https://nova.newcastle.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:39519 Wed 27 Jul 2022 13:59:34 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:52747 Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303), Obukhov (Izv. Akad. Nauk SSSR Geogr. Geofiz, vol. 13, 1949, pp. 58–69) and Corrsin (J. Appl. Phys., vol. 22, 1951, pp. 469–473) require small-scale turbulence to be isotropic, they have only limited relevance to wall-bounded turbulent flows. Here, we put forward a hypothesis whereby small-scale near-wall statistics, when suitably normalized, are independent of the type of flow as well as of the Reynolds and Péclet numbers. The relatively large amount of available wall turbulence direct numerical simulations data, related mainly to second-order statistics, in a channel flow and a boundary layer provides good support for the independence with respect to the Reynolds number. To fully validate the hypothesis, more data are required for higher-order statistics as well as for other wall flows and for different surface conditions.]]> Wed 25 Oct 2023 15:26:28 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:54903 Wed 20 Mar 2024 15:02:41 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:44650 2, in the region beyond the dissipative range, is analyzed via the transport equation for S₂ where a closure model for S₃, the third-order velocity structure function, is introduced. The model [L. Djenidi and R. A. Antonia, Fluid Turbulence Applications in Both Industrial and Environmental Topics, Marseille, 9–11 July, 2019, https://fab60.sciencesconf.org/] is based on a gradient type with an eddy-viscosity formulation and has the following expression: [formula could not be replicated], where [formula could not be replicated] is the mean rate of the turbulent kinetic energy dissipation, r is the spatial increment, and [formula could not be replicated] is a constant. The closed S₂-transport equation is further exploited to derive a model for S₂ for scales beyond the dissipative range. The model for S₂ takes the form [formula could not be replicated] with [formula could not be replicated], where CK is a constant, Reλ is the Taylor microscale Reynolds number, and the function Br accounts for the effect of the large scales. The numerical solutions of the S₂ equation and the predictions based on the model for S₂ agree very well with direct numerical simulation data for steady-state forced homogeneous and isotropic turbulence. The solutions of the S₂-transport equation without large-scale forcing show that S₂ behaves like [formula could not be replicated]. When forcing is applied, S₂ deviates from this behavior. However, increasing the Reynolds number tends to restore this behavior over an increasing range of scales. This is also observed in the predictions of the model for S₂.]]> Wed 19 Oct 2022 09:14:43 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:51032 Wed 16 Aug 2023 10:16:51 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:40503 Wed 13 Jul 2022 15:02:44 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:3130 Wed 11 Apr 2018 16:46:38 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17034 2¯ is reasonably well approximated on the axis of the intermediate wake of a circular cylinder. The similarity, which scales on the Taylor microscale λ and q²¯, is then used to determine s-b-s energy budgets from the data of Antonia, Zhou, and Romano [“Small-scale turbulence characteristics of two-dimensional bluff body wakes,” J. Fluid Mech.459, 67–92 (2002)] for 5 different two-dimensional wake generators. In each case, the budget is reasonably well closed, using the locally isotropic value of the mean energy dissipation rate, except near separations comparable to the wavelength of the coherent motion (CM). The influence of the initial conditions is first felt at a separation L_c¯ identified with the cross-over between the energy transfer and large scale terms of the s-b-s budget. When normalized by q²¯ and L_c , the mean energy dissipation rate is found to be independent of the Taylor microscale Reynolds number. The CM enhances the maximum value of the energy transfer, the latter exceeding that predicted from models of decaying homogeneous isotropic turbulence.]]> Wed 11 Apr 2018 15:47:49 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17050 Wed 11 Apr 2018 15:36:30 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17051 θ) is represented by a power-law function of Reynolds number, and it approaches 5/3 faster than that for the velocity spectrum (mu). Results show that the ratio between the velocity and temperature scaling range exponents, (5/3+m_u)/m_θ, is about 1.98.]]> Wed 11 Apr 2018 15:29:00 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17033 t which exhibits some remarkable universal facets over an impressively wide range of scales. This allows us to model the third-order structure functions in different decaying flows covering a large extent of Reynolds numbers. The model is numerically time integrated to predict the decay of second-order structure functions and compared to experiments in grid turbulence. Agreement between predictions and measurements is satisfactory.]]> Wed 11 Apr 2018 14:57:04 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:3132 Wed 11 Apr 2018 14:48:34 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17030 δ = U ₀δ/ν (U ₀ being the jet inlet velocity and δ the momentum thickness) that ought to be achieved for the one-point statistics to behave in a self-similar fashion is assessed. Second, the relevance of different sets of similarity variables for normalizing the energy spectra and structure functions is explored. In particular, a new set of shear similarity variables, emphasizing the range of scales influenced by the mean velocity and temperature gradient, is derived and tested. Since the Reynolds number based on the Taylor microscale increases with respect to the streamwise distance, complete self-preservation cannot be satisfied; instead, the range of scales over which spectra and structure functions comply with self-preservation depends on the particular choice of similarity variables. A similarity analysis of the two-point transport equation, which features the large scale production term, is performed and confirms this. Log-similarity, which implicitly accounts for the variation of the Reynolds number, is also proposed and appears to provide a reasonable approximation to self-preservation, at least for u and θ.]]