Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

The behavior of a viscous incompressible fluid on a rotating sphere is described by the nonlinear barotropic vorticity equation (BVE). Conditions for the existence of a bounded set that attracts all BVE solutions are given. In addition, sufficient conditions are obtained for a BVE solution to be a global attractor. It is shown that, in contrast to the stationary forcing, the dimension of the global BVE attractor under quasiperiodic forcing is not limited from above by the generalized Grashof number.

Spectral Analyses of the Polygonal Eye of Typhoon Sinlaku

The geometry and behavior of the polygonal eye of Typhoon Sinlaku (T0216) are presented both objectively and quantitatively based on the ground-based radar data by using two types of spectral analyses (i.e., Fourier analysis and time–space cross-spectral analysis). The analyses reveal that the azimuthal wavenumber-2 perturbation is dominant even when the apparent shape of the eye seems pentagonal. Then the wavenumber-5 perturbation dominates second in most of the analytical period although it becomes most dominant during the typhoon’s passage over Okinawa Island, Japan. The counterclockwise phase shift is seen not only in these perturbations but also in, at least, the wavenumber-4, -5, and -6 perturbations. Except for the wavenumber-2 perturbation, the angular velocities are around 130° h−1 and almost coincide with each other. The radial wind profile estimated from the surface observational data suggests the existence of a ring-shaped high-vorticity region enclosing the core of the typhoon. This implies that the formation of the pentagonal eye can be attributed to wave breaking caused by barotropic instability of the circular flow constituting this typhoon. Such a possibility is also discussed by performing the linear stability analysis based on the nondivergent barotropic vorticity equation.