External Intermittency Research Articles

Self-similarity in over-tripped turbulent boundary-layer flows

The scaling universality of structure functions is studied for artificially thickened turbulent boundary-layer flows in over-tripped impacts by using hot-wire measurement datasets. The self-similarity behaviours in the inner and outer regions are examined from the viewpoint of different flow mechanisms. In the inner region, the relative ratios between structure functions for the energy-containing range of scales exhibit universality behaviour, in accordance with Townsend's attached eddy hypothesis. This universality of the energy-containing range of scales extends further away from the wall by increasing the tripping intensity. On the other hand, the impact of the external intermittency on the self-similarity of small-scale turbulence is examined through the intermittent zone in over-tripped conditions. Towards the boundary-layer edge, the structure functions exhibit a growing departure from self-similarity and analytical prediction, and it is demonstrated that the departure is primarily due to external intermittency. Moreover, based on the conditional statistics concentrated in the turbulent regimes, it is revealed that the small scales in the turbulence regime are homogenized in a self-similar behaviour, which is independent of the current tripping conditions.

Similarity of length scales in high-Reynolds-number wall-bounded flows

The wall dependence of length scales used to describe large- and small-scale structures of turbulence is examined using highly resolved experiments in zero-pressure-gradient turbulent boundary layers and pipe flows spanning the range $2000< Re_\tau <37\ 700$ . Of particular interest is the influence of external intermittency on the scaling of these length scales. It is found that when suitable scaling parameters are selected and external intermittency is accounted for, the dissipative motions follow inner scaling even into the outer-scaled regions of the flow, and that certain large-scale descriptions follow outer scaling even in the inner-scaled regions of the flow. The wall dependence is the same for both internal pipe and external boundary layer flows, and the different length scales can be related to recognizable features in the longitudinal wavenumber spectrum.

Self-similarity of turbulent jet flows with internal and external intermittency

Abstract

On the combined effect of internal and external intermittency in turbulent non-premixed jet flames

This paper analyzes the combined effect of internal intermittency and external intermittency on the dynamics of small-scale turbulent mixing in a turbulent non-premixed jet flame. The phenomenon of external intermittency in turbulent jet flames originates from a very thin layer, known as turbulent/non-turbulent interface, that separates the inner turbulent core from the outer irrotational surrounding fluid. The impact of external intermittency on turbulence is evaluated across the jet flame by the self-similarity scaling of higher-order structure functions of the mixture fraction. It is shown that the scaling of structure functions exhibits a growing departure from the prediction of classical scaling laws toward the edge of the flame. Empirical evidence is provided that this departure is primarily due to external intermittency and the associated break down of self-similarity. External intermittency creates local gradients that are significantly more intense compared to those created by internal intermittency alone. As chemical reactions usually take place in thin layers in the vicinity of the turbulent/non-turbulent interface, an accurate statistical description of these intense events is necessary to predict the turbulence-chemistry interaction. The study is based on data from a highly-resolved direct numerical simulation of a temporally evolving planar jet flame.

Comparison of Different Techniques to Calculate Properties of Atmospheric Turbulence from Low-Resolution Data

In this work we study different techniques to estimate basic properties of turbulence, that is its characteristic velocity and length scale from low-resolution data. The methods are based on statistics of the signals like the velocity spectra, second-order structure function, number of signal’s zero-crossings and the variance of velocity derivative. First, in depth analysis of estimates from artificial velocity time series is performed. Errors due to finite averaging window, finite cut-off frequencies and different fitting ranges are discussed. Next, real atmospheric measurement data are studied. It is demonstrated that differences between results of the methods can indicate deviations from the Kolmogorov’s theory or the presence of external intermittency, that is the existence of alternating laminar/turbulent flow patches.

