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Effects of rotation on convective turbulence

Published online by Cambridge University Press:  26 April 2006

Harindra J. S. Fernando ,
Rui-Rong Chen  and
Don L. Boyer
Harindra J. S. Fernando
Affiliation:
Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA
Rui-Rong Chen
Affiliation:
Mechanical Engineering, University of Wyoming, Laramie, WY 82071, USA
Don L. Boyer
Affiliation:
Mechanical Engineering, University of Wyoming, Laramie, WY 82071, USA Present address: Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA.
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Abstract

Laboratory experiments were carried out to investigate the effects of rotation on turbulent convection. The experimental facility was a bottom-heated, water-filled, cubical tank mounted on a turntable. The investigations were performed over a wide range of bottom buoyancy fluxes q0 and rotation rates Ω, including Ω = 0; q0 and Ω were held constant during each experiment. The depth of the water column H was fixed for the entire experimental programme. For the non-rotating experiments, the r.m.s. velocity fluctuations were found to scale well with the convective velocity $w_* = (q_0 H)^{\frac{1}{3}}$, while the mean and r.m.s. fluctuations of buoyancy were found to scale with q0/w*. The spectra of temperature fluctuations were measured and were used to assess the applicability of two types of scaling, one of which is advanced in the present study.

For the rotating experiments, the convective-layer growth is affected by the rotation at a height hc ≈ 4.5(q0Ω−3)½. The r.m.s. horizontal velocity of the rotationally affected mixed layer is uniform throughout the mixed layer and is given by $(\overline{u^{\prime 2}})^{\frac{1}{2}}_{\rm r}\approx 1.7(q_0\Omega^{-1})^{\frac{1}{2}}$. The time growth law of the mixed-layer thickness hr, when hr > hc, is given by hr ≈ 0.7(q0Ω−3)½Ωt, where t is the time. The rotational effects become important when the Rossby number is given by $Ro = (\overline{u^{\prime 2}})^{\frac{1}{2}}_{\rm r}/\omega l_{\rm r}\approx 1.5$, where the integral lengthscale is estimated as lr ≈ 0.25hc. The mean buoyancy gradient in the mixed layer was found to be much higher than in the corresponding non-rotating case, and the r.m.s. fluctuations and mean buoyancies were found to scale satisfactorily with (q0Ω)½. A spectral form for the temperature fluctuations in rotating convection is also proposed and is compared to the experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 228 , July 1991 , pp. 513 - 547
Copyright
© 1991 Cambridge University Press

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