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L. Djenidi - One of the best experts on this subject based on the ideXlab platform.
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power law exponent in the transition period of decay in Grid Turbulence
Journal of Fluid Mechanics, 2015Co-Authors: L. Djenidi, Md Kamruzzaman, R. A. AntoniaAbstract:Hot-wire measurements are carried out in Grid-generated Turbulence at moderate to low Taylor microscale Reynolds number to assess the appropriateness of the commonly used power-law decay for the mean turbulent kinetic energy (e.g. , with ). 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 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 , where is a different constant over a portion 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 differs from its initial and final values. It is suggested that a power law of the form , where is a continuous function of , 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 reported in the literature, and which fall in the transition region, have been mistakenly assigned to the initial stage of decay.
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transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow
Journal of Fluid Mechanics, 2015Co-Authors: S. L. Tang, R. A. Antonia, Tongming Zhou, L. Djenidi, Luminita Danaila, Y ZhouAbstract:The transport equation for the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}$ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}_{iso}/\overline{{\it\epsilon}}$ 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 $\overline{{\it\epsilon}}$ due to vortex stretching and the destruction of $\overline{{\it\epsilon}}$ caused by the action of viscosity is governed by the diffusion of $\overline{{\it\epsilon}}$ 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 $S_{1,1}$ and the destruction coefficient $G$ of enstrophy in different flows, thus resulting in non-universal approaches of $S_{1,1}$ towards a constant value as the Taylor microscale Reynolds number, $R_{{\it\lambda}}$ , increases. For example, the approach is slower for the measured values of $S_{1,1}$ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for $S_{1,1}$ collected in different flows strongly suggest that, in each flow, the magnitude of $S_{1,1}$ is bounded, the value being slightly larger than 0.5.
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a general self preservation analysis for decaying homogeneous isotropic Turbulence
Journal of Fluid Mechanics, 2015Co-Authors: L. DjenidiAbstract:A general framework of self-preservation (SP) is established, based on the transport equation of the second-order longitudinal velocity structure function in decaying homogeneous isotropic Turbulence (HIT). The analysis introduces the skewness of the longitudinal velocity increment, ( and are space increment and time), as an SP controlling parameter. The present SP framework allows a critical appraisal of the specific assumptions that have been made in previous SP analyses. It is shown that SP is achieved when varies in a self-similar manner, i.e. where is a scaling length, and and are dimensionless functions of time and , respectively. When is constant, can be identified with the Kolmogorov length scale , even when the Reynolds number is relatively small. On the other hand, the Taylor microscale is a relevant SP length scale only when certain conditions are met. The decay law for the turbulent kinetic energy ( ) ensuing from the present SP is a generalization of the existing laws and can be expressed as , where is a constant representing the energy of the motions whose scales are excluded from the SP range of scales. When , SP is achieved at all scales of motion and becomes a relevant scaling length together with . The analysis underlines the relation between the initial conditions and the power-law exponent and also provides a link between them. In particular, an expression relating to the initial values of the scaling length and velocity is developed. Finally, the present SP analysis is consistent with both experimental Grid Turbulence data and the eddy-damped quasi-normal Markovian numerical simulation of decaying HIT by Meldi & Sagaut (J. Turbul., vol. 14, 2013, pp. 24–53).
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karman howarth closure equation on the basis of a universal eddy viscosity
Physical Review E, 2013Co-Authors: Fabien Thiesset, R. A. Antonia, Luminita Danaila, L. DjenidiAbstract:This Rapid Communication presents a simple closure for the two-point correlation transport equation in decaying isotropic Turbulence. It relies essentially on an eddy viscosity ${\ensuremath{\nu}}_{t}$ 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.
