Entropy production and Lyapunov instability at the onset of turbulent convection

Journal Article · Tue Dec 01 04:00:00 EST 1998 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.58.7350· OSTI ID:670215

Castillo, V M; Hoover, W G ^[1]

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1. Department of Applied Science, University of California at Davis--Livermore and Lawrence Livermore National Laboratory, Livermore, California 94551-7808 (United States)

Computer simulations of a compressible fluid, convecting heat in two dimensions, suggest that, within a range of Rayleigh numbers, two distinctly different, but stable, time-dependent flow morphologies are possible. The simpler of the flows has two characteristic frequencies: the rotation frequency of the convecting rolls, and the vertical oscillation frequency of the rolls. Observables, such as the heat flux, have a simple-periodic (harmonic) time dependence. The more complex flow has at least one additional characteristic frequency{emdash}the horizontal frequency of the cold, downward- and the warm, upward-flowing plumes. Observables of this latter flow have a broadband frequency distribution. The two flow morphologies, at the same Rayleigh number, have different rates of entropy production and different Lyapunov exponents. The simpler {open_quotes}harmonic{close_quotes} flow transports more heat (produces entropy at a greater rate), whereas the more complex {open_quotes}chaotic{close_quotes} flow has a larger maximum Lyapunov exponent (corresponding to a larger rate of phase-space information loss). A linear combination of these two rates is invariant for the two flow morphologies over the entire range of Rayleigh numbers for which the flows coexist, suggesting a relation between the two rates near the onset of convective turbulence. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 670215
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 6 Vol. 58; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COMPRESSIBLE FLOW
COMPUTERIZED SIMULATION
CONVECTIVE INSTABILITIES
ENTROPY
LYAPUNOV METHOD
NATURAL CONVECTION
NAVIER-STOKES EQUATIONS
TRANSITION FLOW
TURBULENT FLOW