Scalar Statistics Research Articles

Scalar mixing and entrainment in an axisymmetric jet subjected to external turbulence

The present study aims to understand the process of turbulent entrainment into a jet, as affected by background turbulence, using scalar statistics. Planar laser-induced fluorescence was employed to capture the orthogonal cross sections of the jet at a fixed downstream station with varying background turbulence intensities and length scales. The conditional scalar profiles revealed that the thickness of the scalar turbulent/turbulent interface is greater than that of the traditional turbulent/non-turbulent interface, and the interfacial thickness is an increasing function of the background turbulence intensity. Although nibbling remains the primary entrainment mechanism in the far field, increased occurrence of concentration “holes” within the interfacial layer in the presence of ambient turbulence suggests a more significant role of large-scale engulfment in the turbulent/turbulent entrainment process (although still below 1% of the total mass flux). Enhanced contribution of the area of detached jet patches (i.e., “islands”) to that of the main jet is hypothesized to be evidence of intense detrainment events in the background turbulence. This can potentially contribute to a reduced net entrainment into the jet, which manifests as less negative values of scalar skewness within the jet core.

Numerical Simulations of Scalar Transport on Rough Surfaces

Numerical simulations provide unfettered access to details of the flow where experimental measurements are difficult to obtain. This paper summarises the progress achieved in the study of passive scalars in flows over rough surfaces thanks to recent numerical simulations. Townsend’s similarity applies to various scalar statistics, implying the differences due to roughness are limited to the roughness sublayer (RSL). The scalar field exhibits a diffusive sublayer that increasingly conforms to the roughness surface as ks+ or Pr increase. The scalar wall flux is enhanced on the windward slopes of the roughness, where the analogy between momentum and scalar holds well; the momentum and scalar fields, however, have very different behaviours downwind of the roughness elements, due to recirculation, which reduces the scalar wall flux. Roughness causes breakdown of the Reynolds analogy: any increase in St is accompanied by a larger increase in cf. A flattening trend for the scalar roughness function, ΔΘ+, is observed as ks+ increases, suggesting the possibility of a scalar fully rough regime, different from the velocity one. The form-induced (FI) production of scalar fluctuations becomes dominant inside the RSL and is significantly different from the FI production of turbulent kinetic energy, resulting in notable differences between the scalar and velocity fluctuations. Several key questions remain open, in particular regarding the existence of a fully rough scalar regime and its characteristics. With the increase in Re and Pr, various quantities such as scalar roughness function, the dispersive fluxes, FI wall flux, etc., appear to trend towards saturation. However, the limited range of Re and Pr achieved by numerical simulations only allows us to speculate regarding such asymptotic behaviour. Beyond extending the range of Re and Pr, systematic coverage of different roughness types and topologies is needed, as the scalar appears to remain sensitive to the geometrical details.

Predicting Short-Term Intensity Change in Tropical Cyclones Using a Convolutional Neural Network

Abstract This study details a two-method, machine learning approach to predict current and short-term intensity change in global tropical cyclones (TCs), “D-MINT” and “D-PRINT.” D-MINT and D-PRINT use infrared imagery and environmental scalar predictors, while D-MINT also employs microwave imagery. Results show that current TC intensity estimates from D-MINT and D-PRINT are more skillful than three established intensity estimation methods routinely used by operational forecasters for North Atlantic and eastern and western North Pacific TCs. Short-term intensity predictions are validated against five operational deterministic guidances at 6-, 12-, 18-, and 24-h lead times. D-MINT and D-PRINT are less skillful than NHC and consensus TC intensity predictions in North Atlantic and eastern North Pacific TCs, but are more skillful than the other guidances for at least half of the lead times. In western North Pacific, north Indian Ocean, and Southern Hemisphere TCs, D-MINT is more skillful than the JTWC and other individual TC intensity forecasts for over half of the lead times. When probabilistically predicting TC rapid intensification (RI), D-MINT is more skillful in North Atlantic and western North Pacific TCs than three operationally used RI guidances, but less skillful for yes–no RI forecasts. In addition, this work demonstrates the importance of microwave imagery, as D-MINT is more skillful than D-PRINT. Since D-MINT and D-PRINT are convolutional neural network models interrogating two-dimensional structures within TC satellite imagery, this study also demonstrates that those features can yield better short-term predictions than existing scalar statistics of satellite imagery in operational models. Finally, a diagnostics tool is revealed to aid the attribution of the D-MINT/D-PRINT intensity predictions. Significance Statement This study develops a method to predict current and short-term forecasts of tropical cyclone (TC) intensity using artificial intelligence. The resultant models use a convolutional neural network (CNN) that can identify two-dimensional features in satellite imagery that are indicative of TC intensity and future intensity change. The performance results indicate that in several TC basins, the CNN approach is generally more skillful than alternative satellite-based estimates of TC intensity as well as operational short-term forecasts of deterministic intensity change and of similar skill to probabilistic rapid intensification forecasts.