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a spectral chart method for estimating the mean turbulent kinetic energy dissipation rate
Experiments in Fluids, 2012Co-Authors: L. Djenidi, R. A. AntoniaAbstract:We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate \( \left\langle \varepsilon \right\rangle \) in a variety of turbulent flows. The method relies on the validity of the first similarity hypothesis of Kolmogorov (C R (Doklady) Acad Sci R R SS, NS 30:301–305, 1941) (or K41) which implies that spectra of velocity fluctuations scale on the kinematic viscosity ν and \( \left\langle \varepsilon \right\rangle \) at large Reynolds numbers. However, the evidence, based on the DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a −5/3 inertial subrange only when the Taylor microscale Reynods number Rλ 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 ≤ Rλ ≤ 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 \( \left\langle \varepsilon \right\rangle \) in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.
R. A. Antonia - One of the best experts on this subject based on the ideXlab platform.
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power law exponent in the transition period of decay in Grid Turbulence
Journal of Fluid Mechanics, 2015Co-Authors: L. Djenidi, Md Kamruzzaman, R. A. AntoniaAbstract:Hot-wire measurements are carried out in Grid-generated Turbulence at moderate to low Taylor microscale Reynolds number to assess the appropriateness of the commonly used power-law decay for the mean turbulent kinetic energy (e.g. , with ). 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 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 , where is a different constant over a portion 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 differs from its initial and final values. It is suggested that a power law of the form , where is a continuous function of , 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 reported in the literature, and which fall in the transition region, have been mistakenly assigned to the initial stage of decay.
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transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow
Journal of Fluid Mechanics, 2015Co-Authors: S. L. Tang, R. A. Antonia, Tongming Zhou, L. Djenidi, Luminita Danaila, Y ZhouAbstract:The transport equation for the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}$ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}_{iso}/\overline{{\it\epsilon}}$ 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 $\overline{{\it\epsilon}}$ due to vortex stretching and the destruction of $\overline{{\it\epsilon}}$ caused by the action of viscosity is governed by the diffusion of $\overline{{\it\epsilon}}$ 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 $S_{1,1}$ and the destruction coefficient $G$ of enstrophy in different flows, thus resulting in non-universal approaches of $S_{1,1}$ towards a constant value as the Taylor microscale Reynolds number, $R_{{\it\lambda}}$ , increases. For example, the approach is slower for the measured values of $S_{1,1}$ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for $S_{1,1}$ collected in different flows strongly suggest that, in each flow, the magnitude of $S_{1,1}$ is bounded, the value being slightly larger than 0.5.
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karman howarth closure equation on the basis of a universal eddy viscosity
Physical Review E, 2013Co-Authors: Fabien Thiesset, R. A. Antonia, Luminita Danaila, L. DjenidiAbstract:This Rapid Communication presents a simple closure for the two-point correlation transport equation in decaying isotropic Turbulence. It relies essentially on an eddy viscosity ${\ensuremath{\nu}}_{t}$ 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.
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a spectral chart method for estimating the mean turbulent kinetic energy dissipation rate
Experiments in Fluids, 2012Co-Authors: L. Djenidi, R. A. AntoniaAbstract:We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate \( \left\langle \varepsilon \right\rangle \) in a variety of turbulent flows. The method relies on the validity of the first similarity hypothesis of Kolmogorov (C R (Doklady) Acad Sci R R SS, NS 30:301–305, 1941) (or K41) which implies that spectra of velocity fluctuations scale on the kinematic viscosity ν and \( \left\langle \varepsilon \right\rangle \) at large Reynolds numbers. However, the evidence, based on the DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a −5/3 inertial subrange only when the Taylor microscale Reynods number Rλ 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 ≤ Rλ ≤ 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 \( \left\langle \varepsilon \right\rangle \) in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.
