\begin{abstract}
A novel parallel technique for Fourier-Galerkin pseudo-spectral
methods with applications to two-dimensional Navier-Stokes
equations and inviscid Boussinesq approximation equations is
presented. It takes advantage of the programming structure of
the phase-shift de-aliased scheme for pseudo-spectral codes, and
combines the task-distribution strategy [Z. Yin, H.J.H. Clercx, and
D.C. Montgomery, An easily implemented task-based parallel scheme for
the Fourier pseudospectral solver applied to 2D Navier-Stokes turbulence,
Comput. Fluids, Vol.33, 509 (2004).] and parallelized Fast Fourier
Transform scheme. The performances of the resulting MPI Fortran90 codes 
with the new procedure on SGI 3800 are reported. For fixed resolution of
the same problem, the peak speed of the new scheme can be twice as fast
as the old parallel methods. The parallelized codes are used to solve some
challenging numerical problems governed by the Navier-Stokes
equations and Boussinesq equations. Some interesting physical
phenomena (the double-valued $\omega - \psi $ structure in
two-dimensional decaying turbulence and the collapse of the
bubble cap in the Boussinesq simulation), are solved by using the 
proposed parallel algorithms.
\end{abstract}