Da. Nield, CONVECTION INDUCED BY AN INCLINED TEMPERATURE-GRADIENT IN A SHALLOW HORIZONTAL LAYER, International journal of heat and fluid flow, 15(2), 1994, pp. 157-162
A reexamination is made of convection, induced by an applied temperatu
re gradient inclined to the vertical, in a shallow horizontal layer, T
he horizontal component of this gradient induces a Hadley circulation,
which becomes unstable when the vertical component is sufficiently la
rge. A linear stability analysis is carried out, for the case of rigid
conducting horizontal boundaries, in terms of horizontal and vertical
Rayleigh numbers, R(H) and R(V), respectively. This analysis is valid
for any Prandtl number, Pr, and incorporates the case, R(V) = 0. The
differential equation system is solved using a direct Galerkin approxi
mation. This is convenient for numerical calculations in the parameter
range of interest and also enables some general results to be obtaine
d analytically. The results confirm and extend those of previous inves
tigators.