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Spatial resolution of PIV for the measurement of Turbulence
Experiments in Fluids, 2007Co-Authors: Pierre Lavoie, G. P. Romano, Fabrizio Di Gregorio, R. A. AntoniaAbstract:Recent technological advancements have made the use of particle image velocimetry (PIV) more widespread for studying turbulent flows over a wide range of scales. Although PIV does not threaten to make obsolete more mature techniques, such as hot-wire anemometry (HWA), it is justifiably becoming an increasingly important tool for Turbulence research. This paper assesses the ability of PIV to resolve all relevant scales in a classical turbulent flow, namely Grid Turbulence, via a comparison with theoretical predictions as well as HWA measurements. Particular attention is given to the statistical convergence of mean turbulent quantities and the spatial resolution of PIV. An analytical method is developed to quantify and correct for the effect of the finite spatial resolution of PIV measurements. While the present uncorrected PIV results largely underestimate the mean turbulent kinetic energy and energy dissipation rate, the corrected measurements agree to a close approximation with the HWA data. The transport equation for the second-order structure function in Grid Turbulence is used to establish the range of scales affected by the limited resolution. The results show that PIV, due to the geometry of its sensing domain, must meet slightly more stringent requirements in terms of resolution, compared with HWA, in order to provide reliable measurements in Turbulence.
Luminita Danaila - One of the best experts on this subject based on the ideXlab platform.
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transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow
Journal of Fluid Mechanics, 2015Co-Authors: S. L. Tang, R. A. Antonia, Tongming Zhou, L. Djenidi, Luminita Danaila, Y ZhouAbstract:The transport equation for the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}$ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate $\overline{{\it\epsilon}}_{iso}/\overline{{\it\epsilon}}$ 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 $\overline{{\it\epsilon}}$ due to vortex stretching and the destruction of $\overline{{\it\epsilon}}$ caused by the action of viscosity is governed by the diffusion of $\overline{{\it\epsilon}}$ 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 $S_{1,1}$ and the destruction coefficient $G$ of enstrophy in different flows, thus resulting in non-universal approaches of $S_{1,1}$ towards a constant value as the Taylor microscale Reynolds number, $R_{{\it\lambda}}$ , increases. For example, the approach is slower for the measured values of $S_{1,1}$ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for $S_{1,1}$ collected in different flows strongly suggest that, in each flow, the magnitude of $S_{1,1}$ is bounded, the value being slightly larger than 0.5.
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karman howarth closure equation on the basis of a universal eddy viscosity
Physical Review E, 2013Co-Authors: Fabien Thiesset, R. A. Antonia, Luminita Danaila, L. DjenidiAbstract:This Rapid Communication presents a simple closure for the two-point correlation transport equation in decaying isotropic Turbulence. It relies essentially on an eddy viscosity ${\ensuremath{\nu}}_{t}$ 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.
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Similarity of energy structure functions in decaying homogeneous isotropic Turbulence
Journal of Fluid Mechanics, 2003Co-Authors: Robert A. Antonia, Tongming Zhou, R. J. Smalley, Fabien Anselmet, Luminita DanailaAbstract:An equilibrium similarity analysis is applied to the transport equation for $\langle(\delta q)^{2}\rangle$ (${\equiv}\,\langle(\delta u)^{2}\rangle + \langle(\delta v)^{2}\rangle + \langle(\delta w)^{2}\rangle$), the turbulent energy structure function, for decaying homogeneous isotropic Turbulence. A possible solution requires that the mean energy $\langle q^{2}\rangle$ decays with a power-law behaviour ($\langle q^{2}\rangle\,{\sim}\,x^{m}$), and the characteristic length scale, which is readily identifiable with the Taylor microscale, varies as $x^{1/2}$. This solution is identical to that obtained by George (1992) from the spectral energy equation. The solution does not depend on the actual magnitude of the Taylor-microscale Reynolds number $R_{\lambda}$ (${\sim}\,{\langle q^{2}\rangle}^{1/2} \lambda/\nu$); $R_{\lambda}$ should decay as $x^{(m+1)/2}$ when $m < -1$. The solution is tested at relatively low $R_{\lambda}$ against Grid Turbulence data for which $m \simeq -1.25$ and $R_{\lambda}$ decays as $x^{-0.125}$. Although homogeneity and isotropy are poorly approximated in this flow, the measurements of $\langle(\delta q)^{2}\rangle$ and, to a lesser extent, $\langle(\delta u)(\delta q)^{2}\rangle$, satisfy similarity reasonably over a significant range of $r/\lambda$, where $r$ is the streamwise separation across which velocity increments are estimated. For this range, a similarity-based calculation of the third-order structure function $\langle(\delta u)(\delta q)^{2}\rangle$ is in reasonable agreement with measurements. Kolmogorov-normalized distributions of $\langle(\delta q)^{2}\rangle$ and $\langle(\delta u)(\delta q)^{2}\rangle$ collapse only at small $r$. Assuming homogeneity, isotropy and a Batchelor-type parameterization for $\langle(\delta q)^{2}\rangle$, it is found that $R_{\lambda}$ may need to be as large as $10^{6}$ before a two-decade inertial range is observed.
