Laboratory exploration of heat transfer regimes in rapidly rotating turbulent convection

Abstract

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The geostrophic regime of rapidly rotating turbulent convection

“…For large Pr 2 we observe columns above the line Ra/Ra C ≈ 2 (Figure 2(b)). It is clear from DNS [78] and experiments [40,44] that the steep Nu(Ra) scaling is for columns, with exponent β increasing as E is reduced; β = 3.6 at E = 10 −7 is the steepest scaling reported so far [40]. The demarcation between regimes 2 and 3 (as inferred from heat transfer graphs) coincides with the transition between columns and plumes, hence the proposed terminology of columnar convection for regime 3.…”

“…These four flow morphologies have also been found in DNS [78]. In many experiments these flow structures have also been identified using dye [82], shadowgraphy [59], passive tracers [5,40,44,83,84] and thermochromic liquid crystals [67,72]. They could also be identified in quantitative flow measurements using particle image velocimetry (PIV) [45,68,71,73,74,85] or 3D particle tracking velocimetry (PTV) [71].…”

“…These three regimes are recognised from heat transfer data in quite some studies, e.g. [33,36,39,[43][44][45][46][47][48][49]. A third Nu measurement strategy [32,50], varying parameters Ra and E in such a way that Ro remains constant, leads to power-law Nu(Ra) behaviours that are displaced from each other when different Ro are compared.…”

“…There is an overshoot range where rotation enhances heat transfer compared to the nonrotating value. [44]. The black solid line indicates the nonrotating Nu(Ra) scaling.…”

“…To break the E = 10 −6 'barrier' requires dedicated experiments or finely resolved, long-term DNS. The parameter space is mostly filled by three studies employing tall, slender convection cells that rotate rapidly to reduce E as far as possible [86]: H ≤ 0.6 m for [90]; H ≤ 1.6 m for [40]; H ≤ 4 m for [44]. At the same time, the trick is to still be able to reliably provide Rayleigh numbers small enough to explore the rotation-dominated range; no simple task given that Ra ∼ H 3 [86].…”