Travelling Waves and Chaos in DoubleDiffusive Convection.
Abstract
Nonlinear dynamical systems can exhibit a wide variety of oscillations, with periodic motion often replaced by aperiodic or chaotic motion through a succession of transitions as the forcing is increased. Doublediffusive fluid systems such as thermosolutal convection afford excellent opportunities to study such nonlinear transitions by a combination of numerical experiments and theory. Thermosolutal convection is characterized by the competition between the destabilizing effect of heating a fluid layer from below and the stabilizing effect of maintaining a solute concentration which increases with depth. The driving and restoring buoyancy forces are shifted in phase because the solute diffuses less rapidly than heat. If the solute gradient is sufficiently strong, convection can set in (through a Hopf bifurcation) as oscillations even when the mean density decreases upward. Numerical simulations of twodimensional thermosolutal convection have here been carried out employing either periodic or stressfree, impermeable boundary conditions in the horizontal. A significant finding is that travelling waves, in which a pattern of rolls translates horizontally, are the preferred form into which an oscillatory instability develops; standing, modulated and chaotic waves are also found. Hysteretic and nonhysteretic transitions between the different wave states and steady convection are investigated, and are in general agreement with a recently developed bifurcation theory based on the symmetries of the system. The simulations are complemented by considering equations that model the system at small amplitudes. Travelling waves are found in the model equations similar to those observed in the full simulations, along with a variety of modulated waves, only some of which are seen in the simulations. Simulations of convection in a finite container of large aspect ratio reveal solutions that are closely related to those obtained with periodic conditions. Such nonlinear behavior provides an explanation for waves observed in recent laboratory experiments with binary fluid mixtures. An unexpected feature in the simulations is that the travelling waves reverse their direction of propagation in an episodic manner. Modulated waves with two and three frequencies are also found, but they do not change their sense of propagation.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........24D
 Keywords:

 Physics: Fluid and Plasma;
 Chaos;
 Convection;
 Traveling Waves;
 Computerized Simulation;
 Hysteresis;
 Mathematical Models;
 Nonlinear Systems;
 Fluid Mechanics and Heat Transfer