Some further studies on the transition to turbulent convection

Abstract

In a horizontal convecting layer of fluid, several distinct transitions occur at certain distinct Rayleigh numbers R, for a given Prandtl number Pr. The regime diagram has been extended to include the Prandtl-number range2·5 × 10−2 [les ] Pr [les ] 0·85 × 104.In particular it is found that distinct changes in the slope of the heat-flux curve occur even for Pr = 2·5 × 10−2. The flow is steady up to R = Rt = 2·4 × 103. For R > Rt, the period of oscillation is compared with the theoretical values of Busse. For Pr = 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.For R just greater than Rc, the preferred orientation of rolls in various side-wall geometries is investigated. For high Prandtl number, the effect of curvature of the roll axis, forced by curved side walls, upon the second transition at RII is investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering of RII. These results, along with the observed hysteresis, support the view that there are metastable states attainable by finite amplitude instability. Finally the nature of the time-dependent flow at large R and high Prandtl number is investigated in a Hele-Shaw cell. It is shown unequivocally that the observed periodicity at a fixed point is due to hot or cold plumes moving past the point.

Simulations of the rayleigh benard Convection type acoustic streaming Motion in acompressible gas filled Two dimensional rectangular Enclosure

“…Moreover, as the Rayleigh number is increased further, two-frequency quasi-periodic flow is generated from the single-frequency oscillatory state and the flow finally transits to a chaotic state in the fully developed turbulent regime. Early experimental results for the transition to turbulence in Rayleigh-Bénard convection were presented by Krishnamurti [14].…”

Oxygen transfer across the air‐water interface by natural convection in lakes

“…The various forms of convection observed in a horizontal fluid layer are a function of both the Rayleigh and Prandtl numbers (Krishnamurti 1970). Below the critical value of Ra c ϭ 27 4 /4 there is no motion; however, for water (Pr ϭ 7) the flow changes from a steady two-dimensional flow (''rolls'') to a time-dependent three-dimensional flow, and ultimately to a fully turbulent flow at Ra Ͼ 14,000 Pr 0.6 , or 5 ϫ 10 4 for water (Rossby 1969).…”

Back Matter

“…If the liquid element has characteristic size L, then the buoyancy force F), acting on this element may be estimated from Archimedes' principle as Ft, ~ pg0(AT) 'L 3 , where g is acceleration due to gravity, /3 is the temperature coefficient of volume expansion, p is a characteristic {e.g. mean) fluid density, and (AT)' is the The spatio-temporal patterns and the transition to turbulence are, in general, strongly dependent on the value of Pr; see the flow regime di agram of (Krishnamurti, 1973) plex spatio-temporal dynamics as (Ra -Ra c ) increases. For liquids with Pr ~ 1 the deformation of rolls (roll curvature) induces slowly varying, long-range pressure gradients (Siggia and Zippelius, 1981) that generate a mean flow, which in turn alters the roll curvature; see Chapter 9 and also (Croquette et al, 1986;Pocheau and Daviaud, 1997).…”