  The coefficients of the complex Ginzburg-Landau equations that describe
weakly nonlinear convection in a large rotating annulus are calculated for a
range of Prandtl numbers $\sigma$. For fluids with $\sigma \approx 0.15$, we
show that the rotation rate can tune the coefficients of the corresponding
amplitude equations from regimes where coherent patterns prevail to regimes of
spatio-temporal chaos.
