Universal scaling and transient behavior of temporal modes near a Hopf bifurcation: Theory and experiment

Journal Article · Sun Nov 01 00:00:00 EST 1987 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.36.4390· OSTI ID:5511931

Deissler, R J; Ecke, R E; Haucke, H

A forward Hopf bifurcation is characterized by the continuous development of a periodic oscillatory state from a time-independent state as some control parameter is varied. In Rayleigh-Benard convection the control parameter is the Rayleigh number and the transition is from a stationary convective roll structure to periodic time-dependent convection. We show analytically that close to the bifurcation point the amplitudes of the temporal modes of the oscillatory state scale as (R-R/sub 0/)/sup n/2/, where n is the mode number. Complex-amplitude equations are also derived which give the transient behavior of these modes. Experimental data on Rayleigh-Benard convection in a dilute solution of /sup 3/He in superfluid /sup 4/He agree well with the theory.

• Research Organization: Center for Nonlinear Studies, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 5511931
• Journal Information: Phys. Rev. A; (United States), Vol. 36:9
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
FLUIDS
RAYLEIGH-TAYLOR INSTABILITY
TEMPERATURE NOISE
TRANSIENTS
HELIUM II
CONVECTION
BINARY MIXTURES
HELIUM 3
HYDRODYNAMICS
OSCILLATIONS
PARAMETRIC ANALYSIS
SCALING LAWS
SOLUTIONS
DISPERSIONS
ENERGY TRANSFER
EVEN-EVEN NUCLEI
EVEN-ODD NUCLEI
FLUID MECHANICS
HEAT TRANSFER
HELIUM 4
HELIUM ISOTOPES
INSTABILITY
ISOTOPES
LIGHT NUCLEI
MASS TRANSFER
MECHANICS
MIXTURES
NOISE
NUCLEI
QUANTUM FLUIDS
STABLE ISOTOPES
640450* - Fluid Physics- Superfluidity