By Wang Shu-yuan

A contemporary progressive Peking Opera.

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A) Absorbing boundary condition. (b) Reflecting boundary condition Fig. 2 Solutions of time fractional diffusion equation 18 with absorbing boundary conditions at left and right boundaries. Initial condition is taken as delta function at x D 0. Cusp shape is the distinct feature of the curve in the case D 0:5. (a) Standard diffusion D 1:0. (b) Anomalous diffusion D 0:5 Example 2 Consider the TFDE (18) on a box 1 Ä x Ä 1 and t > 0 with absorbing boundaries at x D 1 and 1. Initial data is given by delta function at x D 0.

Weather Rev. 139, 3829–3847 (2011) 21. : Tropical cyclone spin up revisited. Q. J. R. Meteorol. Soc. 135, 1321–1335 (2009) 22. : The evolution of the critical layer of a Rossby wave. Geophys. Astro. Fluid Dyn. 9, 185–200 (1978) 23. : On the development of a Rossby wave critical level. J. Atmos. Sci. 33, 2021–2024 (1976) 24. : The evolution of a nonlinear critical level. Stud. Appl. Math. 59, 37–71 (1978) 25. : Concentric eyewalls, secondary wind maxima, and the evolution of the hurricane vortex.

2. r involves a pseudo-spectral approximation and is based on that described in [4]. J. Campbell 3 Results The results presented here are for the quadratic profile shown in Fig. 2. The waves are forced at r D r1 D 2 with a frequency of ! D 1 and a wavenumber of k D 2 or k D 1. The nonlinear parameter is set to " D 0:05 and the gradient of planetary vorticity is ˇ D 0 or ˇ D 0:05. In each case, the nondimensional parameters ˛ and ˝0 are chosen so that the critical radius is at r D rc D 12. Three configurations are examined here: ˇ D 0, k D 2 ( f -plane); ˇ D 0:05, k D 2 (ˇ-plane); ˇ D 0:05, k D 1 (ˇ-plane).