Journal of Fluid Mechanics

Effect of modulation on the onset of thermal convection

Giulio  Venezian a1p1
a1 California Institute of Technology, Pasadena, California 91109

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The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

(Published Online March 28 2006)
(Received February 21 1968)

p1 Present address: University of Hawaii, Honolulu, Hawaii 96822.