Transitions in doublediffusive convection
Abstract
Results are presented for explicit calculations of flow transitions that occur in twodimensional doublediffusive convection in the case where the motion is governed by a set of coupled nonlinear partial differential equations. Attention is restricted to an oceanographic application of the RayleighBenard problem, where the fluid is considered to occupy the space between two infinite planes separated by some distance, with the upper plane maintained at a certain temperature and salinity and the lower plane maintained at a higher temperature and salinity. Criteria for linear instability of the governing equations are obtained by neglecting nonlinear Jacobian terms and representing the solutions in terms of the lowest normal modes with an exponential time dependence. Effects of increasing and decreasing the nondimensional parameter R are examined. It is shown that in the most general case, as R increases, there is a transition from the conduction state to an oscillatory motion, followed in turn by a transition to a more complicated oscillatory motion, a transition to an aperiodic random state, and a transition to steady motion.
 Publication:

Nature
 Pub Date:
 September 1976
 DOI:
 10.1038/263020a0
 Bibcode:
 1976Natur.263...20H
 Keywords:

 Convective Flow;
 Flow Equations;
 Molecular Diffusion;
 Numerical Stability;
 Transition Flow;
 Turbulent Diffusion;
 Benard Cells;
 Branching (Mathematics);
 Differential Equations;
 Dimensionless Numbers;
 Time Dependence;
 Fluid Mechanics and Heat Transfer