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Wind-tunnel measurements of sensible turbulent heat fluxes over melting ice
- S. Harrison, L. Mydlarski
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- Journal:
- Journal of Fluid Mechanics / Volume 974 / 10 November 2023
- Published online by Cambridge University Press:
- 25 October 2023, A8
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Accelerated glacier melt and the loss of perennial snowfields have been associated with increased warming in polar regions, at rates up to four times faster than the rest of the world, thereby reinforcing the critical need for improved models (and predictions) of glacier melt. An essential requirement for such models is an improved understanding of the sensible heat fluxes over glaciers. Since their complexity makes them difficult to model, and direct measurements of sensible turbulent heat fluxes over real glaciers are both rare and impractical, the present work involves simultaneous hot-wire anemometry and cold-wire thermometry measurements of two components of velocity and temperature above a melting glacier model in a series of wind-tunnel experiments. Both single- and multi-variable statistics were used to compare the turbulent velocity field measured over melting ice with that of a similar flow in the absence of ice. The results demonstrate that the ice's presence reduces the magnitude of the Reynolds stresses and vertical velocity variance, but also increases the streamwise velocity variance. The transient evolution of temperature statistics throughout the melt process was also investigated and found to be similar when suitably non-dimensionalized. The velocity and temperature fields were furthermore evaluated at an equivalent non-dimensional time during the melt process, in which statistics of the temperature field, and joint statistics of the vertical velocity and temperature, were studied. The present work lays the foundation for future laboratory-scale replications of the flow above melting glaciers, and provides additional insight into turbulent heat transfer over melting ice.
Investigation of internal intermittency by way of higher-order spectral moments
- S. Lortie, L. Mydlarski
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- Journal:
- Journal of Fluid Mechanics / Volume 932 / 10 February 2022
- Published online by Cambridge University Press:
- 03 December 2021, A20
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The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$. Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.
Evolution of the scalar dissipation rate downstream of a concentrated line source in turbulent channel flow
- E. Germaine, L. Mydlarski, L. Cortelezzi
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- Journal:
- Journal of Fluid Mechanics / Volume 749 / 25 June 2014
- Published online by Cambridge University Press:
- 15 May 2014, pp. 227-274
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The dissipation rate, $\varepsilon _{\theta }$, of a passive scalar (temperature in air) emitted from a concentrated source into a fully developed high-aspect-ratio turbulent channel flow is studied. The goal of the present work is to investigate the return to isotropy of the scalar field when the scalar is injected in a highly anisotropic manner into an inhomogeneous turbulent flow at small scales. Both experiments and direct numerical simulations (DNS) were used to study the downstream evolution of $\varepsilon _{\theta }$ for scalar fields generated by line sources located at the channel centreline $(y_s/h = 1.0)$ and near the wall $(y_s/h = 0.17)$. The temperature fluctuations and temperature derivatives were measured by means of a pair of parallel cold-wire thermometers in a flow at $Re_{\tau } = 520$. The DNS were performed at $Re_{\tau } = 190$ using a spectral method to solve the continuity and Navier–Stokes equations, and a flux integral method (Germaine, Mydlarski & Cortelezzi, J. Comput. Phys., vol. 174, 2001, pp. 614–648) for the advection–diffusion equation. The statistics of the scalar field computed from both experimental and numerical data were found to be in good agreement, with certain discrepancies that were attributable to the difference in the Reynolds numbers of the two flows. A return to isotropy of the small scales was never perfectly observed in any region of the channel for the downstream distances studied herein. However, a continuous decay of the small-scale anisotropy was observed for the scalar field generated by the centreline line source in both the experiments and DNS. The scalar mixing was found to be more rapid in the near-wall region, where the experimental results exhibited low levels of small-scale anisotropy. However, the DNS, which were performed at lower $Re_{\tau }$, showed that persistent anisotropy can also exist near the wall, independently of the downstream location. The role of the mean velocity gradient in the production of $\varepsilon _{\theta }$ (and therefore anisotropy) in the near-wall region was highlighted.
