Andrew Jackson ,  University of Leeds

  
Spectral methods have been the mainstay of numerical
solution of partial differential equations for many
years. On the sphere the spactral basis of choice
has been the spherical harmonics. Here we present
a new representation - double Fourier series defined
on a new coordinate system. We show that the new basis is complete, in that a finite number of terms
can reresent any arbitrary spherical harmonic.
The advantage of this basis is in the speed of the transform between physical and spectral space,
needed for the computation of nonlinear terms.
The prospects for implementation in representations of fluid flow on the sphere are explored.