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Experimental and numerical investigation of turbulent convection in a rotating cylinder

Published online by Cambridge University Press:  23 December 2009

R. P. J. KUNNEN ,
B. J. GEURTS  and
H. J. H. CLERCX
R. P. J. KUNNEN*
Affiliation:
Fluid Dynamics Laboratory, Department of Physics, International Collaboration for Turbulence Research (ICTR) & J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
B. J. GEURTS
Affiliation:
Fluid Dynamics Laboratory, Department of Physics, International Collaboration for Turbulence Research (ICTR) & J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Department of Applied Mathematics, International Collaboration for Turbulence Research (ICTR) & J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
H. J. H. CLERCX
Affiliation:
Fluid Dynamics Laboratory, Department of Physics, International Collaboration for Turbulence Research (ICTR) & J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Department of Applied Mathematics, International Collaboration for Turbulence Research (ICTR) & J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Present address: Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062 Aachen, Germany. Email address for correspondence: [email protected]
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Abstract

The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent Rayleigh–Bénard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena.

A constant Rayleigh number (dimensionless strength of the destabilizing temperature gradient) Ra = 109 and Prandtl number (describing the diffusive fluid properties) σ = 6.4 are applied. The rotation rate, given by the convective Rossby number Ro (ratio of buoyancy and Coriolis force), takes values in the range 0.045 ≤ Ro ≤ ∞, i.e. between rotation-dominated flow and zero rotation. Generally, rotation attenuates the intensity of the turbulence and promotes the formation of slender vertical tube-like vortices rather than the global circulation cell observed without rotation. Above Ro ≈ 3 there is hardly any effect of the rotation on the flow. The root-mean-square (r.m.s.) values of vertical velocity and vertical vorticity show an increase when Ro is lowered below Ro ≈ 3, which may be an indication of the activation of the Ekman pumping mechanism in the boundary layers at the bottom and top plates. The r.m.s. fluctuations of horizontal and vertical velocity, in both experiment and simulation, decrease with decreasing Ro and show an approximate power-law behaviour of the shape Ro0.2 in the range 0.1 ≲ Ro ≲ 2. In the same Ro range the temperature r.m.s. fluctuations show an opposite trend, with an approximate negative power-law exponent Ro−0.32. In this Rossby number range the r.m.s. vorticity has hardly any dependence on Ro, apart from an increase close to the plates for Ro approaching 0.1. Below Ro ≈ 0.1 there is strong damping of turbulence by rotation, as the r.m.s. velocities and vorticities as well as the turbulent heat transfer are strongly diminished. The active Ekman boundary layers near the bottom and top plates cause a bias towards cyclonic vorticity in the flow, as is shown with probability density functions of vorticity. Rotation induces a correlation between vertical vorticity and vertical velocity close to the top and bottom plates: near the top plate downward velocity is correlated with positive/cyclonic vorticity and vice versa (close to the bottom plate upward velocity is correlated with positive vorticity), pointing to the vortical plumes. In contrast with the well-mixed mean isothermal bulk of non-rotating convection, rotation causes a mean bulk temperature gradient. The viscous boundary layers scale as the theoretical Ekman and Stewartson layers with rotation, while the thermal boundary layer is unaffected by rotation. Rotation enhances differences in local anisotropy, quantified using the invariants of the anisotropy tensor: under rotation there is strong turbulence anisotropy in the centre, while near the plates a near-isotropic state is found.

JFM classification

Convection: Convection Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 445 - 476
Copyright
Copyright © Cambridge University Press 2010

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