Effect of background turbulence on an axisymmetric turbulent jet
- B. Khorsandi, S. Gaskin, L. Mydlarski
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- Journal:
- Journal of Fluid Mechanics / Volume 736 / 10 December 2013
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- 04 November 2013, pp. 250-286
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The effect of different levels of background turbulence on the dynamics and mixing of an axisymmetric turbulent jet at different Reynolds numbers has been investigated. Approximately homogeneous and isotropic background turbulence was generated by a random jet array and had a negligible mean flow (${\langle {U}_{\alpha } \rangle }/ {u}_{\alpha \mathit{rms}} \ll 1$). Velocity measurements of a jet issuing into two different levels of background turbulence were conducted for three different jet Reynolds numbers. The results showed that the mean axial velocities decay faster with increasing level of background turbulence (compared with a jet in quiescent surroundings), while the mean radial velocities increase, especially close to the edges of the jet. Furthermore, the axial root-mean-square velocities of the jet increased in the presence of background turbulence, as did the jet’s width. However, the mass flow rate of the jet decreased, from which it can be inferred that the entrainment into the jet is reduced in a turbulent background. The effect of background turbulence on the entrainment mechanisms is discussed.
Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions
- J. Lepore, L. Mydlarski
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- Journal:
- Journal of Fluid Mechanics / Volume 713 / 25 December 2012
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- 26 October 2012, pp. 453-481
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The effect of scalar-field (temperature) boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov $n/ 3$ prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertial-convective-range scaling exponents of the mixed, sixth-order, velocity–temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency – a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration – an effect that is notably less prominent in the other measures of internal intermittency.
Lateral dispersion from a concentrated line source in turbulent channel flow
- J. LEPORE, L. MYDLARSKI
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- Journal:
- Journal of Fluid Mechanics / Volume 678 / 10 July 2011
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- 03 May 2011, pp. 417-450
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The dispersion of a passive scalar (temperature) from a concentrated line source in fully developed, high-aspect-ratio turbulent channel flow is studied herein. The line source is oriented in the direction of the inhomogeneity of the velocity field, resulting in a thermal plume that is statistically three-dimensional. This configuration is selected to investigate the lateral dispersion of a passive scalar in an inhomogeneous turbulent flow (i.e. dispersion in planes parallel to the channel walls). Measurements are recorded at six wall-normal distances (y/h = 0.10, 0.17, 0.33, 0.50, 0.67 and 1.0), six downstream positions (x/h = 4.0, 7.4, 10.8, 15.2, 18.6 and 22.0) and a Reynolds number of Re ≡ 〈U〉y = hh/v = 10200 (Reτ ≡ u∗h/v = 502). The lateral mean temperature excess profiles were found to be well represented by Gaussian distributions. The root-mean-square (r.m.s.) profiles, on the other hand, were symmetric, but non-Gaussian. Consistent with homogeneous flows (and in contrast to the work of Lavertu & Mydlarski (J. Fluid Mech., vol. 528, 2005, p. 135) studying transverse dispersion in the same flow), (i) the downstream growth rate of the centreline mean temperature excess, centreline r.m.s. temperature fluctuation and half-width of the mean and r.m.s. temperature profiles followed a power law evolution in the downstream direction, and (ii) the r.m.s. profiles evolved from single-peaked to double-peaked profiles far downstream. By comparing the measured ratios of the centreline r.m.s. temperature fluctuation to the mean temperature excess to the ratios measured in other flows, it was hypothesized that the mean-flow shear, as well as the turbulence intensity, played an important, cooperative role in increasing the mixedness of the flow. The probability density functions (PDFs) were quasi-Gaussian near the wall as well as for large-enough downstream distances. Closer to both the source and the channel centreline, the PDFs were better approximated by exponential distributions, with a sharp peak corresponding to the free-stream temperature. For intermediate downstream distances, the PDFs of the lateral dispersion were better mixed than analogous PDFs of the transverse dispersion, consistent with the mixedness measurements.