> Wed 11 Apr 2018 14:43:41 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:4415 Wed 11 Apr 2018 14:33:14 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:77 Wed 11 Apr 2018 14:27:01 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:1743 Wed 11 Apr 2018 13:22:16 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:2528 Wed 11 Apr 2018 13:02:20 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:3131 Wed 11 Apr 2018 12:39:22 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17035 2~(t-t_o)ⁿ, q'²0 is the virtual origin) at low Reynolds numbers based on Taylor microscale R_λ(≡ u'λ/v) ≤ 64. Hot wire measurements are carried out in a grid turbulence subjected to a 1.36:1 contraction. The grid consists in large square holes (mesh size 43.75 mm and solidity 43%); small square holes (mesh size 14.15 mm and solidity 43%) and woven mesh grid (mesh size 5 mm and solidity 36%). The decay exponent (n) is determined using three different methods: (i) decay of q'², (ii) transport equation for ɛ, the mean dissipation of the turbulent kinetic energy and (iii) λ method (Taylor microscale λ ≡ √5〈q'²〉/〈ɛ_d〉 angular bracket denotes the ensemble). Preliminary results indicate that the magnitude n increases while R_λ(≡ u'λ/v) decreases, in accordance with the turbulence theory.]]> Wed 11 Apr 2018 12:31:39 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17032 a, ya, x and the transverse direction y (ε_{a, yhom}) and homogeneity in the transverse plane, (ε ), are assessed. All the approximations are in agreement with ε¯ when the distance downstream of the obstacle is larger than about 40 diameters. Closer to the obstacle, the agreement remains reasonable only for ε¯_a,x , ε¯_hom and ε¯_4x. The probability density functions (PDF) and joint PDFs of ε and its surrogates show that ε_4x correlates best with ε while ε_iso and ε_hom present the smallest correlation. The results indicate that ε4x is a very good surrogate for ε and can be used for correctly determining the behaviour of ε.]]> Wed 11 Apr 2018 12:08:09 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:15262 102) indicate that, to obtain a 5/3 scaling range, R λ must exceed 103. The ratio (5/3 + m u )/m θ is approximately 2, in close conformity with the proposal of Danaila and Antonia [“Spectrum of a passive scalar in moderate Reynolds number homogeneous isotropic turbulence,” Phys. Fluids21, 111702 (2009)].]]> Wed 11 Apr 2018 11:48:55 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17029 Wed 11 Apr 2018 11:35:47 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:3032 Wed 11 Apr 2018 10:45:40 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26268 λ is examined for different turbulent flows by considering the locally isotropic form of the transport equation for the mean energy dissipation rate ⋷_iso. In each flow, the equation can be expressed in the form S + 2G/Re_λ = C/Re_λ, where G is a non-dimensional rate of destruction of ⋷_iso and C is a flow-dependent constant. Since 2G/Re_λ is found to be very nearly constant for Re_λ ≥ 70, S should approach a universal constant when Re_λ is sufficiently large, but the way this constant is approached is flow dependent. For example, the approach is slow in grid turbulence and rapid along the axis of a round jet. For all the flows considered, the approach is reasonably well supported by experimental and numerical data. The constancy of S at large Re_λ has obvious ramifications for small-scale turbulence research since it violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) but is consistent with the original similarity hypothesis (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299-303).]]> Wed 11 Apr 2018 10:06:08 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:3129 Wed 11 Apr 2018 09:58:36 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:3133 Wed 11 Apr 2018 09:22:36 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45594 Wed 02 Nov 2022 13:39:04 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:50689 Wed 02 Aug 2023 11:09:25 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:33015 r = λ, is assessed in various turbulent flows at small to moderate values of the Taylor microscale Reynolds number R_λ. It is found that the contribution of the large-scale terms to the scale by scale energy budget differs from flow to flow. For a fixed R_λ, this contribution is largest on the centreline of a fully developed channel flow but smallest for stationary forced periodic box turbulence. For decaying-type flows, the contribution lies between the previous two cases. Because of the difference in the large-scale term between flows, the third-order longitudinal velocity structure function at r = λ differs from flow to flow at small to moderate R_λ. The effect on the second-order velocity structure functions appears to be negligible. More importantly, the effect of R_λ on the scaling range exponent of the longitudinal velocity structure function is assessed using measurements of the streamwise velocity fluctuation u, with R_λ in the range 500–1100, on the axis of a plane jet. It is found that the magnitude of the exponent increases as R_λ increases and the rate of increase depends on the order n. The trend of published structure function data on the axes of an axisymmetric jet and a two-dimensional wake confirms this dependence. For a fixed R_λ, the exponent can vary from flow to flow and for a given flow, the larger R_λ is, the closer the exponent is to the value predicted by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 299–303) (hereafter K41). The major conclusion is that the finite Reynolds number effect, which depends on the flow, needs to be properly accounted for before determining whether corrections to K41, arising from the intermittency of the energy dissipation rate, are needed. We further point out that it is imprudent, if not incorrect, to associate the finite Reynolds number effect with a consequence of the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) (K62); we contend that this association has misled the vast majority of post K62 investigations of the consequences of K62.]]