Estimating Turbulence Kinetic Energy Dissipation Rates in the Numerically Simulated Stratocumulus Cloud-Top Mixing Layer: Evaluation of Different Methods

AbstractIn this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation rate ε from one-dimensional (1D) intersections that resemble experimental series. Results of these estimates are compared with “true” (DNS) values of ε in buoyant and inhomogeneous atmospheric flows. We focus on recently proposed methods of the TKE dissipation-rate retrievals based on zero crossings and recovering the missing part of the spectrum. These methods are tested on fully resolved turbulence fields and compared to standard retrievals from power spectra and structure functions. Anisotropy of turbulence due to buoyancy is shown to influence retrievals based on the vertical velocity component. TKE dissipation-rate estimates from the number of crossings correspond well to spectral estimates. The method based on the recovery of the missing part of the spectrum works best for Pope’s model of the dissipation spectrum and is sensitive to external intermittency. This allows for characterization of external intermittency by the Taylor-to-Liepmann scale ratio. Further improvements of this method are possible when the variance of the velocity derivative is used instead of the number of zero crossings per unit length. In conclusion, the new methods of TKE dissipation-rate retrieval from 1D series provide a valuable complement to standard approaches.

Submeso Motions and Intermittent Turbulence Across a Nocturnal Low-Level Jet: A Self-Organized Criticality Analogy

One of the hallmarks of the stable boundary layer is the switching between turbulent (active) and non-turbulent (passive) states. In very stable conditions, the boundary layer becomes layered with fully-developed turbulence confined to a shallow region near the surface. In the quiescent region above this near-surface layer, the turbulence is weak, intermittent and detached from the ground. These conditions promote the development of a low-level jet that re-energizes the turbulence through an elevated shear layer. The Monin–Obukhov similarity theory fails in the layered stable boundary layer thereby making the quantification of mixing and transport properties challenging for numerical models. In the present study, multi-level time series from a tall (140 m) meteorological tower are analyzed using the telegraphic approximation to investigate analogies with a general class of intermittency models that include self-organized criticality. The analogy between turbulence and self-organized criticality is restricted to clustering properties of sign changes of flow variables for describing switching between turbulent and non-turbulent states. The telegraphic approximation provides a new perspective on clustering and on external and internal intermittency for periods dominated by turbulent motions, a low-level jet and submeso motions. Some of these periods are characterized by the absence of turbulence but occasionally punctuated by bursts of intermittent turbulent events. The switching probability of active–inactive states and the lifetimes of inactive states (related to intermittent turbulent bursts) show evidence of self-organized-criticality like behaviour in terms of scaling laws. The coexistence of self-organized criticality and intermittent turbulence may offer new perspectives on the genesis of scaling laws and similarity arguments, thereby improving the performance of numerical models in the stable boundary layer.

External intermittency compensation of dissipation scale distributions in a turbulent boundary layer

We investigate the effect of external intermittency on dissipation scales in turbulent boundary layer flow at $R\phantom{\rule{0}{0ex}}{e}_{\ensuremath{\tau}}\ensuremath{\approx}1000$ using a single hot wire probe for one point longitudinal velocity measurements. We find improved scaling universality by accounting for external intermittency throughout the flow.

Analyses of external and global intermittency in the logarithmic layer of Ekman flow

Existence of non-turbulent flow patches in the vicinity of the wall of a turbulent flow is known as global intermittency. Global intermittency challenges the conventional statistics approach when describing turbulence in the inner layer and calls for the use of conditional statistics. We extend the vorticity-based conditioning of a flow to turbulent and non-turbulent sub-volumes by a high-pass filter operation. This modified method consistently detects non-turbulent flow patches in the outer and inner layers for stratifications ranging from the neutral limit to extreme stability, where the flow is close to a complete laminarization. When applying this conditioning method to direct numerical simulation data of stably stratified Ekman flow, we find the following. First, external intermittency has a strong effect on the logarithmic law for the mean velocity in Ekman flow under neutral stratification. If instead of the full field, only turbulent sub-volumes are considered, the data fit an idealized logarithmic velocity profile much better; in particular, a problematic dip in the von Kármán measure$\unicode[STIX]{x1D705}$in the surface layer is decreased by approximately 50 % and our data only support the reduced range$0.41\lesssim \unicode[STIX]{x1D705}\lesssim 0.43$. Second, order-one changes in turbulent quantities under strong stratification can be explained by a modulation of the turbulent volume fraction rather than by a structural change of individual turbulence events; within the turbulent fraction of the flow, the character of individual turbulence events measured in terms of turbulence dissipation rate or variance of velocity fluctuations is similar to that under neutral stratification.