Stochastic modeling of multiple scalar mixing in a three-stream concentric coaxial jet based on one-dimensional turbulence

Modeling turbulent mixing is a standing challenge for nonpremixed chemically reacting flows. Key complications arise from the requirement to capture all relevant scales of the flow and the necessity to distinguish between turbulent advective transport and molecular diffusive transport processes. In addition, anisotropic mean shear, variable advection time scales, and the coexistence of turbulent and nonturbulent regions need to be represented. The fundamental issues at stake are addressed by investigating multi-scalar mixing in a three-stream coaxial jet with a map-based stochastic one-dimensional turbulence model. ODT provides full-scale resolution at affordable costs by a radical reduction of complexity compared to high-fidelity Navier–Stokes solvers. The approach is partly justified by an application of the boundary-layer approximation, but neglects fluctuating axial pressure gradients. It is demonstrated that low-order scalar statistics are reasonably but not fully captured. Despite this shortcoming, it is shown that the model is able to reproduce experimental state-space statistics of multi-stream multi-scalar mixing. The model therefore offers physics-compatible improvements in multi-stream mixing modeling despite some fundamental limitations that remain from unjustified assumptions.

Comment on “Effect of viscous-convective subrange on passive scalar statistics at high Reynolds number”

Comment on “Effect of viscous-convective subrange on passive scalar statistics at high Reynolds number”

Calibration of P-values for calibration and for deviation of a subpopulation from the full population

The author’s recent research papers, “Cumulative deviation of a subpopulation from the full population” and “A graphical method of cumulative differences between two subpopulations” (both published in volume 8 of Springer’s open-access Journal of Big Data during 2021), propose graphical methods and summary statistics, without extensively calibrating formal significance tests. The summary metrics and methods can measure the calibration of probabilistic predictions and can assess differences in responses between a subpopulation and the full population while controlling for a covariate or score via conditioning on it. These recently published papers construct significance tests based on the scalar summary statistics, but only sketch how to calibrate the attained significance levels (also known as “P-values”) for the tests. The present article reviews and synthesizes work spanning many decades in order to detail how to calibrate the P-values. The present paper presents computationally efficient, easily implemented numerical methods for evaluating properly calibrated P-values, together with rigorous mathematical proofs guaranteeing their accuracy, and illustrates and validates the methods with open-source software and numerical examples.

Fast Models for Predicting Pollutant Dispersion inside Urban Canopies

A fast pollutant dispersion model for urban canopies is developed by coupling mean wind profiles to a parameterisation of turbulent diffusion and solving the time-dependent advection–diffusion equation. The performance of a simplified, coarse-grained representation of the velocity field is investigated. Spatially averaged mean wind profiles within local averaging regions or repeating units are predicted by solving the three-dimensional Poisson equation for a set of discrete vortex sheets. For each averaging region, the turbulent diffusion is parameterised in terms of the mean wind profile using empirical constants derived from large-eddy simulation (LES). Nearly identical results are obtained whether the turbulent fluctuations are specified explicitly or an effective diffusivity is used in their place: either version of the fast dispersion model shows much better agreement with LES than does the Gaussian plume model (e.g., the normalized mean square error inside the canopy is several times smaller). Passive scalar statistics for a regular cubic building array show improved agreement with LES when wind profiles vary in the horizontal. The current implementation is around 50 times faster than LES. With its combination of computational efficiency and moderate accuracy, the fast model may be suitable for time-critical applications such as emergency dispersion modelling.