Differential diffusion of high-Schmidt-number passive scalars in a turbulent jet
- T. M. LAVERTU, L. MYDLARSKI, S. J. GASKIN
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- Journal:
- Journal of Fluid Mechanics / Volume 612 / 10 October 2008
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- 10 October 2008, pp. 439-475
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The separate evolution, or differential diffusion, of high-Schmidt-number passive scalars in a turbulent jet is studied experimentally. The two scalars under consideration are disodium fluorescein (Sc ≡ ν/D = 2000) and sulforhodamine 101 (Sc = 5000). The objectives of the research are twofold: to determine (i) the Reynolds-number-dependence, and (ii) the radial distribution of differential diffusion effects in the self-similar region of the jet. Punctual laser-induced fluorescence (LIF) measurements were obtained 50 jet diameters downstream of the nozzle exit for five Reynolds numbers (Re ≡ uod/ν = 900, 2100, 4300, 6700 and 10600, where u0 is the jet exit velocity, d is the jet diameter, and ν is the kinematic viscosity) and for radial positions extending from the centreline to the edges of the jet cross-section (0 ≤ r/d ≤ 7.5). Statistics of the normalized concentration difference, Z, were used to quantify the differential diffusion. The latter were found to decay slowly with increasing Reynolds number, with the root mean square of Z scaling as Zrms ≡ 〈Z2〉1/2 ∝ Re−0.1, (or alternatively 〈Z2〉 ∝ Re−0.2). Regardless of Reynolds number, differential diffusion effects were found to increase away from the centreline. The increase in differential diffusion effects with radial position, along with their increase with decreasing Reynolds number, support the hypothesis of increased differential diffusion at interfaces between the jet and ambient fluids. Power spectral densities of Z were also studied. These spectra decreased with increasing wavenumber – an observation attributed to the decay of the scalar fluctuations in a turbulent jet. Furthermore, these spectra showed that significant differential diffusion effects persist at scales larger than the Kolmogorov scale, even for moderately high Reynolds numbers.
Mixing of two thermal fields emitted from line sources in turbulent channel flow
- E. COSTA-PATRY, L. MYDLARSKI
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- Journal:
- Journal of Fluid Mechanics / Volume 609 / 25 August 2008
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- 31 July 2008, pp. 349-375
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The interaction of two passive scalars (both temperature in air) emitted from concentrated line sources in fully developed high-aspect-ratio turbulent channel flow is studied. The thermal fields are measured using cold-wire thermometry in a flow with a Reynolds number (Uh/ν) of 10200.
The transverse total root-mean-square (RMS) temperature profiles are a function of the separation distance between the line sources (d/h), their average wall-normal position (ysav/h), and the downstream location (x/h), measured relative to the line sources. Similarly, profiles of the non-dimensional form of the scalar covariance, the correlation coefficient (ρ), are a function of the same parameters and quantify the mixing of the two scalars.
The transverse profiles of the correlation coefficient are generally largest at the edges of the thermal plume and smallest in its core. When the line sources are not symmetrically located about the channel centreline, the minimum in the correlation coefficient transverse profiles drifts towards the (closer) channel wall. For source locations that are equidistant from the channel centreline, the minimum correlation coefficient occurs at the centreline, due to the underlying symmetry of this geometry. The initial downstream evolution of the correlation coefficient depends significantly on d/h, similar to that in homogeneous turbulence. However, there is always a dependence on ysav/h, which increases in importance as both the downstream distance is increased and the wall is approached. Lastly, the correlation coefficient profiles tend towards positive values in the limit of large downstream distances (relative to the source separation), though further measurements farther downstream are required to confirm the exact value(s) of their asymptotic limit(s).