> Tue 21 Aug 2018 11:32:55 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:38239 3 based on d and the free-stream velocity. A multi-wire probe is deployed to measure simultaneously the fluctuating temperature and its gradient vector, at nominally the same spatial point in the plane of the mean shear. It is found that the coherent streamwise and spanwise temperature derivatives are similarly distributed with respect to the spanwise vortex, exhibiting twin peaks at the temperature fronts, while the coherent lateral component is linked to the rib-like structures. The temperature variance dissipation rate is found to be statistically independent of the temperature fluctuation when the Kármán vortex is so weak (say at x/d = 40) that the large-scale temperature front resulting from the vortex entrainment ceases to be present and the coherent strain rate at the saddle region is relatively small. In addition, the most effective turbulent mixing is found to take place around the temperature front near the wake centerline, which is in contrast to the conjecture by Hussain and Hayakawa (1987).]]> Tue 17 Aug 2021 09:45:53 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:36610 ∈, on the distance from the wall and the Taylor microscale Reynolds number, Re_λ. The locally isotropic expression <∈_iso> is used as a surrogate for the mean turbulent kinetic energy dissipation rate, <∈>, for calculating [formula could not be replicated] are the integral length scale and the rms of the longitudinal velocity fluctuation, respectively. The measurements show that C_∈ varies significantly near the wall, but becomes almost constant in the region 0.2≤y/δ≤0.6 of the boundary layer, a region where Re_λ is also practically constant.]]> Tue 16 Jun 2020 10:44:42 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:44263 u_i and ω_i (i=1,2,3 ), are simultaneously measured, along with the fluctuating temperature θ and the temperature gradient vector, at nominally the same spatial point in the plane of mean shear at x/d=10 , where x is the streamwise distance from the cylinder axis and d is the cylinder diameter. We believe this is the first time the properties of fluctuating velocity, temperature, vorticity and temperature gradient vectors have been explored simultaneously within the Kármán vortex in detail. The Reynolds number based on d and the free-stream velocity is 2.5 x 10³ . The phase-averaged distributions of θ and ui follow closely the Gaussian distribution for r/d⩽0.2 (r is the distance from the vortex centre), but not for r/d>0.2 . The collapse of the distributions of the mean-square streamwise derivative of the velocity fluctuations within the Kármán vortex implies that the velocity field within the vortex tends to be more locally isotropic than the flow field outside the vortex. A possible physical explanation is that the large and small scales of velocity and temperature fields are statistically independent of each other near the Kármán vortex centre, but interact vigorously outside the vortex, especially in the saddle region, due to the action of coherent strain rate.]]> Tue 11 Oct 2022 13:03:27 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:39305 n of the longitudinal velocity increment, (𝛿𝑢), can be described by a simple power-law 𝑟^𝜁𝑛, where the scaling exponent ζ_n depends on n and, except for 𝜁₃(=1), needs to be determined. In this Letter, we show that applying Hölder's inequality to the power-law form (𝛿𝑢)³⎯⎯⎯⎯⎯⎯⎯⎯ ∼(𝑟/𝐿) ^𝜁𝑛 (with 𝑟/𝐿≪1; L is an integral length scale) leads to the following mathematical constraint: 𝜁_2𝑝=𝑝𝜁₂. When we further apply the Cauchy–Schwarz inequality, a particular case of Hölder's inequality, to |(𝛿𝑢)³⎯⎯⎯⎯⎯⎯⎯⎯| with 𝜁₃=1, we obtain the following constraint: 𝜁₂≤2/3. Finally, when Hölder's inequality is also applied to the power-law form (|𝛿𝑢|)³⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ ∼(𝑟/𝐿)^𝜁𝑛 (this form is often used in the extended self-similarity analysis) while assuming 𝜁₃=1, it leads to 𝜁₂=2/3. The present results show that the scaling exponents predicted by the 1941 theory of Kolmogorov in the limit of infinitely large Reynolds number comply with Hölder's inequality. On the other hand, scaling exponents, except for ζ₃, predicted by current small-scale intermittency models do not comply with Hölder's inequality, most probably because they were estimated in finite Reynolds number turbulence. The results reported in this Letter should guide the development of new theoretical and modeling approaches so that they are consistent with the constraints imposed by Hölder's inequality.]]> Tue 09 Aug 2022 11:22:16 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:34526 p*(k*) where Ep and k are the pressure spectrum and the wavenumber, respectively (the symbol * represents the Kolmogorov normalization). Direct numerical simulations of forced HIT suggest that this integral converges toward a constant as the Reynolds number increases.]]