Genesis of the Northeast Brazil Upper-Tropospheric Cyclonic Vortex: A Primitive Equation Barotropic Instability Study

Abstract

The primitive equation barotropic unstable linear normal modes are computed using an eigenvalue approach for daily latitudinal profiles of zonal flow in the upper-tropospheric layer of 100?350 hPa before and after formation of cyclonic vortices during January 1993 and November 2001 off the coast of northeast Brazil. The wave kinetic energy equation for u- and ?-motion is presented. Equations are derived to isolate the contribution of divergence and other dynamical processes in the movement and growth of unstable modes. Numerical accuracy and physical nature of unstable modes are tested. In a short span of 2?3 days, prior to formation of vortices, a progressive and a sharp intensification of the basic flow shear zone and its barotropic instability are seen with time. The horizontal structure, momentum transport, and zonal and meridional scales of the most unstable normalized wave are obtained and compared with the vortex extracted from the 200-hPa observed winds using a bandpass smoother. A close agreement is found between them. It is shown that the zonal and meridional scales of the preferred wave are related to the length scale of the shear zone. The wave is confined to the shear zone and its maximum amplitude is located at the latitude of maximum ? ? uyy. The role of divergence in the movement and growth of the wave is investigated. The energetics of the unstable wave u- and ?-motion is computed, and it is inferred that the energy source for the growth of wave u- (?-) motion is the energy conversion (work done by pressure force), which lies in the shear zone. It is emphasized that a deeper insight regarding the genesis of the cyclonic vortex can be gained on the basis of stability analysis of daily observed zonal flow profiles, which may not be possible using idealized or mean profiles. An explanation for nonmanifestation of the instability in the monthly mean flow is provided.