Spectral analysis of the cospectra and coherency spectra indicates that the large scales evolve more rapidly than the small ones. Furthermore, the fast evolution of the large scales was most evident when the sources were located close to the wall. This presumably derives from the large-scale nature of turbulence production, which is strong in the near-wall region.
On the onset of high-Reynolds-number grid-generated wind tunnel turbulence
- L. Mydlarski, Z. Warhaft
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- Journal:
- Journal of Fluid Mechanics / Volume 320 / 10 August 1996
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- 26 April 2006, pp. 331-368
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Using an active grid devised by Makita (1991), shearless decaying turbulence is studied for the Taylor-microscale Reynolds number, Rλ, varying from 50 to 473 in a small (40 × 40 cm2 cross-section) wind tunnel. The turbulence generator consists of grid bars with triangular wings that rotate and flap in a random way. The value of Rλ is determined by the mean speed of the air (varied from 3 to 14 m s–1) as it passes the rotating grid, and to a lesser extent by the randomness and rotation rate of the grid bars. Our main findings are as follows. A weak, not particularly well-defined scaling range (i.e. a power-law dependence of both the longitudinal (u) and transverse (v) spectra, F11(k1) and F22(k1) respectively, on wavenumber k1) first appears at Rλ ∼ 50, with a slope, n1, (for the u spectrum) of approximately 1.3. As Rλ was increased, n1 increased rapidly until Rλ ∼ 200 where n ∼ 1.5. From there on the increase in n1 was slow, and even by Rλ = 473 it was still significantly below the Kolmogorov value of 1.67. Over the entire range, 50 [les ] Rλ [les ] 473, the data were well described by the empirical fit: $n_1 = \frac{5}{3}(1-3.15R_\lambda^{-2/3})$. Using a modified form of the Kolmogorov similarity law: F11(k1) = C1*ε2/3k1–5/3(k1η)5/3–n1 where ε is the turbulence energy dissipation rate and η is the Kolmogorov microscale, we determined a linear dependence between n1 and C1*: C1* = 4.5 – 2.4n1. Thus for n1 = 5/3 (which extrapolation of our results suggests will occur in this flow for Rλ ∼ 104), C1* = 0.5, the accepted high-Reynolds-number value of the Kolmogorov constant. Analysis of the p.d.f. of velocity differences Δu(r) and Δv(r) where r is an inertial subrange interval, conditional dissipation, and other statistics showed that there was a qualitative difference between the turbulence for Rλ < 100 (which we call weak turbulence) and that for Rλ > 200 (strong turbulence). For the latter, the p.d.f.s of Δu(r) and Δv(r) had super Gaussian tails and the dissipation (both of the u and v components) conditioned on Δu(r) and Δv(r) was a strong function of the velocity difference. For Rλ < 100, p.d.f.s of Δu(r) and Δv(r) were Gaussian and conditional dissipation statistics were weak. Our results for Rλ > 200 are consistent with the predictions of the Kolmogorov refined similarity hypothesis (and make a distinction between the dynamical and kinematical contributions to the conditional statistics). They have much in common with similar statistics done in shear flows at much higher Rλ, with which they are compared.
