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On the Wavelength of Maximum Baroclinic Instability

D. O. StaleyDepartment of Atmospheric Sciences, The University of Arizona, Tucson 85721

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R. L. GallDepartment of Atmospheric Sciences, The University of Arizona, Tucson 85721

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Abstract

A four-level quasigeostrophic model of a baroclinic atmosphere is used to examine the instability of short (∼2000 km) baroclinic waves. It is determined that only a slight decrease in the low-level static stability or increase in the low-level wind shear relative to the stale stability and wind shear in the middle and upper troposphere can mean the difference between the maximum growth rate occurring at a wavelength of 4000 km (∼wavenumber 7) or 2000 km (∼wavenumber 15). Similar changes of static stability in the upper troposphere relative to the middle and lower troposphere have very little effect on the growth-rate spectrum.

This effect of vertical variations in the static stability and wind shear on the growth-rate spectrum is consistent with the structure of the short wavelengths. Wavelengths <3000 km are essentially confined below 500 mb, while wavelengths >4000 km extend through the depth of the troposphere. Therefore, changes in the static stability of the basic zonal flow near the earth's surface have a more profound effect on the short wavelengths than on the longer waves.

It is noted that the spurious short-wave neutrality shifts to shorter and shorter wavelengths as the number of model levels is increased. This shift is related to lowering of the level of maximum vertical velocity with decreasing wavelength until, at a sufficiently short wavelength, the difference form of ∂ω/∂p in the lowest layer fails to describe the derivative accurately.

Abstract

A four-level quasigeostrophic model of a baroclinic atmosphere is used to examine the instability of short (∼2000 km) baroclinic waves. It is determined that only a slight decrease in the low-level static stability or increase in the low-level wind shear relative to the stale stability and wind shear in the middle and upper troposphere can mean the difference between the maximum growth rate occurring at a wavelength of 4000 km (∼wavenumber 7) or 2000 km (∼wavenumber 15). Similar changes of static stability in the upper troposphere relative to the middle and lower troposphere have very little effect on the growth-rate spectrum.

This effect of vertical variations in the static stability and wind shear on the growth-rate spectrum is consistent with the structure of the short wavelengths. Wavelengths <3000 km are essentially confined below 500 mb, while wavelengths >4000 km extend through the depth of the troposphere. Therefore, changes in the static stability of the basic zonal flow near the earth's surface have a more profound effect on the short wavelengths than on the longer waves.

It is noted that the spurious short-wave neutrality shifts to shorter and shorter wavelengths as the number of model levels is increased. This shift is related to lowering of the level of maximum vertical velocity with decreasing wavelength until, at a sufficiently short wavelength, the difference form of ∂ω/∂p in the lowest layer fails to describe the derivative accurately.

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