The equation that is central to this study and which will be discretized spectrally describes the horizontal advection
In the accompanying paper (Part I; W. T. M. Verkley, 1997, J.
Comput. Phys. 100-114 136) a spectral numerical scheme is devel-of the absolute vorticity q by a nondivergent velocity field oped for two-dimensional incompressible fluid flow in a circular v ฯญ k ฯซ ู, where k is a vertically pointing unit vector basin. The model is formulated in terms of basis functions that are and is a streamfunction. The streamfunction is assumed products of Jacobi polynomials and complex exponentials. The to be zero at the circular boundary, implying no-normal Jacobi polynomials are used for the radial dependence of the fields flow at the boundary. The equation reads:
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 calcu-
lated 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 where the absolute vorticity q is given by ฯฉ f, with the showing examples of time integrations. The differences between relative vorticity being k ะธ ู ฯซ v ฯญ ู 2 and f being the these examples concern the spatial structure of the planetary vorticplanetary vorticity. The operators ู 2 and J are the Laplace ity (อฒ-plane, อฑ-plane, f-plane), the temporal and spatial resolution and Jacobi operators, respectively, the expressions of of the model, and the form, strength, and type of the forcing and which are given in Subsection 2.2 of Part I. The system is dissipation. แฎ 1997 Academic Press forced by a source of vorticity ฯช and damped by Ekman friction ฯช. Here is the spatial structure of the forcing (taken to be constant in space and time) and and