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Register a new userLogarithmically modified scaling of temperature structure functions in thermal convection
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Added by
Alexander Bershadskii
Publication date
2005
fields
Physics
and research's language is
English
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Using experimental data on thermal convection, obtained at a Rayleigh number of 1.5 $times 10^{11}$, it is shown that the temperature structure functions $<Delta T_{r}^p>$, where $Delta T_r$ is the absolute value of the temperature increment over a distance $r$, can be well represented in an intermediate range of scales by $r^{zeta_p} phi (r)^{p}$, where the $zeta_p$ are the scaling exponents appropriate to the passive scalar problem in hydrodynamic turbulence and the function $phi (r) = 1-a(ln r/r_h)^2$. Measurements are made in the midplane of the apparatus near the sidewall, but outside the boundary layer.
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Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.5x10^{11}. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.
Different scaling behavior has been reported in various shell models proposed for turbulent thermal convection. In this paper, we show that buoyancy is not always relevant to the statistical properties of these shell models even though there is an explicit coupling between velocity and temperature in the equations of motion. When buoyancy is relevant (irrelevant) to the statistical properties, the scaling behavior is Bolgiano-Obukhov (Kolmogorov) plus intermittency corrections. We show that the intermittency corrections of temperature could be solely attributed to fluctuations in the entropy transfer rate when buoyancy is relevant but due to fluctuations in both energy and entropy transfer rates when buoyancy is irrelevant. This difference can be used as a criterion to distinguish whether temperature is behaving as an active or a passive scalar.
A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers is achieved. The local scaling properties of the Lagrangian velocity increments for the experimental and numerical data are in good quantitative agreement for all time lags. The degree of intermittency changes when measured close to the Kolmogorov time scales or at larger time lags. This study resolves apparent disagreements between experiment and numerics.
All previous experiments in open turbulent flows (e.g. downstream of grids, jet and atmospheric boundary layer) have produced quantitatively consistent values for the scaling exponents of velocity structure functions. The only measurement in closed turbulent flow (von Karman swirling flow) using Taylor-hypothesis, however, produced scaling exponents that are significantly smaller, suggesting that the universality of these exponents are broken with respect to change of large scale geometry of the flow. Here, we report measurements of longitudinal structure functions of velocity in a von Karman setup without the use of Taylor-hypothesis. The measurements are made using Stereo Particle Image Velocimetry at 4 different ranges of spatial scales, in order to observe a combined inertial subrange spanning roughly one and a half order of magnitude. We found scaling exponents (up to 9th order) that are consistent with values from open turbulent flows, suggesting that they might be in fact universal.
For many driven-nonequilibrium systems, the probability distribution functions of magnitude and recurrence-time of large events follow a powerlaw indicating a strong temporal correlation. In this paper we argue why these probability distribution functions are ubiquitous in driven nonequilibrium systems, and we derive universal scaling laws connecting the magnitudes, recurrence-time, and spatial intervals of large events. The relationships between the scaling exponents have also been studied. We show that the ion-channel current in Voltage-dependent Anion Channels obeys the universal scaling law.
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