1,088 research outputs found

    Temperature spectra in shear flow and thermal convection

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    We show that the P_u(\om) \propto \om^{-7/3} shear velocity power spectrum gives rise to a P_\Theta (\om ) \propto \om^{-4/3} power spectrum for a passively advected scalar, as measured in experiment [K. Sreenivasan, Proc. R. Soc. London A {\bf 434}, 165 (1991)]. Applying our argument to high Rayleigh number Rayleigh Benard flow, we can account for the measured scaling exponents equally well as the Bolgiano Obukhov theory (BO59). Yet, of the two explanations, only the shear approach might be able to explain why no classical scaling range is seen in between the shear (or BO59) range and the viscous subrange of the experimental temperature spectrum [I. Procaccia {\it et al.}, Phys. Rev. A {\bf 44}, 8091 (1991)].Comment: 9 pages, 1 figure, 1 tabl

    On geometry effects in Rayleigh-Benard convection

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    Various recent experiments hint at a geometry dependence of scaling relations in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is offered which can account for such dependences. It is based on Prandtl's theory for laminar boundary layers and on the conservation of volume flux of the large scale wind. The mechanism implies the possibility of different thicknesses of the kinetic boundary layers at the sidewalls and the top/bottom plates, just as experimentally found by Qiu and Xia (Phys. Rev. E58, 486 (1998)), and also different RaRa-scaling of the wind measured over the plates and at the sidewalls. In the second part of the paper a scaling argument for the velocity and temperature fluctuations in the bulk is developeVarious recent experiments hint at a geometry dependence of scaling relations in Rayleigh-Benard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is offered which can account for such dependences. It is based on Prandtl's theory for laminar boundary layers and on the conservation of volume flux of the large scale wind. The mechanism implies the possibility of different thicknesses of the kinetic boundary layers at the sidewalls and the top/bottom plates, just as experimentally found by Qiu and Xia (Phys. Rev. E58, 486 (1998)), and also different RaRa-scaling of the wind measured over the plates and at the sidewalls. In the second part of the paper a scaling argument for the velocity and temperature fluctuations in the bulk is developeComment: 4 pages, 1 figur

    Scaling in thermal convection: A unifying theory

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    A systematic theory for the scaling of the Nusselt number NuNu and of the Reynolds number ReRe in strong Rayleigh-Benard convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large scale convection roll (``wind of turbulence'') and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number versus Prandtl number phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra smaller than 10^{11}) the leading terms are NuRa1/4Pr1/8Nu\sim Ra^{1/4}Pr^{1/8}, ReRa1/2Pr3/4Re \sim Ra^{1/2} Pr^{-3/4} for Pr<1Pr < 1 and NuRa1/4Pr1/12Nu\sim Ra^{1/4}Pr^{-1/12}, ReRa1/2Pr5/6Re \sim Ra^{1/2} Pr^{-5/6} for Pr>1Pr > 1. In most measurements these laws are modified by additive corrections from the neighboring regimes so that the impression of a slightly larger (effective) Nu vs Ra scaling exponent can arise. -- The presented theory is best summarized in the phase diagram figure 1.Comment: 30 pages, latex, 7 figures, under review at Journal of Fluid Mec

    Scale resolved intermittency in turbulence

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    The deviations δζm\delta\zeta_m ("intermittency corrections") from classical ("K41") scaling ζm=m/3\zeta_m=m/3 of the mthm^{th} moments of the velocity differences in high Reynolds number turbulence are calculated, extending a method to approximately solve the Navier-Stokes equation described earlier. We suggest to introduce the notion of scale resolved intermittency corrections δζm(p)\delta\zeta_m(p), because we find that these δζm(p)\delta\zeta_m(p) are large in the viscous subrange, moderate in the nonuniversal stirring subrange but, surprisingly, extremely small if not zero in the inertial subrange. If ISR intermittency corrections persisted in experiment up to the large Reynolds number limit, our calculation would show, that this could be due to the opening of phase space for larger wave vectors. In the higher order velocity moment u(p)m\langle|u(p)|^m\rangle the crossover between inertial and viscous subrange is (10ηm/2)1(10\eta m/2)^{-1}, thus the inertial subrange is {\it smaller} for higher moments.Comment: 12 pages, Latex, 2 tables, 7 figure

    Why surface nanobubbles live for hours

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    We present a theoretical model for the experimentally found but counter-intuitive exceptionally long lifetime of surface nanobubbles. We can explain why, under normal experimental conditions, surface nanobubbles are stable for many hours or even up to days rather than the expected microseconds. The limited gas diffusion through the water in the far field, the cooperative effect of nanobubble clusters, and the pinned contact line of the nanobubbles lead to the slow dissolution rate.Comment: 5 pages, 3 figure

    Application of extended self similarity in turbulence

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    From Navier-Stokes turbulence numerical simulations we show that for the extended self similarity (ESS) method it is essential to take the third order structure function taken with the modulus and called D3(r)D_3^*(r), rather than the standard third order structure function D3(r)D_3(r) itself. If done so, we find ESS towards scales larger than roughly 10 eta, where eta is the Kolmogorov scale. If D3(r)D_3(r) is used, there is no ESS. We also analyze ESS within the Batchelor parametrization of the second and third order longitudinal structure function and focus on the scaling of the transversal structure function. The Re-asymptotic inertial range scaling develops only beyond a Taylor-Reynolds number of about 500.Comment: 12 pages, 7 eps-figures, replaces version from April 11th, 1997; paper now in press at Phys. Rev.

    Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

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    The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. Rei=5×103Re_i=5\times 10^3 and Rei=2×104Re_i=2\times 10^4; the deformability of the bubbles is controlled through the Weber number which is varied in the range We=0.012.0We=0.01 - 2.0. Our numerical simulations show that increasing the deformability of bubbles i.e., WeWe leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder
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