Reply to "Comment on 'Statistical symmetries of the Lundgren-Monin-Novikov hierarchy' ".

In this Reply we respond to the criticism of Frewer et al. presented in the Comment on "Statistical symmetries of the Lundgren-Monin-Novikov hierarchy" by Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)]. We discuss physical interpretation of the statistical symmetries, and respond to criticism on the violation of the causality principle. We derive the Lundgren-Monin-Novikov equations for a flow with boundaries. Last, we stress that our work addressed the phenomenon of "external intermittency" (separation between laminar and turbulent flow), and not "internal intermittency" (strong fluctuations at small scales).

Global Intermittency and Collapsing Turbulence in the Stratified Planetary Boundary Layer

Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as $$\beta \approx 5.7$$ in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.

Effects of external intermittency and mean shear on the spectral inertial-range exponent in a turbulent square jet

This study investigates by experiment the dependence of the inertial-range exponent m of the streamwise velocity spectrum on the external intermittency factor γ (≡ the fraction of time the flow is fully turbulent) and the mean shear S in a turbulent square jet. Velocity measurements were made using hot-wire anemometry in the jet at 15 < x/D(e) < 40, where D(e) denotes the exit equivalent diameter, and for an exit Reynolds number of Re = 50,000. The Taylor microscale Reynolds number R(λ) varies from about 70 to 450 in the present study. The TERA (turbulent energy recognition algorithm) method proposed by Falco and Gendrich [in Near-Wall Turbulence: 1988 Zoran Zariç Memorial Conference, edited by S. J. Kline and N. H. Afgan (Hemisphere Publishing Corp., Washington, DC, 1990), pp. 911-931] is discussed and applied to estimate the intermittency factor from velocity signals. It is shown that m depends strongly on γ but negligibly on S. More specifically, m varies with γ following m=m(t)+(lnγ(-0.0173))(1/2), where m(t) denotes the spectral exponent found in fully turbulent regions.

Gradient trajectory analysis in a Jet flow for turbulent combustion modelling

Based on planar high-speed Rayleigh scattering measurements of the mixture fraction Z of propane discharging from a turbulent round jet into co-flowing carbon dioxide at nozzle-based Reynolds numbers Re 0 = 3000–8600, we use scalar gradient trajectories to investigate the local structure of the turbulent scalar field with a focus on the scalar turbulent/non-turbulent interface. The latter is located between the fully turbulent part of the jet and the outer flow. Using scalar gradient trajectories, we partition the turbulent scalar field into these three regions according to an approach developed by Mellado et al. (J.P. Mellado, L. Wang, and N. Peters, Gradient trajectory analysis of a scalar field with external intermittency, J. Fluid Mech. 626 (2009), pp. 333–365.). Based on these different regions, we investigate in a next step zonal statistics of the scalar probability density function (pdf) P(Z) as well as the scalar difference along the trajectory ΔZ and its mean scalar value Zm , where the latter two quantities are used to parameterize the scalar profile along gradient trajectories. We show that the scalar pdf P(Z) can be reconstructed from zonal gradient trajectory statistics of the joint pdf P(Zm , ΔZ). Furthermore, on the one hand we relate our results for the scalar turbulent/non-turbulent interface to the findings made in other experimental and numerical studies of the turbulent/non-turbulent interface, and on the other hand discuss them in the context of the flamelet approach and the modelling of pdfs in turbulent non-premixed combustion. Finally, we compare the zonal statistics for P(Z) with the composite model of Effelsberg and Peters (E. Effelsberg and N. Peters, A composite model for the conserved scalar pdf, Combust. Flame 50 (1983), pp. 351–360) and observe a very good qualitative and quantitative agreement.

