SUBCRITICAL TRANSITIONS TO CHAOS AND HYSTERESIS IN A FLUID LAYR HEATED FROM BELOW

摘要

The route to chaos in a fluid layer heated from below is investigated by using the weak non-linear theory as well as Adomian's decomposition method to solve a system of ordinary differential equations which result from a truncated Galerkin representation of the governing equations. This representation yields the familiar Lorenz equations. While the weak non-linear method of solution provides significant insight to the problem, to its solution and corresponding bifurcations and other transitions, it is limited because of its local domain of validity, which in the present case is in the neighbourhood of any one (but only one) of the two steady state convective solutions. This method is expected to loose accuracy and gradually breakdown as one moves away from this neighbourbhood.