Global stability of time-dependent flows. Part 2. Modulated fluid layers

Abstract

The method of energy is used to develop two stability criteria for a large class of modulated Bénard problems. Both criteria give stability limits which hold for disturbances of arbitrary amplitude. The first of these, designated as strong global stability, requires the energy of all disturbances to decay monotonically and exponentially in time. Application of this criterion results in a prediction of Rayleigh numbers below which the diffusive stagnant solution to the Bous-sinesq equations is unique. The second criterion requires only that disturbances decay asymptotically to zero over many cycles of modulation, and is a weaker concept of stability. Computational results using both criteria are given for a wide range of specific cases for which linear asymptotic stability results are available, and it is seen that the energy and linear limits often lie close to one another.