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The evolution of grid-generated turbulence under conditions of stable thermal stratification

Published online by Cambridge University Press:  26 April 2006

Kyunghwan Yoon  and
Z. Warhaft
Kyunghwan Yoon
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Z. Warhaft
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

We investigate the evolution of grid turbulence under the action of a stable (negatively buoyant), linear, temperature profile. The experiment was carried out in a large, open circuit, low-speed wind tunnel 0.91 × 0.91 m2 and 9.14 m in length specially designed for the study of stratified turbulence. The temperature gradient, formed at the entrance to the plenum chamber of the tunnel by means of an array of 72 horizontal, differentially heated elements was varied from 0 to 55 °C/m, giving a maximum Brunt–Väisälä frequency N of 1.3 s−1. The grid mesh M was 2.54 cm and the mean velocity U was varied from 2.8 to 4.2 m/s. Thus the mesh Froude number FrM = U/(NM) was varied from ∞ to 84.8 for the passive and most stable case respectively. We show that there are distinct stages in the evolution of the flow and these are determined by the turbulence Richardson number Riu, which is the square of the ratio of the turbulence to stratification timescales (Nτ)2. For Riu < 0.1 the flow is dynamically passive and the vertical heat flux correlation coefficient ρwθ is constant with a value of −0.7. From Riu ≈ 0.1 (where the turbulent potential energy is approximately 5% of the vertical kinetic energy) to Riu ≈ 1 the heat flux begins to decay under the action of the buoyancy forces and the vertical velocity variance $overline{\omega ^2}$ decays more rapidly than for the neutral case. By Riu ≈ 1 the turbulent potential energy is nearly as large as the vertical kinetic energy and the magnitude of the ratio of the buoyancy to mechanical dissipation terms in the kinetic energy budget reaches a maximum and then rapidly diminishes as the heat flux completely collapses (by Riu ≈ 2). For Riu > 2 the heat flux remains small except for the most stable case studied where a significant net counter gradient heat flux occurs. Here the vertical velocity variance increases as it draws its energy from the potential energy field. For all experiments the mechanical to thermal timescale ratio remains relatively constant up until Riu ≈ 1 and then increases from 1.1 to a maximum value of 2. The ratio of the r.m.s. longitudinal to vertical velocity fluctuations $(\overline {u^2}^{\frac{1}{2}}/(\overline{W^2}^{\frac{1}{2}}$, increases from the passive value (of 1.1) to a maximum of approximately 1.6 at Riu ≈ 1 and then decreases as the heat flux collapses. No direct evidence of internal waves is found from the single-point measurements. The results are presented in terms of relevant lengthscale ratios determined from auto-correlation functions, spectra and from integrated quantities such as variance and dissipation rates. Particular attention is paid to a comparison with previous work, especially that of Lienhard & Van Atta (1990), the only other wind-tunnel experiment on strongly stratified grid-generated turbulence without shear. It is shown that the evolution of the flow is very sensitive to initial conditions and in order to collapse the data of different experiments the turbulence time (τ) rather than the elapsed clock time (t) must be used, i.e. the data collapse well with Riu but not with Nt (which is more traditionally used).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 215 , June 1990 , pp. 601 - 638
Copyright
© 1990 Cambridge University Press

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