Scalar mixing from a concentrated source in turbulent channel flow
- R. A. LAVERTU, L. MYDLARSKI
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- Journal:
- Journal of Fluid Mechanics / Volume 528 / 10 April 2005
- Published online by Cambridge University Press:
- 24 March 2005, pp. 135-172
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The mixing of a scalar (temperature) emitted from a concentrated line source in fully developed high-aspect-ratio turbulent channel flow is studied. The motivation for the work is to study the effect of the inhomogeneity on the scalar dispersion. It is most readily carried out in a flow that is inhomogeneous in only one direction, i.e. channel flow. Experiments were performed at two Reynolds numbers ($\hbox{\it Reacute;\,{\equiv}\,\langle U(y=h)\rangle h/\nu\,{=}\,10\,400$ and 22800), three wall-normal source locations ($y_s/h\,{=}\,0.067$, 0.17 and 1.0) and six downstream distances ($4.0 \,{\le}\, x/h \,{\le}\,22.0$). Both the mean and r.m.s. temperature profiles were found to be described well by truncated Gaussian distributions. In contrast to homogeneous flows, (i) the growth rates of the mean profile widths did not exhibit power law behaviours, (ii) the centres of the r.m.s. profiles were found to drift towards the centre of the channel for plumes emanating from off-centreline source locations and (iii) the r.m.s. profiles showed no tendency towards double peaks far downstream, as are observed in homogeneous flows. For near-wall source locations, the probability density function (PDF) of the scalar fluctuations evolved from a quasi-Gaussian distribution near the wall to a strongly positively skewed PDF (with a large spike at the cold-fluid temperature) for transverse locations away from the wall. Increasing the Reynolds number was found to improve the mixing, even though this decreases the amount of time for which the scalar can mix (owing to the more rapid advection). For the centreline source location, the PDF shape was, in general, more spiked, indicating the importance of the flapping of the plume in this case. The effect of the meandering of the plume was less significant when the plume was bounded by the wall. Second- and third-order velocity–temperature correlations were presented. The differences in their profiles for the near-wall and centreline source locations were distinct.
Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence
- L. MYDLARSKI
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- Journal:
- Journal of Fluid Mechanics / Volume 475 / 25 January 2003
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- 17 February 2003, pp. 173-203
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Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.
Passive scalar statistics in high-Péclet-number grid turbulence
- L. MYDLARSKI, Z. WARHAFT
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- Journal:
- Journal of Fluid Mechanics / Volume 358 / 10 March 1998
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- 10 March 1998, pp. 135-175
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The statistics of a turbulent passive scalar (temperature) and their Reynolds number dependence are studied in decaying grid turbulence for the Taylor-microscale Reynolds number, Rλ, varying from 30 to 731 (21[les ]Peλ[les ]512). A principal objective is, using a single (and simple) flow, to bridge the gap between the existing passive grid-generated low-Péclet-number laboratory experiments and those done at high Péclet number in the atmosphere and oceans. The turbulence is generated by means of an active grid and the passive temperature fluctuations are generated by a mean transverse temperature gradient, formed at the entrance to the wind tunnel plenum chamber by an array of differentially heated elements. A well-defined inertial–convective scaling range for the scalar with a slope, nθ, close to the Obukhov–Corrsin value of 5/3, is observed for all Reynolds numbers. This is in sharp contrast with the velocity field, in which a 5/3 slope is only approached at high Rλ. The Obukhov–Corrsin constant, Cθ, is estimated to be 0.45–0.55. Unlike the velocity spectrum, a bump occurs in the spectrum of the scalar at the dissipation scales, with increasing prominence as the Reynolds number is increased. A scaling range for the heat flux cospectrum was also observed, but with a slope around 2, less than the 7/3 expected from scaling theory. Transverse structure functions of temperature exist at the third and fifth orders, and, as for even-order structure functions, the width of their inertial subranges dilates with Reynolds number in a systematic way. As previously shown for shear flows, the existence of these odd-order structure functions is a violation of local isotropy for the scalar differences, as is the existence of non-zero values of the transverse temperature derivative skewness (of order unity) and hyperskewness (of order 100). The ratio of the temperature derivative standard deviation along and normal to the gradient is 1.2±0.1, and is independent of Reynolds number. The refined similarity hypothesis for the passive scalar was found to hold for all Rλ, which was not the case for the velocity field. The intermittency exponent for the scalar, μθ, was found to be 0.25±0.05 with a possible weak Rλ dependence, unlike the velocity field, where μ was a strong function of Reynolds number. New, higher-Reynolds-number results for the velocity field, which smoothly follow the trends of Mydlarski & Warhaft (1996), are also presented.