The stability of an asymmetric zonal current in the atmosphere

This paper considers the barotropic stability of an asymmetric zonal current on a rotating earth. The current is of hyperbolic tangent form in latitude. For this stability problem the neutral wave solutions are found and estimates of the growth rates for the unstable waves are obtained from the neutral solutions as in earlier investigations by the writer. It is again found that the beta effect which is due to the earth's curvature and rotation tends to stabilize the basic flow. The stability of the basic flow is examined for a special case. For this case the current is centered at 35 degrees latitude, has a total shear of 30 m sec −1 and a half-width of 550 km. The most unstable waves are found to be wave-numbers 6 and 7 which amplify by a factor of e in 2·9 days. In addition, wave-numbers 5, 8 and 9 are also unstable. The stability of the symmetric jet is also examined for a comparable case. It is found that a wider band of wave-numbers is unstable. The most unstable wave is wave-number 8 which amplifies by a factor of e in 2·7 days. In conclusion it is noted that these growth rates are slower than the amplification rates for the unstable waves associated with the baroclinic stability problem.