Hermann F Fasel - One of the best experts on this subject based on the ideXlab platform.
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effect of free stream Turbulence on the structure and dynamics of laminar separation bubbles
53rd AIAA Aerospace Sciences Meeting 2015, 2015Co-Authors: Shirzad Hosseinverdi, Hermann F FaselAbstract:Laminar separation is always associated with considerable unsteadiness. This unsteadiness is caused by large coherent structures that are a consequence of hydrodynamic instability mechanisms of the mean flow. The mean-flow topology and unsteady behavior of laminar separation bubbles (LSB) is in fact mainly governed by instability and transition. In this paper, laminar separation bubbles, which are generated on a flat plate by imposing a streamwise adverse pressure gradient, are investigated by means of Direct Numerical Simulations (DNS). The streamwise pressure gradient for the DNS is chosen such that the inviscid wall pressure distribution, as reported in the Gaster 1 experimental series I, case IV, is closely matched. This case was classified as a “short” laminar separation bubble. The timeaveraged flow field obtained from the DNS with no external disturbances introduced (no freestream Turbulence), reveals that the bubble is longer than observed in the experiments. In fact, the bubble obtained in the simulations appeared to be a “long” bubble. This was confirmed by comparing the simulation results with the measurements by Gaster 1 for a long bubble. The discrepancy between the numerical simulations and experiments is possibly due to an earlier onset of transition in the experiments. In the present simulations, instead of forcing with random disturbances to promote transition, isotropic Grid Turbulence, which was modeled using a superposition of eigenmodes from the continuous spectrum of the Orr-Sommerfeld and Squire operators is introduced at the inflow boundary. It was observed that as the freestream Turbulence (FST) intensity was increased, the bubble became smaller. The separation bubble was in fact shortened from both sides (separation and reattachment sides) in the presence of free-stream Turbulence. Comparing the wall pressure distribution for 0.2% freestream Turbulence with Gaster 1 experiment revealed that then the bubble could be classified as a “short” bubble. Based on the simulations performed, FST can change a separation bubbles form “long” to “short”. In order to investigate bubble “bursting”, the development of bubble, that had became short due to FST, was simulated after the FST was turned-off. The short bubble grew for a short period of time. Surprisingly however, it did not return to the original, state without FST.
