Numerical calculations have been performed to investigate the natural convection in a horizontal fluid layer with spatially periodic boundary temperatures. Using spectral method, which is of Fourier-Galerkin type in the x direction and of Chebyshev-tau type in the y direction, the flow patterns and the temperature field of air(Pr=0.7) for a wide range of Rayleigh numbers have been obtained.
The induced flow becomes stronger as Ra increases. The symmetric mode of flow breaks into a new mode at a moderately high Ra when there is a phase shift of p between upper and lower surface temperatures, which the symmetry is maintained up to Ra=10,000 if there is no phase shift. As wave number increases the flow tends to remain unchanged regardless of the temperature distribution.
The results are generally in good agreement with those obtained earlier by the the finite difference method. However, symmetric mode occurs at a higher Ra in the present calculation. This is expected as a spectral method is more accurate and thus generates less numerical disturbances.
