Barotropic instability in the tropical cyclone outer region

Abstract

AbstractThe growth of asymmetric perturbations and their interactions with the symmetric flow are investigated for wind profiles in a tropical cyclone with instability in its outer region. Three tangential wind profiles are examined: TC1, a strong barotropic instability profile in the outer region; TC2, a stable wind profile; and TC3, a weaker instability profile comparing to TC1 with a larger distance between the inner negative and the outer positive vorticity gradient centres.An eigenvalue analysis indicates that azimuthal wave‐number two is the most unstable mode in both TC1 and TC3, with an e‐folding time‐scale of about 1 and 9 days, respectively. Numerical simulations using a linear barotropic model, with an initial asymmetry specified in the outer region, confirm the eigenvalue analysis. A mechanism is provided to explain the difference between simulations in TC1 and TC2. In both the stable and unstable case, an inner asymmetry is induced by the initial outer asymmetry acting on the symmetric vorticity gradient. Subsequently, the newly generated inner asymmetry feeds back positively to the outer asymmetry with the unstable profile. Because of this positive feedback, the inner and the outer asymmetries maintain an up‐shear phase tilting, leading to a continuous energy transfer from the symmetric flow to the asymmetric perturbation. In the stable TC2, the inner asymmetry could not amplify the outer initial asymmetry as there is no basic‐state radial vorticity gradient there. Also due to this feedback process, disturbances grow faster where the (absolute) basic‐state vorticity gradients are large. Therefore, the position of an initial disturbance plays a minor role in determining the outcome of the system.Simulations with a nonlinear barotropic model and a primitive equation model further confirm the significant weakening of the maximum tangential wind due to the positive feedback process in TC1. Simulations for TC3 show a smaller change of the symmetric tangential wind, as expected. Copyright © 2009 Royal Meteorological Society