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direct numerical simulations of the effect of free stream Turbulence on long laminar separation bubbles
42nd AIAA Fluid Dynamics Conference and Exhibit 2012, 2012Co-Authors: Shirzad Hosseinverdi, Wolfgang Balzer, Hermann F FaselAbstract:Laminar separation bubbles on a flat plate boundary layer in the presence of freestream Turbulence (FST) were investigated by means of Direct Numerical Simulations (DNS). A suction/blowing velocity distribution was applied along the free-stream boundary of the computational domain to induce separation on the flat plate. For numerically generating free-stream Turbulence, isotropic Grid Turbulence, which is obtained from a superposition of eigenmodes from the continuous spectrum of OrrSommerfeld and Squire Equations, was introduced at the inflow boundary. The effect of the spanwise extent of the computational domain was investigated by carrying out computations with two different spanwise domain widths. The main characteristics of the separation bubble, such as the bubble length and the skin-friction distribution were very similar for both spanwise domain sizes. However, for the wider domain the 2-D “rollers” were modulated in the spanwise direction and broke up earlier than for the narrow domain. For the narrow domain counter-rotating streamwise vortices appeared (“braids”). Detailed numerical simulations were performed to investigate the effect of the free-stream Turbulence energy spectrum. It was found that the transition location was essentially independent of the integral length scale of the free-stream Turbulence. Also, the dependence of the separation length on the integral length scale was found to be very weak for the range of length scales considered in our studies. In contrast, the separation length was significantly reduced already for relatively low free-stream Turbulence intensity (0.1%) when compared to the baseline case with zero FST. When the FST was increased further the length and height of the bubble continued to decrease. Instantaneous flow field visualizations revealed that the spanwise coherence of the dominant 2D structures was weakened with increasing FST intensity. In addition, proper orthogonal decomposition (POD) analyses of the instantaneous flow data revealed that streamwise “vortical” structures became dominant for high FST levels. Based on a detailed analysis of the time-dependent flow field and a comparison between DNS results and linear stability theory (LST) calculations, it was found that for freestream Turbulence intensities up to 2%, transition in the bubble was still due to an inviscid (Kelvin-Helmholtz) instability of the inflectional velocity profile in the separated flow region, and not due to nonlinear bypass mechanisms.
Paolo Burattini - One of the best experts on this subject based on the ideXlab platform.
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power law of decaying homogeneous isotropic Turbulence at low reynolds number
Physical Review E, 2006Co-Authors: Paolo Burattini, Philippe Lavoie, Amit Agrawal, L. DjenidiAbstract:We focus on an estimate of the decay exponent $(m)$ in the initial period of decay of homogeneous isotropic Turbulence at low Taylor microscale Reynolds number ${R}_{\ensuremath{\lambda}}$ $(\ensuremath{\simeq}20--50)$. Lattice Boltzmann simulations in a periodic box of ${256}^{3}$ points are performed and compared with measurements in Grid Turbulence at similar ${R}_{\ensuremath{\lambda}}$. Good agreement is found between measured and calculated energy spectra. The exponent $m$ is estimated in three different ways: from the decay of the turbulent kinetic energy, the decay of the mean energy dissipation rate, and the rate of growth of the Taylor microscale. Although all estimates are close, as prescribed by theory, that from the Taylor microscale has the largest variability. It is then suggested that the virtual origin for the decay rate be determined from the Taylor microscale, but the actual value of $m$ be estimated from the decay rate of the kinetic energy. The dependence of $m$ on ${R}_{\ensuremath{\lambda}}(0)$ (the value of ${R}_{\ensuremath{\lambda}}$ at the beginning of the simulation) is also analyzed, using the present data as well as data from the literature. The results confirmed that $m$ approaches 1, as ${R}_{\ensuremath{\lambda}}(0)$ increases.
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approach to the 4 5 law in homogeneous isotropic Turbulence
Journal of Fluid Mechanics, 2006Co-Authors: Paolo BurattiniAbstract:Kolmogorov's similarity hypotheses and his 4/5 law are valid at very large Reynolds numbers. For flows encountered in the laboratory, the effect of a finite Reynolds number and of the non-stationarity or inhomogeneity associated with the large scales can affect the behaviour of the scales in the inertial range significantly. This paper focuses on the source of inhomogeneity 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. Results based on a parameterization of the second-order velocity structure function indicate that the normalized third-order structure function approaches 4/5 much more rapidly for forced than for decaying Turbulence. This trend is supported by Grid Turbulence measurements and numerical data in a periodic box.
