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Baroclinic–Barotropic Adjustments in a Meridionally Wide Domain

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  • 1 Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois
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Abstract

Baroclinic adjustment hypothesis fails to account for the enhancement of the barotropic jet observed in idealized baroclinic-wave life-cycle simulations. In this paper, an adjustment theory more consistent with the numerical results is developed through a careful examination of life-cycle experiments and nonseparable eigenvalue problems using the two-layer model.

In all cases examined, nonlinear eddies emanate from an unstable normal mode of meridionally concentrated gradients of the zonal-mean potential vorticity (PV). The flows are neither forced nor damped, except that moderate second-order horizontal diffusion is used to achieve an eddy-free state in a finite computational time. The final zonal-mean states are typically characterized by a well-defined barotropic jet that is not sufficiently stable in the sense of Charney and Stern but stable for all zonal wavenumbers allowed by the geometry of the channel. It is shown that vertical asymmetry in the meridional arrangement of PV leads to (a) production of barotropically sheared jet and (b) shift in the zonal scale of baroclinic instability and subsequent neutralization. It is argued that the extent of the meridional arrangement necessary to suppress the most momentum-transporting baroclinic wave determines the width of the adjusted flow. This width is roughly proportional to the initial zonal scale of the mode on the f plane but constrained by a beta-related critical mixing length on the beta plane.

Relationship to other theories (e.g., barotropic governor and geostrophic turbulence) is discussed, along with the relevance of the theory to the earth’s midlatitude troposphere.

Corresponding author address: Dr. Noboru Nakamura, Department of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Avenue, Chicago, IL 60637.

Email: nnn@bethel.uchicago.edu

Abstract

Baroclinic adjustment hypothesis fails to account for the enhancement of the barotropic jet observed in idealized baroclinic-wave life-cycle simulations. In this paper, an adjustment theory more consistent with the numerical results is developed through a careful examination of life-cycle experiments and nonseparable eigenvalue problems using the two-layer model.

In all cases examined, nonlinear eddies emanate from an unstable normal mode of meridionally concentrated gradients of the zonal-mean potential vorticity (PV). The flows are neither forced nor damped, except that moderate second-order horizontal diffusion is used to achieve an eddy-free state in a finite computational time. The final zonal-mean states are typically characterized by a well-defined barotropic jet that is not sufficiently stable in the sense of Charney and Stern but stable for all zonal wavenumbers allowed by the geometry of the channel. It is shown that vertical asymmetry in the meridional arrangement of PV leads to (a) production of barotropically sheared jet and (b) shift in the zonal scale of baroclinic instability and subsequent neutralization. It is argued that the extent of the meridional arrangement necessary to suppress the most momentum-transporting baroclinic wave determines the width of the adjusted flow. This width is roughly proportional to the initial zonal scale of the mode on the f plane but constrained by a beta-related critical mixing length on the beta plane.

Relationship to other theories (e.g., barotropic governor and geostrophic turbulence) is discussed, along with the relevance of the theory to the earth’s midlatitude troposphere.

Corresponding author address: Dr. Noboru Nakamura, Department of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Avenue, Chicago, IL 60637.

Email: nnn@bethel.uchicago.edu

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