> Tue 03 Sep 2019 18:23:29 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:41375 Tue 02 Aug 2022 15:34:25 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:52755 nh-order velocity structure function S_n homogeneous isotropic turbulence is usually represented by S_n ∼ r^ζn, where the spatial separation r lies within the inertial range. The first prediction for ζ_n (i.e. ζ₃ = n/3) was proposed by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941) using a dimensional argument. Subsequently, starting with Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85), models for the intermittency of the turbulent energy dissipation have predicted values of ζ_n that, except for n = 3, differ from n/3. In order to assess differences between predictions of ζ_n, we use the Hölder inequality to derive exact relations, denoted plausibility constraints. We first derive the constraint (p₃ − p₁)ζ_2p2 = (p₃ − p₂)ζ_2p1 + (p₂ − p₁)ζ_2p3 between the exponents ζ_2p, where p₁ ≤ p₂ ≤ p₃ are any three positive numbers. It is further shown that this relation leads to ζ_2p = pζ₂. It is also shown that the relation ζ_n = n/3, which complies with ζ_2p = pζ₂, can be derived from constraints imposed on ζ_n using the Cauchy-Schwarz inequality, a special case of the Hölder inequality. These results show that while the intermittency of ϵ, which is not ignored in the present analysis, is not incompatible with the plausible relation ζ_n = n/3, the prediction ζ_n = n/3 + α_n is not plausible, unless α_n = 0.]]> Thu 26 Oct 2023 09:59:09 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:52749 Thu 26 Oct 2023 09:18:46 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:39648 Thu 16 Jun 2022 15:16:03 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:39635 Thu 16 Jun 2022 13:38:03 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:31548 χ/d = 10, 20 and 40, where χ is the streamwise distance from the cylinder axis and d is the cylinder diameter, with a Reynolds number of 2.5 x 10³ based on the cylinder diameter and the free-stream velocity. A probe consisting of eight hot wires (four X-wires) and four cold wires is used to measure simultaneously the three components of the fluctuating velocity and vorticity vectors, as well as the fluctuating temperature gradient vector at nominally the same point in the plane of the mean shear. It is found that the enstrophy and scalar dissipation spectra collapse approximately at all wavenumbers except around the Kármán vortex street wavenumber for χ/d ≽ 20. The spectral similarity between the streamwise velocity fluctuation u and the passive scalar θ is better than that between the velocity fluctuation vector q and θ. This is closely related to the highly organized lateral velocity fluctuation v in this flow. The present observations are fully consistent with the expectation that small scales of the velocity and temperature fields are more likely to exhibit a close relationship than scales associated with the bulk of the turbulent energy or scalar variance. The variation across the wake of the time scale ratio between scalar and velocity fields is significantly smaller than that of the turbulent Prandtl number.]]> Sat 24 Mar 2018 08:44:26 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9303 Sat 24 Mar 2018 08:41:19 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:8815 Sat 24 Mar 2018 08:38:26 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:6959 Sat 24 Mar 2018 08:38:09 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:6960 Sat 24 Mar 2018 08:38:08 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:8143 Sat 24 Mar 2018 08:36:08 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9626 Sat 24 Mar 2018 08:35:24 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:12474 m dependence of the KH instability frequency (f _KH) with different values of m over different ranges of Re, as reported previously in the literature. However, it is found that this power-law dependence is not exact, and a third-order polynomial dependence appears to fit the data well over the full range of Re. Importantly, it is found that the wake shear-layer instabilities can be grouped into three categories: (1) one with frequencies much smaller than the Bénard–Kármán-vortex shedding frequency, (2) one associated with the vortex shedding and (3) one related to the KH instability. The low-frequency shear-layer instabilities from both sides of the cylinder are in-phase, in contrast to the anti-phase high-frequency KH instabilities. Finally, the observed streamwise decrease in the mean KH frequency provides strong support for the occurrence of vortex pairing in wake shear layers from a circular cylinder, thus implying that both the wake shear layer and a mixing layer develop in similar fashion.]]> Sat 24 Mar 2018 08:16:30 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11425 Sat 24 Mar 2018 08:13:01 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11523 Sat 24 Mar 2018 08:10:22 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:20918 r on the phase ϕ of the CM. This tool allows the dependence of the RM to be followed as a function of the CM dynamics. Scale-by-scale energy budget equations are established on the basis of phase-averaged structure functions. They reveal that energy transfer at a scale r is sensitive to an additional forcing mechanism due to the CM. Second, these concepts are tested using hot-wire measurements in a cylinder wake, in which the CM is characterized by a well-defined periodicity. Because the interaction between large and small scales is most likely enhanced at moderate/low Reynolds numbers, and is also likely to depend on the amplitude of the CM, we choose to test our findings against experimental data at Rλ∼102 and for downstream distances in the range 10≤x/D≤40. The effects of an increasing Reynolds number are also discussed. It is shown that: (i) a simple analytical expression describes the second-order structure functions of the purely CM. The energy of the CM is not associated with any single scale; instead, its energy is distributed over a range of scales. (ii) Close to the obstacle, the influence of the CM is perceptible even at the smallest scales, the energy of which is enhanced when the coherent strain is maximum. Further downstream from the cylinder, the CM clearly affects the largest scales, but the smallest scales are not likely to depend explicitly on the CM. (iii) The isotropic formulation of the RM energy budget compares favourably with experimental results.]]