External Intermittency Simulation in Turbulent Round Jets

Direct numerical and large eddy simulation (DNS and LES) are applied to study passive scalar mixing and intermittency in turbulent round jets. Both simulation techniques are applied to the case of a low Reynolds number jet with Re = 2,400, whilst LES is also used to predict a high Re = 68,000 flow. Comparison between time-averaged results for the scalar field of the low Re case demonstrate reasonable agreement between the DNS and LES, and with experimental data and the predictions of other authors. Scalar probability density functions (pdfs) for this jet derived from the simulations are also in reasonable accord, although the DNS results demonstrate the more rapid influence of scalar intermittency with radial distance in the jet. This is reflected in derived intermittency profiles, with LES generally giving profiles that are too broad compared to equivalent DNS results, with too low a rate of decay with radial distance. In contrast, good agreement is in general found between LES predictions and experimental data for the mixing field, scalar pdfs and external intermittency in the high Reynolds number jet. Overall, the work described indicates that improved sub-grid scale modelling for use with LES may be beneficial in improving the accuracy of external intermittency predictions by this technique over the wide range of Reynolds numbers of practical interest.

Mixing, intermittency and large eddy simulation of a turbulent round jet

Large Eddy Simulation (LES) is a promising technique for accurate prediction of turbulent free shear flows in a wide range of applications. Here the LES technique has been applied to study the intermittency in a high Reynolds number turbulent round jet in a co-flow environment. The objective of this work is to study the external intermittency of velocity and scalar fields. LES based time averaged statistics show good agreement with the experimental measurements. The calculated probability density distributions show a Gaussian shape near the centreline region and a delta function at the furthest radial locations. The agreement between LES results and experimental data are good for the external intermittency indicating that the dynamic LES subgrid model accurately predicts the external intermittency.

External intermittency prediction using AMR solutions of RANS turbulence and transported PDF models

External intermittency in turbulent round jets is predicted using a Reynolds-averaged Navier-Stokes modelling approach coupled to solutions of the transported probability density function (pdf) equation for scalar variables. Solutions to the descriptive equations are obtained using a finite-volume method, combined with an adaptive mesh refinement algorithm, applied in both physical and compositional space. This method contrasts with conventional approaches to solving the transported pdf equation which generally employ Monte Carlo techniques. Intermittency-modified eddy viscosity and second-moment turbulence closures are used to accommodate the effects of intermittency on the flow field, with the influence of intermittency also included, through modifications to the mixing model, in the transported pdf equation. Predictions of the overall model are compared with experimental data on the velocity and scalar fields in a round jet, as well as against measurements of intermittency profiles and scalar pdfs in a number of flows, with good agreement obtained. For the cases considered, predictions based on the second-moment turbulence closure are clearly superior, although both turbulence models give realistic predictions of the bimodal scalar pdfs observed experimentally.

Swirl effects on external intermittency in turbulent jets

In this paper we present the modelled results of velocity and mixture fraction intermittency for selected isothermal swirling jet flows using Large Eddy Simulation (LES). The modelled problems considered three different swirl numbers S=0.3, 0.54 and 0.8 respectively. The probability density functions (pdfs) and intermittency of velocity and mixture fraction are presented. The simulations capture well complex flow features such as centre jet precession, a bluff body stabilised recirculation zone, and swirl induced vortex breakdown and also describe the effects of far field flow as well as scalar distributions. The calculated probability density distributions exhibit changes from a Gaussian to a delta function with increased radial distance from the jet centreline, and also a non-Gaussian shape on the jet centreline near the precession region. The radial variation of the intermittency shows differences between results with increased swirl number, especially inside the downstream swirl-induced recirculation region.

