decrease induces an increase in the scale of the disturbances and a growth associated with downgradient momentum fluxes. The PV edge waves grow by mutual interactions when properly phase shifted. This growth is due to a downgradient flux of heat.

These ideas are illustrated on a paradigm of type-B cyclogenesis. The nonlinear dynamics is also computed in the spirit of a weakly nonlinear analysis. This simple weakly nonlinear model captures the asymmetry between westward tilts in the vertical of geopotential minima and maxima found in the fully nonlinear evolution of baroclinic waves on cyclonically and anticyclonically sheared jets.

Corresponding author’s address: Dr. Albert Barcilon, Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, FL 32306-4360.

Email: barcilon@gfdi.fsu.edu

Abstract

The evolution of waves in a basic state containing a constant vertical shear and a smaller constant horizontal shear is considered. The “PV-thinking” associated with counterpropagating Rossby potential vorticity (PV) edge waves found at the horizontal boundaries is used to interpret the evolution of the waves.

The presence of the barotropic shear introduces a time-dependent y wavenumber, which, in turn, makes the total horizontal wavenumber a function of time. For properly configured initial (x, y) wavenumbers, the horizontal wavenumber decreases at first. This decrease induces an increase in the scale of the disturbances and a growth associated with downgradient momentum fluxes. The PV edge waves grow by mutual interactions when properly phase shifted. This growth is due to a downgradient flux of heat.

These ideas are illustrated on a paradigm of type-B cyclogenesis. The nonlinear dynamics is also computed in the spirit of a weakly nonlinear analysis. This simple weakly nonlinear model captures the asymmetry between westward tilts in the vertical of geopotential minima and maxima found in the fully nonlinear evolution of baroclinic waves on cyclonically and anticyclonically sheared jets.

Corresponding author’s address: Dr. Albert Barcilon, Geophysical Fluid Dynamics Institute, The Florida State University, Tallahassee, FL 32306-4360.

Email: barcilon@gfdi.fsu.edu

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