> Sat 24 Mar 2018 08:06:11 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:19088 Sat 24 Mar 2018 08:05:23 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:21391 λ is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30 ≤ R_λ ≤ 400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of ⟨ε⟩ in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.]]> Sat 24 Mar 2018 08:05:03 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:18219 Sat 24 Mar 2018 08:04:39 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:18223 Sat 24 Mar 2018 08:04:39 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:18296 Sat 24 Mar 2018 08:04:25 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:21748 Sat 24 Mar 2018 08:03:33 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:18885 Sat 24 Mar 2018 08:03:11 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:19671 Sat 24 Mar 2018 08:01:13 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:17808 −4, where x₀ is a virtual origin, follows immediately from the variation of the mean velocity, the constancy of the local turbulent intensity and the ratio between the axial and transverse velocity variance. Second, the limit at small separations of the two-point budget equation yields an exact relation illustrating the equilibrium between the skewness of the longitudinal velocity derivative S and the destruction coefficient G of enstrophy. By comparing the latter relation with that for homogeneous isotropic decaying turbulence, it is shown that the approach towards the asymptotic state at infinite Reynolds number of S+2G/Rλ in the jet differs from that in purely decaying turbulence, although +2G/R_λ∝R⁻¹_λ in each case. This suggests that, at finite Reynolds numbers, the transport equation for ϵ¯ imposes a fundamental constraint on the balance between S and G that depends on the type of large-scale forcing and may thus differ from flow to flow. This questions the conjecture that S and G follow a universal evolution with R_λ; instead, S and G must be tested separately in each flow. The implication for the constant C_ϵ2 in the k−ϵ¯ model is also discussed.]]> Sat 24 Mar 2018 07:57:35 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:19119 λ drops below about 20, the Kolmogorov normalised spectra deviate from those at higher R_λ; the deviation increases with decreasing R_λ. It is shown that at R_λ ≃ 20, the contribution of the energy transfer in the scale-by-scale energy budget becomes smaller than the contributions from the viscous and (large-scale) non-homogeneous terms at all scales, but never vanishes, at least for the range of Reynolds investigated here. A phenomenological argument based on the ratio N between the energy-containing timescale and the dissipative range timescale leads to the condition [formula could not be replicated] for KSH1 to hold. The numerical data indicate that N = 5, yielding R_λ ≃ 20, thus confirming our numerical finding. The present results show that KSH1, unlike the second Kolmogorov similarity hypothesis (KSH2,) does not require the existence of an inertial range. While it may seem remarkable that KSH1 is validated at much lower Reynolds numbers than required for KSH2 in grid turbulence (R_λ ≥ 1000,), KSH1 applies to small scales which include both dissipative scales and inertial range (if it exists). One can expect that, as the Reynolds number increases, the dissipative scales should satisfy KSH1 first; then, as the Reynolds number attains very high values, the inertial range is established in conformity with KSH2.]]> Sat 24 Mar 2018 07:55:56 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:19416 nu and 〈θ²〉 ~ (χ - χ₀)^nθ (χ₀ is the virtual origin of the flow) and with the further assumption that the one-point energy and scalar variance budgets are represented closely by a balance between the rates of change of 〈u²〉 and 〈θ²〉 and the corresponding mean energy dissipation rates, the products 〈u²〉λ_u^-2nu and 〈θ²〉λ_θ^-2nθ must remain constant with respect to χ. Here λ_u and λ_θ are the Taylor and Corrsin microscales. This is unambiguously supported by previously available data, as well as new measurements of u and θ made at small Reynolds numbers downstream of three different biplane grids. Implications for invariants based on measured integral length scales of u and θ are also tested after confirming that the dimensionless energy and scalar variance dissipation rate parameters are approximately constant with χ. Since the magnitudes of n_u and n_θ vary from grid to grid and may also depend on the Reynolds number, the Saffman and Corrsin invariants which correspond to a value of -1.2 for n_u and n_θ are unlikely to apply in general. The effect of the Reynolds number on n_u is discussed in the context of published data for both passive and active grids.]]> Sat 24 Mar 2018 07:52:08 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:5137 0.2. Similar results were also observed for second-order structure functions (not shown) for Kolmogorov normalised radius r* < 10. Although, the quality of collapsed is poorer for transverse component, the result highlights that Kolmogorov similarity hypothesis is reasonably well satisfied. However, the suction results shows a significant departure from the no suction case of the Kolmogorov normalised spectra and second-order structure functions for k₁* < 0.2 and r* > 20, respectively. The departure at the larger scales with collapse at the small scales suggests that suction induce a change in the small-scale motion. This is also reflected in the alteration of mean turbulent energy dissipation rate and Taylor microscale Reynolds number. This change is a result of the weakening of the large-scale structures. The effect is increased as the suction rate is increased.]]