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An Assessment of the Balance Approximation in Hurricanes

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
  • | 2 Hurricane Research Division, NOAA/AOML, Miami, Florida
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Abstract

The validity of the traditional balance approximation for the asymmetric flow above the boundary layer generally in hurricanes is examined here. Scaling considerations of the divergence equation show that the validity of the balance approximation hinges on the smallness of the nondimensional product (δn/ζn)×(nυ/ηr). The first term represents the ratio of asymmetric horizontal divergence to asymmetric vertical vorticity for azimuthal wavenumber n, while the second term represents a Rossby number based upon the azimuthal mean tangential wind and absolute vertical vorticity of the hurricane vortex. Wind observations of Hurricane Gloria (1985) indicate that this product is not at all small in the near-vortex region (several hundred kilometers beyond the radius of maximum tangential winds) where asymmetric convergence forced by surface friction and cumulus convection is typically large. Although the Gloria observations represent only a single case, there are dynamical reasons to expect this product to be O(1) just above the hurricane boundary layer in steadily translating hurricanes. The meteorological relevance of these results to the problem of balance dynamics in hurricanes is briefly discussed.

Corresponding author address: Dr. Michael T. Montgomery, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523.

Email: mtm@charney.atmos.colostate.edu

Abstract

The validity of the traditional balance approximation for the asymmetric flow above the boundary layer generally in hurricanes is examined here. Scaling considerations of the divergence equation show that the validity of the balance approximation hinges on the smallness of the nondimensional product (δn/ζn)×(nυ/ηr). The first term represents the ratio of asymmetric horizontal divergence to asymmetric vertical vorticity for azimuthal wavenumber n, while the second term represents a Rossby number based upon the azimuthal mean tangential wind and absolute vertical vorticity of the hurricane vortex. Wind observations of Hurricane Gloria (1985) indicate that this product is not at all small in the near-vortex region (several hundred kilometers beyond the radius of maximum tangential winds) where asymmetric convergence forced by surface friction and cumulus convection is typically large. Although the Gloria observations represent only a single case, there are dynamical reasons to expect this product to be O(1) just above the hurricane boundary layer in steadily translating hurricanes. The meteorological relevance of these results to the problem of balance dynamics in hurricanes is briefly discussed.

Corresponding author address: Dr. Michael T. Montgomery, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523.

Email: mtm@charney.atmos.colostate.edu

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