Turbulent diffusion of scalar and heat in an off-source heated steady round jet

We study, using direct numerical simulation, the characteristics of an off-source heated jet (OSHJ), the rate of heat addition being proportional to the local concentration of a scalar. The heating disturbs the self-similar state of the unheated jet (UJ) entering the heat injection zone (HIZ). Based on the characteristics of the velocity and scalar statistics, the evolution of the OSHJ is demarcated into three axial zones. Zone I, which is dynamically the most active region, exhibits rapid variations in quantities like the mean radial velocity, the scalar-to-velocity width ratio and the second-order correlations. Zone II represents the relaxation of these quantities towards a new self-similar state which is realized in Zone III above the HIZ. We find that the temperature–velocity correlation is negative in the core of the OSHJ in Zone I, which becomes positive for all radial locations in Zones II and III. We interpret this behavior by decomposing the effect of heat addition into “heating” and “buoyancy” factors; the former describes the effect of axial velocity on heating while the latter describes the effect of added buoyancy on flow acceleration. The heating factor dominates in Zone I leading to the negative temperature–velocity correlation, which we conjecture to be the reason for the “disruption” of coherent structures in the OSHJ reported in the literature. Based on wavelet analysis of the scalar field we identify the length scale of the ring-like coherent structure that gets disrupted upon heat addition, which enhances the scalar homogeneity in the core of the OSHJ near the base of the HIZ. Where possible, we compare our results with the literature on heated jets within the context of the three demarcated zones. We find that external heating decreases the scalar-to-velocity flow widths relative to the UJ to a value in Zone III that is largely insensitive to the precise details of heat addition , such as the amount of heat added and the extent of the HIZ. We also present the effect of heat addition on turbulent Schmidt and Prandtl numbers. Our findings are relevant to the dynamics of cumulus clouds which are governed by a similar interplay of scalar, velocity and temperature fields as reported here.

Contribution of direct numerical simulations to the budget and modelling of the transport equations for passive scalar turbulent fields with wall scalar fluctuations

We perform direct numerical simulations (DNS) of the fully developed turbulent channel flow with a passive scalar subjected to constant time-averaged scalar fluxes at the wall. The first case (case I) considers a constant time-averaged scalar flux $\left \langle q_w \right \rangle$ along with the specific condition of a non-fluctuating scalar $\theta _w$ imposed at the wall implying zero wall scalar fluctuation $\theta '_w=0$ and zero variance (isoscalar boundary condition) whereas the second case (case II) accounts for a constant instantaneous scalar flux $q_w$ in time and space leading to zero gradient of scalar fluctuation along the normal to the wall $(\partial \theta '/ \partial x_n)_w = 0$ (isoflux boundary condition) implying a non-zero variance. The friction Reynolds number takes on the value $R_\tau =395$ and the molecular Prandtl numbers considered are $P_r=0.01$ , 0.1, 1 and 10. The purpose is to investigate the effect of the wall scalar fluctuations on the scalar field. Emphasis is put on the mean passive scalar $\left \langle \theta \right \rangle$ , the half-scalar variance $k_\theta$ , the turbulent scalar fluxes $\tau _{i \theta }$ , the correlation coefficients $R_{i \theta }$ , the passive scalar to dynamic time-scale ratio $\mathcal {R}$ , the turbulent Prandtl number $Pr_t$ and higher-order scalar statistics. Systematic comparisons between these two scalar fields are undertaken. As a result of interest, it is found that the mean scalar remains almost the same whatever the type of the boundary layer condition but not the scalar variance. The budgets of transport equations for the half-scalar variance and turbulent fluxes reveal that some scalar quantities such as the dissipation-rate and the molecular diffusion terms are highly modified in the near-wall region but not really the production, diffusion and the scalar-pressure gradient correlation terms in a first approximation. Visualization of the instantaneous scalar fields indicates that the topology of the structures is strongly modified as the Prandtl number increases from $P_r=0.01$ up to $10$ . Finally, it is shown how to use this DNS database to devise and calibrate scalar flux equation models in the framework of both first and second moment closures. This study suggests that accounting for wall scalar fluctuations should be considered in the simulation of turbulent flows involving fluid and solid combinations at the interface and provides a useful high resolution DNS database.

