Onset of turbulent convection in large cells

✍ Scribed by Eric Siggia

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 65 KB
• Volume: 118
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(83)90201-7

✦ Synopsis

Convection experiments in small aspect ratio (=lateral size/depth) cells have shown many of the sharp changes in temporal properties that are characteristic of low order dissipative dynamical systems'). In large cells; there are generally no sharp transitions between regimes with different temporal signatures and broad band noise develops relatively smoothly from low frequencies. One infers that the multiplicity of spatial patterns allowed in the larger cells is responsible for this difference (see for instance the review of J. Gollub; these proceedings p. 329).

Because of the complexity of doing realistic calculations with the Boussinesq equations a number of effects which act together in a real experiment have been isolated for theoretical study. Refs. 2 and 3 examine under varying assumptions what stationary patterns will emerge if one waits sufficiently long and one is close to onset. There is an obvious analogy between dislocations, as understood by metallurgists, and an extra roll pair that terminates in the middle of an otherwise ideal convection pattern. Ref. 4 examines the dynamics of these hydrodynamic "dislocations".

In a third class of problems one seeks to determine the effective long wavelength dynamics of a locally ordered convection pattern following much the same reasoning that takes one from microscopic physics to hydrodynamics. The first equations of this kind that get beyond the Ginzburg-Landau from (which obviously cannot describe persistent time dependent flow) were described in ref. 5.