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Convectively driven shear and decreased heat flux

  • David Goluskin (a1), Hans Johnston (a2), Glenn R. Flierl (a3) and Edward A. Spiegel (a4) (a5)


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.


Corresponding author

Present address: Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA. Email address for correspondence:


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Type Description Title

Goluskin et al. supplementary movie
Supplement to figure 2(a): Temperature in non-shearing convection with Ra=2•105 and Pr=10. The hottest fluid (red) is one dimensionless degree warmer than the coldest fluid (blue). The dimensionless time span is 0.04.

 Video (2.1 MB)
2.1 MB

Goluskin et al. supplementary movie
Supplement to figure 2(b): Temperature in sustained shearing convection with Ra=2•106 and Pr=10. The hottest fluid (red) is one dimensionless degree warmer than the coldest fluid (blue). The dimensionless time span is 6•10-3.

 Video (3.1 MB)
3.1 MB

Goluskin et al. supplementary movie
Supplement to figure 2(c): Temperature in sustained shearing convection with Ra=2•107 and Pr=10. The hottest fluid (red) is one dimensionless degree warmer than the coldest fluid (blue). The dimensionless time span is 1.2•10-3.

 Video (3.1 MB)
3.1 MB

Goluskin et al. supplementary movie
Supplement to figure 2(d): Temperature in sustained shearing convection with Ra=2•108 and Pr=10. The hottest fluid (red) is one dimensionless degree warmer than the coldest fluid (blue). The dimensionless time span is 2.4•10-4.

 Video (3.5 MB)
3.5 MB

Goluskin et al. supplementary movie
Supplement to figure 8: Temperature in bursting shearing convection with Ra=2•108 and Pr=1. The hottest fluid (red) is one dimensionless degree warmer than the coldest fluid (blue). The time span matches that of the time series shown in the figure.

 Video (10.0 MB)
10.0 MB

Convectively driven shear and decreased heat flux

  • David Goluskin (a1), Hans Johnston (a2), Glenn R. Flierl (a3) and Edward A. Spiegel (a4) (a5)


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