> Sat 24 Mar 2018 07:49:39 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:30242 n is a positive integer). It is found that the relation M_2n+1(∂u/∂z)∼R⁻¹_λ is supported reasonably well by hot-wire data up to the seventh order (n=3) on the wake centreline, although it is also dependent on the initial conditions. The present relation N3(∂u/∂y)∼R⁻¹_λ is obtained more rigorously than that proposed by Lumley (Phys Fluids 10:855–858, 1967) via dimensional arguments. The effect of the mean shear at locations away from the wake centreline on M_2n+1(∂u/∂z) and N_2n+1(∂u/∂y) is addressed and reveals that, although the non-dimensional shear parameter is much smaller in wakes than in a homogeneous shear flow, it has a significant effect on the evolution of N_2n+1(∂u/∂y) in the direction of the mean shear; its effect on M_2n+1(∂u/∂z) (in the non-shear direction) is negligible.]]> Sat 24 Mar 2018 07:41:58 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26852 iso/⋶ is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of ⋶ due to vortex stretching and the destruction of ⋶ caused by the action of viscosity is governed by the diffusion of ⋶ by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative S₁,₁ and the destruction coefficient G of enstrophy in different flows, thus resulting in non-universal approaches of S₁,₁ towards a constant value as the Taylor microscale Reynolds number, R_λ, increases. For example, the approach is slower for the measured values of S₁,₁ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for S₁,₁ collected in different flows strongly suggest that, in each flow, the magnitude of S₁,₁ is bounded, the value being slightly larger than 0.5.]]> Sat 24 Mar 2018 07:41:48 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26851 Sat 24 Mar 2018 07:41:47 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26107 -4 (x is the streamwise direction). It is important to stress that this derivation does not use the constancy of the non-dimensional dissipation rate parameter C_∊ = ⋷u^'3/L_u (L_u and u' are the integral length scale and root mean square of the longitudinal velocity fluctuation respectively). We show, in fact, that the constancy of C_∊ is simply a consequence of complete SP (i.e. SP at all scales of motion). The significance of the analysis relates to the fact that the SP requirements for the mean velocity and mean turbulent kinetic energy (i.e. U ~ x^-1 and k ~ x^-2 respectively) are derived without invoking the transport equations for and . Experimental hot-wire data along the axis of a turbulent round jet show that, after a transient downstream distance which increases with Reynolds number, the turbulence statistics comply with complete SP. For example, the measured ⋷ agrees well with the SP prediction, i.e. ⋷ ~ x^-4, while the Taylor microscale Reynolds number Reλ remains constant. The analytical expression for the prefactor A_∊ for ⋷ ~ (x - X₀)^-4(where x₀ is a virtual origin), first developed by Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) and rederived here solely from the SP analysis of the s.b.s. energy budget, is validated and provides a relatively simple and accurate method for estimating ⋷ along the axis of a turbulent round jet.]]> Sat 24 Mar 2018 07:39:53 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:27364 Sat 24 Mar 2018 07:36:42 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:27921 Sat 24 Mar 2018 07:36:07 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:27919 J. Fluid Mech., vol. 250, 1993, pp. 651-668) or MA, the new model provides a more detailed description of the role the rib-like structures undertake in transporting heat and momentum, and also underlines the importance of the upstream half of the spanwise vortex rollers, instead of only one quadrant of these rollers, as in the MA model, in diffusing heat out of the vortex.]]> Sat 24 Mar 2018 07:36:07 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:30078 Sat 24 Mar 2018 07:31:16 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:30203 q² diffusion term is negligible compared to advection term along the axis and the advection and energy dissipation terms dominate the budget. However, in the CC wake, aside from the advection and energy dissipation terms, the q² diffusion term also contributes significantly to the budget. At the region close to the centreline, the gain of the energy due to the contributions from the advection and diffusion terms is equal to the loss due to the isotropic dissipation, indicating that the isotropic dissipation rate ε iso is a good surrogate of the mean TKE dissipation rate ε.]]> Sat 24 Mar 2018 07:31:04 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:25900 isoalong the centreline in the far-wake of a circular cylinder is derived by applying the limit at small separations to the two-point energy budget equation. It is found that the imbalance between the production and the destruction of ⋶_iso, respectively due to vortex stretching and viscosity, is governed by both the streamwise advection and the lateral turbulent diffusion (the former contributes more to the budget than the latter). This imbalance differs intrinsically from that in other flows, e.g. grid turbulence and the flow along the centreline of a fully developed channel, where either the streamwise advection or the lateral turbulent diffusion of ⋶_iso governs the imbalance. More importantly, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative S and the destruction coefficient of enstrophy G. This results in a non-universal approach of S towards a constant value as the Taylor microscale Reynolds number R_λ increases. For the present flow, the magnitude of S decreases initially (R_λ≤40) before increasing (R_λ>40) towards this constant value. The constancy of S at large Rλ violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) but is consistent with the original similarity hypotheses (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941b, pp. 299-303 (see also 1991 Proc. R. Soc. Lond. A, vol. 434, pp. 9-13)) , and, more importantly, with the almost completely self-preserving nature of the plane far-wake.]]