Statistics of a Passive Scalar in a 2D Shear Flow with Fluctuations

Statistics of a Passive Scalar in a 2D Shear Flow with Fluctuations

Flame structure and broadening in turbulent premixed jet flames

High-resolution and high signal-to-noise (SNR) planar Rayleigh scattering thermometry measurements are performed to investigate preheat and reaction zone broadening, turbulent transport of high-temperature gases, and the internal flame structure in a series of highly turbulent, lean (ϕ = 0.75), premixed methane-air turbulent jet flames. These flames are characterized by turbulence intensities ranging from u′/SL of 35 to 150 and turbulent Reynolds numbers approaching 104, as determined from separate particle image velocimetry (PIV) measurements. Average flame profiles obtained using a gradient-based flame reconstruction method and probability density functions (PDFs) of the preheat, reaction, and thermal layer thicknesses show substantial broadening of the preheat and thermal layers. Instantaneous preheat zones are broadened by as much as a factor of 30 compared to laminar flames, with an average broadening approaching a factor of 14 for the most turbulent case. Moderate broadening of the reaction layer is observed with up to a factor of eight times that of a laminar premixed flame for instantaneous realizations and an average broadening of four times that of a laminar flame for the most turbulent case. Conditional statistics of temperature obtained at isodistance contours within and upstream of the preheat zone show large shifts towards significantly higher temperatures compared to laminar flame values. In addition, broad temperature distributions and reduced thermal gradients at each position provide strong evidence of persistent turbulent transport of high-temperature gases ahead of the preheat zone. Finally, a detailed analysis of scalar dissipation rate statistics and dissipation layer topology was conducted. The conditional mean scalar dissipation rates for the turbulent flames show significant reductions compared to calculated laminar flame values and a shift towards higher values of the reaction progress variable (CT) for increasing turbulence levels. PDFs show a transition from near-Gaussian to highly negatively skewed with increasing turbulence levels, where the most probable values of the scalar dissipation rate shift towards higher values of CT, indicating that the primary reaction zone and flame front are subjected to increased strain. In terms of structure, no significant broadening of the small-scale dissipation layers was observed with increasing turbulence intensity. However, as turbulence intensity increases, there is a transition from a sparse number of continuous layers to a large number of shorter, ”broken”, nearly straight segments. The reduction of individual layer lengths (i.e., ”breaking”) is favored over increases in dissipation layer wrinkling, where the sharp decreases in the local dissipation rate values are highly correlated with regions of high curvature. A final notable outcome of this work is that there were negligible differences in all statistical and topological results when moving between the two highest turbulent cases, even though the turbulence intensity, turbulent Reynolds number, and the turbulence Karlovitz number increased substantially (70 - 120%). This implies that there may be an asymptotic limit in which turbulence affects flame behavior for the current configuration.

Derived scalar statistics from multiscalar measurements via surrogate composition spaces

Multiscalar point and line measurements have provided a wealth of data to extract measured scalars’ statistics in laboratory flames. These measurements are partial, since only a subset of scalars are measured, and carry experimental uncertainty to the degree that derived scalars, such as reaction rates, cannot be adequately evaluated from the raw data alone. In this study, we propose and investigate a method to extract derived scalar statistics via a surrogate composition space. This space is parameterized using principal components (PCs) from principal component analysis (PCA). The resulting low-dimensional manifold based only on statistics from measured scalars is complemented with homogeneous chemistry calculations to recover missing species and evaluate species reaction rates. The method is validated using direct numerical simulation (DNS) data on which Gaussian noise is added to emulate experimental uncertainly and with a subset of major species, a radical OH, and temperature assumed to be known/measured. The results show the proposed procedure is able to recover unmeasured species and predict the species reaction rates.

Budget-limited distribution learning in multifidelity problems

Multifidelity methods are widely used for estimating quantities of interest (QoI) in computational science by employing numerical simulations of differing costs and accuracies. Many methods approximate numerical-valued statistics that represent only limited information, e.g., scalar statistics, about the QoI. Further quantification of uncertainty, e.g., for risk assessment, failure probabilities, or confidence intervals, requires estimation of the full distributions. In this paper, we generalize the ideas in (Xu et al. in SIAM J Sci Comput 44(1):A150–A175, 2022) to develop a multifidelity method that approximates the full distribution of scalar-valued QoI. The main advantage of our approach compared to alternative methods is that we require no particular relationships among the high and lower-fidelity models (e.g. model hierarchy), and we do not assume any knowledge of model statistics including correlations and other cross-model statistics before the procedure starts. Under suitable assumptions in the framework above, we achieve provable 1-Wasserstein metric convergence of an algorithmically constructed distributional emulator via an exploration–exploitation strategy. We also prove that crucial policy actions taken by our algorithm are budget-asymptotically optimal. Numerical experiments are provided to support our theoretical analysis.

