We address the problem of parity mixing using fast algorithms where the projection of a variable expressed as a finite series of half-period cosine (sine) functions onto a half-period sine (cosine) function basis is in finite. We propose a method for computing these complicated projections exactly up to some arbitrary degree using fast Fourier transforms. This method has immediate applications for pseudospectral solutions of many systems of partial differential equations. Using the pseudospectral techniques we introduce a numerical code designed to efficiently simulate incompressible convection in a confined rotating domain. In our numerical tests we find that a correct accounting for parity leads to clear behavior that has been observed in laboratory experiments.

with Nicholas Brummell (Applied Mathematics, Santa Cruz) and Keith Julien (APPM)

Retrograde precession of a rotating convecting flow (1.2MB,.mov)

(Above) A time sequence showing the precession of temperature perturbations in the horizontal midplane, z = 1=2. Relatively warm regions are shown with red tones and relative cool regions are show with blue tones. The sense of rotation is in a counterclockwise direction, and the precession is in a clockwise (retrograde) sense. The relative time is given in units of rotation period, where T_omega= 4 pi/f =0.036 in the thermal time units.

Volume renderingn of precessing flow

(Above) A volume rendering (see [16]) showing temperature perturbations, theta(x, y, z), for a typical time snapshot. Relatively warm regions are shown with red tones and relative cool regions are shown with blue tones. The yellow lines trace a number of instantaneous flow stream lines. The warm regions generally correspond to rising flow, and the cool regions generally correspond to downward flow. The rotation axis is aligned with the z-direction and is in a right-handed orientation.