> Sat 24 Mar 2018 07:28:16 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:28197 τ and the error in the origin, d₀, which are the two prominent issues that surround rough-wall boundary layers. In addition, velocity measurements are taken at several streamwise locations using hot-wire anemometry to obtain C_f from the momentum integral equation. Results showed that both methods give consistent values for U_τ, indicating that the contribution of the viscous drag over this rough wall is negligible. This supports the results of Perry et al. (J Fluid Mech 177:437–466, 1969) and Antonia and Luxton (J Fluid Mech 48(04):721–761, 1971) in a boundary layer and of Leonardi et al. (2003) in a channel flow but does not agree with those of Furuya et al. (J Fluids Eng 98(4):635–643, 1976). The results show that both U_τ and d₀ can be unambiguously measured on this particular rough wall. This paves the way for a proper comparison between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.]]> Sat 24 Mar 2018 07:23:52 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:28198 τ) and the error in the origin. It is found that U_τ remained practically constant in the streamwise direction suggesting that the boundary layer over this surface is evolving in a self-similar manner. This is further corroborated by the similarity observed at all scales of motion, in the region 0.2≤y/δ≤0.6, as reflected in the constancy of Reynolds number (R_λ) based on Taylor's microscale and the collapse of Kolmogorov normalized velocity spectra at all wavenumbers. A scale-by-scale budget for the second-order structure function 〈(δu)²〉 (δu=u(x+r)-u(x), where u is the fluctuating streamwise velocity component and r is the longitudinal separation) is carried out to investigate the energy distribution amongst different scales in the boundary layer. It is found that while the small scales are controlled by the viscosity, intermediate scales over which the transfer of energy (or 〈(δu)³〉) is important are affected by mechanisms induced by the large-scale inhomogeneities in the flow, such as production, advection and turbulent diffusion. For example, there are non-negligible contributions from the large-scale inhomogeneity to the budget at scales of the order of λ, the Taylor microscale, in the region of the boundary layer extending from y/δ=0.2 to 0.6 (δ is the boundary layer thickness).]]> Sat 24 Mar 2018 07:23:52 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24369 e), when the mean viscous stress is zero or negligible compared to the form drag across the entire boundary layer. In this case, the velocity scale u∗ must be constant, the length scale l should vary linearly with the streamwise distance x and the roughness height k must be proportional to l. Although this result is consistent with that of Rotta (Prog. Aeronaut. Sci., vol. 2 (1), 1962, pp. 1–95), it is derived in a more rigorous manner than the method employed by Rotta. Further, it is noted that complete SP is not possible in a smooth-wall ZPG turbulent boundary layer. The SP conditions are tested against published experimental data on both a smooth wall (Kulandaivelu, 2012, PhD thesis, The University of Melbourne) and a rough wall, where the roughness height increases linearly with x (Kameda et al., J. Fluid Sci. Technol., vol. 3 (1), 2008, pp. 31–42). Complete SP in a ZPG rough-wall turbulent boundary layer seems indeed possible when k∝x.]]> Sat 24 Mar 2018 07:16:18 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:22847 Re_λ to assess the appropriateness of the commonly used power-law decay for the mean turbulent kinetic energy (e.g. k ∼ xⁿ, with n ⩽−1). It is found that in the region outside the initial and final periods of decay, which we designate a transition region, a power law with a constant exponent n cannot describe adequately the decay of turbulence from its initial to final stages. One is forced to use a family of power laws of the form xⁿⁱ, where n_i is a different constant over a portion i of the decay time during the decay period. Accordingly, it is currently not possible to determine whether any grid-generated turbulence reported in the literature decays according to Saffman or Batchelor because the reported data fall in the transition period where n differs from its initial and final values. It is suggested that a power law of the form k ∼ x^ninit+m(x), where m(x) is a continuous function of x, could be used to describe the decay from the initial period to the final stage. The present results, which corroborate the numerical simulations of decaying homogeneous isotropic turbulence of Orlandi & Antonia (J. Turbul., vol. 5, 2004, doi:10.1088/1468-5248/5/1/009) and Meldi & Sagaut (J. Turbul.,vol. 14, 2013, pp. 24–53), show that the values of n reported in the literature, and which fall in the transition region, have been mistakenly assigned to the initial stage of decay.]]> Sat 24 Mar 2018 07:16:03 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24300 Sat 24 Mar 2018 07:14:38 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45528 Mon 31 Oct 2022 14:45:03 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:47777 Mon 30 Jan 2023 09:56:24 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:43578 Cε is measured in a fully rough wall turbulent boundary layer at several Reynolds numbers using hot-wire anemometry. The study aims to determine the dependence of Cε = ̅εL/u′³ on the distance from the wall and the Reynolds number. The results shows that Cε decreases as the distance from the wall increases and reaches a minimum value, which appears to be independent of the Reynolds number. Further, this value, which is about 0.40.5, is the same as in homogeneous isotropic turbulence at high Reynolds numbers. This lends support to the possibility that a universal value for Cε at large Reynolds numbers cannot be ruled out.]]