Jul 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt.........1u&link_type=abstract
Thesis (PhD). COLUMBIA UNIVERSITY, Source DAI-B 60/01, p. 222, Jul 1999, 207 pages.
Physics
1
Heat Transport, Nonadiabatic, Stability
Scientific paper
This thesis explores issues of nonadiabatic acoustic stability of a polytropic atmosphere in which there is negligible viscosity and where thermal conduction of constant coefficient is the only form of nonadiabatic heat transport. Using both numerical and asymptotic methods, it is shown that there are qualitatively two new overstability mechanisms of the atmosphere. The first of these involves heat conduction induced by deformations of the basic state temperature profile while the second of these is suggested to be the atmospheric analogue of the classical thermoacoustic engine. The overstability is strongest in the lowest eigenmode of the system, but it also occurs for higher overtones, although preferring the even ones. In some parameter regimes, acoustic overstability is observed for atmospheres which are subadiabatic. Consequently, the validity of the β- mechanism at explaining the overstability of acoustic motions in a density and thermally stratified atmosphere is called into question. From the criterion for acoustic marginality in the limit of large conductivity as a starting point, weakly nonlinear overtone coupled amplitude equations are derived for acoustic modes in a polytrope between perfectly insulating boundaries. The evolution of only the fundamental modes is investigated. The resulting amplitude equations are numerically evolved in one spatial dimension. Traveling and steady pulse solutions are obtained. A brief look is taken at the problem of Boussinesq convection in a fluid of low-Prandtl number with perfectly insulating boundaries. The noncommutativity of various manners in which the low-Prandtl number limit is achieved is mentioned and one approach that avoids ambiguities is proposed and implemented. It is found that the governing equations describing the amplitude evolution for roll states (one horizontal dimension) differ from that obtained from previous studies on order one Prandtl number fluids.
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