A Comparison between Statistical Behaviours of Scalar Dissipation Rate between Homogeneous MILD Combustion and Premixed Turbulent Flames

Three-dimensional Direct Numerical Simulations (DNS) data has been utilised to analyse statistical behaviours of the scalar dissipation rate (SDR) and its transport for homogeneous methane-air mixture turbulent Moderate or Intense Low oxygen Dilution (MILD) combustion for different O2 dilution levels and turbulence intensities for different reaction progress variable definitions. Additional DNS has been conducted for turbulent premixed flames and passive scalar mixing for the purpose of comparison with the SDR statistics of the homogeneous mixture MILD combustion with that in conventional premixed combustion and passive scalar mixing. It has been found that the peak mean value of the scalar dissipation rate decreases with decreasing O2 concentration for MILD combustion cases. Moreover, SDR magnitudes increase with increasing turbulence intensity for both MILD and conventional premixed combustion cases. The profiles and mean values of the scalar dissipation rate conditioned upon the reaction progress variable are found to be sensitive to the choice of the reaction progress variable definition. This behaviour arises due to the differences in the distributions of the species mass fractions within the flame. The strain rate contribution and the molecular dissipation term are found to be the leading order contributors in the scalar dissipation rate transport for MILD combustion; whereas, in conventional premixed flames, the terms rising from density variation and reaction rate gradient also play leading roles in addition to the strain rate and molecular dissipation contributions. By contrast, the terms due to density gradient and reaction rate gradient remain negligible in comparison to the leading order contributors in MILD combustion cases due to small density variation because of moderate temperature rise and small reaction rate gradient magnitudes. Furthermore, the qualitative behaviour of the strain rate contribution to the SDR transport in premixed flames is significantly different to that in the case of MILD combustion and passive scalar mixing. The findings of the current analysis indicate that the scalar dissipation rate statistics in MILD combustion show several qualitative similarities to the passive scalar mixing despite major differences with the SDR transport in conventional turbulent premixed flames. This further suggests that the scalar dissipation rate models, which were originally proposed in the context of passive scalar mixing, have the potential to be applicable for MILD combustion but the models for the premixed turbulent combustion may not be applicable for MILD combustion of homogeneous mixtures.

Wasserstein-based texture analysis in radiomic studies.

The emerging field of radiomics that transforms standard-of-care images to quantifiable scalar statistics endeavors to reveal the information hidden in these macroscopic images. The concept of texture is widely used and essential in many radiomic-based studies. Practice usually reduces spatial multidimensional texture matrices, e.g., gray-level co-occurrence matrices (GLCMs), to summary scalar features. These statistical features have been demonstrated to be strongly correlated and tend to contribute redundant information; and does not account for the spatial information hidden in the multivariate texture matrices. This study proposes a novel pipeline to deal with spatial texture features in radiomic studies. A new set of textural features that preserve the spatial information inherent in GLCMs is proposed and used for classification purposes. The set of the new features uses the Wasserstein metric from optimal mass transport theory (OMT) to quantify the spatial similarity between samples within a given label class. In particular, based on a selected subset of texture GLCMs from the training cohort, we propose new representative spatial texture features, which we incorporate into a supervised image classification pipeline. The pipeline relies on the support vector machine (SVM) algorithm along with Bayesian optimization and the Wasserstein metric. The selection of the best GLCM references is considered for each classification label and is performed during the training phase of the SVM classifier using a Bayesian optimizer. We assume that sample fitness is defined based on closeness (in the sense of the Wasserstein metric) and high correlation (Spearman's rank sense) with other samples in the same class. Moreover, the newly defined spatial texture features consist of the Wasserstein distance between the optimally selected references and the remaining samples. We assessed the performance of the proposed classification pipeline in diagnosing the coronavirus disease 2019 (COVID-19) from computed tomographic (CT) images. To evaluate the proposed spatial features' added value, we compared the performance of the proposed classification pipeline with other SVM-based classifiers that account for different texture features, namely: statistical features only, optimized spatial features using Euclidean metric, non-optimized spatial features with Wasserstein metric. The proposed technique, which accounts for the optimized spatial texture feature with Wasserstein metric, shows great potential in classifying new COVID CT images that the algorithm has not seen in the training step. The MATLAB code of the proposed classification pipeline is made available. It can be used to find the best reference samples in other data cohorts, which can then be employed to build different prediction models.

Thirty years of geometric morphometrics: Achievements, challenges, and the ongoing quest for biological meaningfulness.

The foundations of geometric morphometrics were worked out about 30 years ago and have continually been refined and extended. What has remained as a central thrust and source of debate in the morphometrics community is the shared goal of meaningful biological inference through a tight connection between biological theory, measurement, multivariate biostatistics, and geometry. Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric components and into different spatial scales, the interpretation of various geometries in shape or form space, and models of the association between shape or form and other variables, such as environmental, genetic, or behavioral data. We focus on recent developments and current methodological challenges, especially those arising from the increasing number of landmarks and semilandmarks, and emphasize the importance of thorough exploratory multivariate analyses rather than single scalar summary statistics. We outline promising directions for further research and for the evaluation of new developments, such as “landmark‐free” approaches. To illustrate these methods, we analyze three‐dimensional human face shape based on data from the Avon Longitudinal Study of Parents and Children (ALSPAC).