> Mon 26 Sep 2022 10:12:09 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:36517 Mon 25 May 2020 14:14:48 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:32998 Exp. Fluids, vol. 53, 2012, pp. 1005–1013) based on the universality of the dissipation range of the longitudinal velocity spectrum normalized by the Kolmogorov scales also applies in the present flow despite the strong perturbation from the Kármán vortex street and violation of local isotropy at small x/d. The appropriateness of the spectral chart method is consistent with Antonia et al.’s (Phys. Fluids, vol. 26, 2014, 45105) observation that the two major assumptions in Kolmogorov’s first similarity hypothesis, i.e. very large Taylor microscale Reynolds number and local isotropy, can be significantly relaxed. The data also indicate that vorticity spectra are more sensitive, when testing the first similarity hypothesis, than velocity spectra. They also reveal that the velocity derivatives δu/δy and δv/δx play an important role in the interaction between large and small scales in the present flow. The phase-averaged data indicate that the energy dissipation is concentrated mostly within the coherent spanwise vortex rollers, in contrast with the model of Hussain (J. Fluid Mech., vol. 173, 1986, pp. 303–356) and Hussain & Hayakawa (J. Fluid Mech., vol. 180, 1987, p. 193), who conjectured that it resides mainly in regions of strong turbulent mixing.]]> Mon 20 Aug 2018 15:42:53 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:54720 Mon 11 Mar 2024 11:59:05 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:47907 Mon 06 Feb 2023 14:48:54 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:41306 Mon 01 Aug 2022 12:23:31 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:41272 Mon 01 Aug 2022 09:56:30 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45502 Fri 28 Oct 2022 16:07:26 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:52689 Fri 20 Oct 2023 11:08:13 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:28196 0.95−y_0.10) is in the range of 6560 ≤ Re_δ(=U_sδ/ν)≤ 12540, where U_s is the velocity difference between the high and low speeds. The measurements show that the mixing layer thickness δ grows linearly with x. The mean velocity profiles (U) collapse relatively well at all stations when the distance y is normalised by the variable η(=(y−y_0.50)/δ). Further, the Reynolds stress profiles at x/M₁=60 and 65 collapse well suggesting that the decaying turbulent in the SML has reached self-preservation.]]> Fri 14 Jul 2017 14:28:59 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:27672 θ is derived by applying the limit at small separations to the generalized form of Yaglom's equation in two types of flows, those dominated mainly by a decay of energy in the streamwise direction and those which are forced, through a continuous injection of energy at large scales. In grid turbulence, the imbalance between the production of ∈_θ due to stretching of the temperature field and the destruction of ∈_θ by the thermal diffusivity is governed by the streamwise advection of ∈_θ by the mean velocity. This imbalance is intrinsically different from that in stationary forced periodic box turbulence (or SFPBT), which is virtually negligible. In essence, the different types of imbalance represent different constraints imposed by the large-scale motion on the relation between the so-called mixed velocity-temperature derivative skewness S_T and the scalar enstrophy destruction coefficient G_θ in different flows, thus resulting in non-universal approaches of S_T towards a constant value as Re_λ increases. The data for S_T collected in grid turbulence and in SFPBT indicate that the magnitude of S,sub>T is bounded, this limit being close to 0.5.]]> Fri 10 Nov 2023 15:44:15 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:34584 Fri 10 Nov 2023 15:41:28 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:52774 Fri 10 Nov 2023 15:39:09 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:37033 θ, the mean dissipation rate of θ̅²/2, where θ̅² is the temperature variance. The analytical approach follows that of Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for ϵ_κ, the mean turbulent kinetic energy dissipation rate, using the transport equation for (δu)², the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as: η, λ, λθ, R_U, R_Θ (all representing characteristic length scales), the mean temperature excess Θ₀, the mixed velocity–temperature moments uθ², vθ² and θ² and ∈_θ. Simple models are proposed for uθ² and vθ² in order to derive an analytical expression for A_∈θ, the prefactor of the power law describing the streamwise evolution of ∈θ. Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.]]> Fri 07 Aug 2020 10:22:14 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:34634 𝜖 =̅∈L/u'³(where 𝜖 is the mean turbulent kinetic energy dissipation rate, is an integral length scale and is the velocity root-mean-square) is investigated in decaying turbulence. Expressions for C_𝜖 in homogeneous isotropic turbulent (HIT), as approximated by grid turbulence, and in local HIT, as on the axis of the far field of a turbulent round jet, are developed from the Navier–Stokes equations within the framework of a scale-by-scale energy budget. The analysis shows that when turbulence decays/evolves in compliance with self-preservation (SP), C_𝜖 remains constant for a given flow condition, e.g. a given initial Reynolds number. Measurements in grid turbulence, which does not satisfy SP, and on the axis in the far field of a round jet, which does comply with SP, show that C_𝜖 decreases in the former case and remains constant in the latter, thus supporting the theoretical results. Further, while C_𝜖 can remain constant during the decay for a given initial Reynolds number, both the theory and measurements show that it decreases towards a constant, C_𝜖, as Re_𝜆 increases. This trend, in agreement with existing data, is not inconsistent with the possibility that C_𝜖 tends to a universal constant.]]> Fri 05 Apr 2019 15:31:13 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45753 Fri 04 Nov 2022 10:40:56 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45738 Fri 04 Nov 2022 10:06:08 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45739 Fri 04 Nov 2022 10:06:06 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:45709 Fri 04 Nov 2022 09:03:17 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:50758 Fri 04 Aug 2023 12:16:51 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:49836 Fri 02 Jun 2023 15:57:06 AEST ]]>