Effects of rotation on convective turbulence

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 q 0 and rotation rates Ω, including Ω = 0; q 0 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 q 0 / 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 h c ≈ 4.5( q 0 Ω −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 h r , when h r > h c , is given by h r ≈ 0.7( q 0 Ω −3 ) ½ Ω t , 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 l r ≈ 0.25 h c . 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 ( q 0 Ω) ½ . A spectral form for the temperature fluctuations in rotating convection is also proposed and is compared to the experimental results.