A spectral model for two-dimensional incompressible fluid flow in a circular basin .2. Numerical examples

In the accompanying paper (Part I; W. T. M. Verkley, 1997, J. Comput Phys. 100-114 136) a spectral numerical scheme is developed for two-dimensional incompressible fluid flow in a circular basin. The model is formulated in terms of basis functions that are products of Jacobi polynomials and complex exponentials. The Jacobi polynomials are used for the radial dependence of the fields and the complex exponentials for the angular dependence. The basis functions are orthogonal with respect to the natural inner product for a circular domain. The nonlinear advection term is calculated without aliasing using the transform method, based on a grid of which the radii are Gaussian and the angles are equidistant. In the present paper we discuss the performance of the model by showing examples of time integrations. The differences between these examples concern the spatial structure of the planetary vorticity (gamma-plane, beta-plane, f-plane), the temporal and spatial resolution of the model, and the form, strength, and type of the forcing and dissipation. (C) 1997 Academic Press.