Focused Information Criterion for Restricted Mean Survival Times: Non-Parametric or Parametric Estimators

Restricted Mean Survival Time (), the average time without an event of interest until a specific time point, is a model-free, easy to interpret statistic. The heavy reliance on non-parametric or semi-parametric methods in the survival analysis has drawn criticism, due to the loss of efficacy compared to parametric methods. This assumes that the parametric family used is the true one, otherwise the gain in efficacy might be lost to interpretability problems due to bias. The Focused Information Criterion () considers the trade-off between bias and variance and offers an objective framework for the selection of the optimal non-parametric or parametric estimator for scalar statistics. Herein, we present the framework for the selection of the estimator with the best bias-variance trade-off. The aim is not to identify the true underling distribution that generated the data, but to identify families of distributions that best approximate this process. Through simulation studies and theoretical reasoning, we highlight the effect of censoring on the performance of . Applicability is illustrated with a real life example. Censoring has a non-linear effect on s performance that can be traced back to the asymptotic relative efficiency of the estimators. s performance is sample size dependent; however, with censoring percentages common in practical applications selects the true model at a nominal probability (0.843) even with small or moderate sample sizes.

Stirring by anisotropic squirming

We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault and Childress, Phys. Lett. A (2010) and Lin et al., J. Fluid Mech. (2011) to the case in which the swimmers move in anisotropically random directions. A non-diagonal effective diffusivity tensor is derived with which the diffusive preference of a passive particle along any given direction can be computed to provide more details of the phenomena beyond scalar statistics. We further identify a fraction from the orthogonal decomposition of the drift-induced particle displacement to distinguish the underlying nonlinear mixing mechanism for different types of swimmers. Numerical simulations verify the analytical results with explicit examples of prescribed, anisotropic stirring motions. We also connect our formulation to several measures used in clinical medical research such as diffusion tensor imaging where anisotropic diffusion has a significant consequence.

Effect of viscous-convective subrange on passive scalar statistics at high Reynolds number

In modeling turbulent mixing at high Reynolds number (Re), the small-scale statistics of a passive scalar are assumed similar to those of the velocity. Research shows this to be invalid at either high Re or high Schmidt number individually. We hypothesize that both inertial-convective and viscous-convective subranges are needed for sufficient scale separation in both velocity and scalar fields, such that small-scale statistics of the scalar approach those of the velocity. We explore this using direct numerical simulations of up to ${14256}^{3}$ and find that at high Taylor Reynolds number of 633, similarity may be assumed between velocity and scalar statistics for mixing in water, but not in air.

The dynamics of an axisymmetric turbulent jet in ambient turbulence interpreted from the passive scalar field statistics

The effect of approximately homogeneous isotropic turbulence on the dynamics of an axisymmetric turbulent jet (Re = 10 600 and 5800) in an ambient with a negligible mean flow is interpreted from the statistics of the passive scalar field. The ambient turbulence is generated by a random jet array and scalar concentrations are measured in orthogonal cross sections of the jet using planar laser-induced fluorescence. Statistics of the scalar field of the jet in a turbulent ambient are compared to those in a quiescent ambient, using classical Eulerian averages and those conditioned on the jet centroid. A two-region model for the jet structure in ambient turbulence is proposed based on the centroidal statistics. Following the developing region of the jet, the ambient turbulence disrupts the jet structure, due to modulation of the jet interface, meandering of the jet by large eddies, and entrainment of the turbulent ambient fluid, resulting in a faster concentration decay and reduced entrainment compared to the quiescent ambient. Further downstream, once the ambient turbulence has destroyed the jet, only molecular and turbulent diffusion modify the scalar concentrations. The regions' relative lengths depend primarily on the relative turbulence intensity (ξ) between the ambient and the jet, as assessed using centroidal analysis, which removes the effect of the relative length scale (l) on the jet behavior in the turbulent ambient. The centroidal scalar statistics reveal self-similarity and self-preservation in mean scalar properties before jet breakup, which occurs abruptly once ξ> 0.5. The smaller scales of ambient turbulence modulate the jet boundary and, when entrained, lead to a wider range of centerline concentrations and root mean square concentrations, which are hypothesized to increase local concentration gradients within the jet and reduce jet mixing.