In:
Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 759 ( 2014-11-25), p. 360-385
Abstract:
We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh–Bénard convection between free-slip boundaries. We focus on the ability of the convection to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ( $\mathit{Pr}$ ) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ( $\mathit{Ra}$ ) sufficiently, and we explore the resulting convection for $\mathit{Ra}$ up to $10^{10}$ . When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $\mathit{Ra}\rightarrow \infty$ . The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $\mathit{Ra}$ . When the large-scale shear is present with $\mathit{Pr}\lesssim 2$ , the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $\mathit{Ra}$ for $\mathit{Pr}=1$ . When the shear is present with $\mathit{Pr}\gtrsim 3$ , the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $\mathit{Ra}$ , but the growth rates are slower than any previously reported for Rayleigh–Bénard convection without large-scale shear. We find that the Nusselt numbers grow proportionally to $\mathit{Ra}^{0.077}$ when $\mathit{Pr}=3$ and to $\mathit{Ra}^{0.19}$ when $\mathit{Pr}=10$ . Analogies with tokamak plasmas are described.
Type of Medium:
Online Resource
ISSN:
0022-1120
,
1469-7645
DOI:
10.1017/jfm.2014.577
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2014
detail.hit.zdb_id:
1472346-3
detail.hit.zdb_id:
218334-1
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