Stability of time-periodic temperature fields

Abstract

The energy method developed by Joseph [4], Davis [2], and Homsy [3] is applied to the time-periodic temperature fields considered by Yih and Li [11] to obtain Rayleigh numbers below which the fluid is stable. This is done to see how far the Rayleigh numbers so determined fall below the critical Rayleigh numbers, above which the flow is unstable, as determined by the linear theory [11]. It is found that, unlike the case of classical Bénard cells, the gray area, or area of ignorance, is quite large, indicating the need for some improvement of the energy method to give sharper lower bounds on the Rayleigh number.