Stability of Jets in a Divergent Barotropic Fluid

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  • 1 The University of Chicago
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Abstract

The stability of a two-layer incompressible fluid system on a rotating earth is investigated. The upper layer has infinite depth and is inert; the lower layer has finite depth and a basic west to east zonal velocity of form sech2y. The linearized potential vorticity equation is used for the stability investigation. It is found that both the beta effect due to the curvature of the earth and the divergence tend to stabilize the jet if the winds are from west to cast everywhere. However, if there are easterly winds away from the center of the jet, the divergence may not be stabilizing.

This stability theory is applied to a jet at 45 deg latitude in the atmosphere. The maximum wind is 60 m sec1 and the half-width of the jet is 1000 km. For the case of no divergence the most unstable wavelength is 5500 km and this disturbance has an e-fold amplification in 1.8 days. If we include divergence, the most unstable wavelength is again 5500 km but the e-fold amplification time is 14 days.

The theory can also be applied to the Gulf Stream. For a current with a maximum velocity of 1.5 m sec−1, a half-width of 31 km and a depth of 550 m, the most unstable wavelength is 180 km and the e-fold amplification time is 4 days.

Abstract

The stability of a two-layer incompressible fluid system on a rotating earth is investigated. The upper layer has infinite depth and is inert; the lower layer has finite depth and a basic west to east zonal velocity of form sech2y. The linearized potential vorticity equation is used for the stability investigation. It is found that both the beta effect due to the curvature of the earth and the divergence tend to stabilize the jet if the winds are from west to cast everywhere. However, if there are easterly winds away from the center of the jet, the divergence may not be stabilizing.

This stability theory is applied to a jet at 45 deg latitude in the atmosphere. The maximum wind is 60 m sec1 and the half-width of the jet is 1000 km. For the case of no divergence the most unstable wavelength is 5500 km and this disturbance has an e-fold amplification in 1.8 days. If we include divergence, the most unstable wavelength is again 5500 km but the e-fold amplification time is 14 days.

The theory can also be applied to the Gulf Stream. For a current with a maximum velocity of 1.5 m sec−1, a half-width of 31 km and a depth of 550 m, the most unstable wavelength is 180 km and the e-fold amplification time is 4 days.

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