an:04102667
Zbl 0673.76045
Daniels, P. G.
Stationary instability of the convective flow between differentially heated vertical planes
EN
J. Fluid Mech. 203, 525-540 (1989).
00154325
1989
j
76E15 80A20 76M99
asymptotic theory; stationary instability of convective flow; differentially heated vertical planes; boundary-layer type approximation; critical-layer structure
Summary: An asymptotic theory describes the stationary instability of convective flow between differentially heated vertical planes at large Prandtl numbers. The theory is concerned with the structure for \(A\gg 1\), where A is a Rayleigh number based on the horizontal temperature difference and the distance between the planes. As such it is relevant to the instability of flow in a vertical slot of aspect ratio \(h\gg 1\) where the convective regime corresponds to order-one values of a non-dimensional parameter \(\gamma\) which partly depends on the vertical temperature gradient generated in the slot and can be approximated by \(\gamma^ 4=A/8h\). Instability is shown to set in at a critical value of \(\gamma\) that compares well with experimental observation. The lower branch of the neutral curve conforms to a boundary-layer type approximation while the upper branch has a critical-layer structure midway between the planes which becomes fully developed as the first reversal of the vertical velocity of the base flow is encountered near the centreline.