Onset of Multicellular Convection in a Shallow Laterally Heated Cavity

Shallow cavity flows, driven by horizontal thermal gradients, are analysed over a range of Rayleigh numbers R and Prandtl numbers σ. Emphasis is placed on the limit in which R is comparable in size to the cavity aspect ratio L. Departures from two-dimensional steady Hadley cells, defined by the limit L→ ∞ at fixed R and σ, are shown to be associated with nonlinear end effects. Eigenvalue calculations indicate the existence of a critical Prandtl number σc, below which the core structure is not necessarily parallel with the horizontal boundaries. For σ < σc the parallel flow core is destroyed at Rayleigh numbers R > Rc(σ). Results for the stability boundary Rc(σ) are presented.