Prediction of external intermittency using RANS-based turbulence modelling and a transported PDF approach

This paper investigates the modelling of external intermittency in turbulent round jets using a RANS approach coupled to solutions of the transported probability density function (PDF) equation for scalar variables. Solutions to the descriptive equations are obtained using a finite-volume method, combined with an adaptive mesh refinement algorithm, applied in both physical and compositional space. The effects of intermittency on the flow field are accommodated using intermittency-modified eddy viscosity and second-moment turbulence closures, as well as through modifications to the mixing model embodied within the transported PDF equation. Predictions of the model are validated against data on the velocity and scalar fields in jets, as well as against measurements of scalar PDFs and intermittency profiles, with reasonable agreement obtained. From the cases examined, predictions of the second-moment closure are superior, although both approaches provide realistic predictions of the bimodal features to the measured PDFs.

Probability density functions in the cloud-top mixing layer

The cloud-top mixing layer is an idealized configuration often employed in the literature to study local aspects (over length scales of the order of 10 m) of the top of stratocumulus-topped mixed layers. Latent heat effects are further investigated here by means of direct numerical simulations, discussing the probability density functions of the horizontal and vertical velocities, as well as the mixture fraction (equal to a normalized enthalpy and total water-specific humidity). The focus is on the turbulent convection layer that develops from the buoyancy reversal instability as a consequence of the evaporative cooling at the upper cloud boundary. An approximately self-similar behavior is found, where the convection scales based on the molecular buoyancy flux at the cloud top characterize the distributions at different times, at least to leading order and within the statistical convergence achieved in the simulations. However, a very strong vertical variation in the density functions across the turbulent convection layer is found, which is of relevance to possible models. Non-Gaussian behavior is often observed, even in the horizontal component of the velocity vector. In particular, large values of skewness and flatness are measured at the lower end of the turbulent zone, where external intermittency is very strong.

Gradient trajectory analysis of a scalar field with external intermittency

The passive scalar field of a temporally evolving shear layer is investigated using gradient trajectories as a means to analyse the scalar probability density function and the conditional scalar dissipation rate in the presence of external intermittency. These results are of significance for turbulent combustion, where improved predictions of the statistics of the conditional dissipation rate are needed in several models. First, the variation of the conventional first and second moments of the conditional dissipation rate across the layer is quantitatively documented in detail. A strong dependence of the conditional dissipation rate on the lateral position and on the conditioning value of the scalar is observed. The dependence on the transverse distance to the centre-plane partially explains the double-hump profile usually reported when this dependence is ignored. The variation with the scalar observed in the ratio between the second and first moments would invalidate certain assumptions commonly done in turbulent combustion. It is also seen that conditioning on the scalar does not reduce the fluctuation of the dissipation rate with respect to unconditional values. Next, the role of external intermittency in these results is investigated. For that purpose, the flow is partitioned into different zones based on different types of gradient trajectories passing through each point, thereby introducing non-local information in comparison with the standard turbulent/non-turbulent separation based on the conventional intermittency function. In addition to the homogeneous outer regions, three zones are identified: a turbulent zone, a turbulence interface and quasi-laminar diffusion layers. The relative contribution from each of these zones to the conventional intermittency factor is reported. The statistics are then conditioned on each of these zones, and the spatial variation of the scalar distribution and of the conditional scalar dissipation rate is explained in terms of the observed zonal statistics. For the Reynolds numbers of the present simulation, between 1500 and 3000 based on the vorticity thickness and the velocity difference, and a Schmidt number equal to 1, it results that the major contribution to both statistics is due to the turbulence interfaces. At the same time, the turbulent zone shows a distinct behaviour, being approximately homogeneous but anisotropic.