Direct Numerical Simulation Data Research Articles

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Turbulence modeling of stratified turbulence using a constrained artificial neural network

For large eddy simulations (LES) of stratified turbulence in the strongly stratified regime, an artificial neural network (ANN) with five hidden layers is used to construct a sub-grid scale (SGS) model. The ANN is assessed by comparing it to the Smagorinsky model, the dynamic Smagorinsky model, the gradient model, and filtered direct numerical simulation data. In the a priori test, the SGS model using ANN performed better than the Smagorinsky model and the gradient model in terms of the correlation coefficient and relative error of the energy transfer rate. However, the ANN does not provide sufficient energy dissipation when it is applied to LES with a larger filter width because it overpredicts backscatter. To address this problem, we also trained a constrained ANN using a custom loss function that penalizes excessive backscatter. It is shown that the constrained ANN successfully predicts less backscatter, maintaining the high correlation coefficient without ad hoc clipping. These results show that ANN is a promising tool for realizing a highly accurate and stable SGS model for stratified turbulence.

Large eddy simulation of a turbulent channel flow using dynamic Smagorinsky subgrid scale model and differential equation wall model

A large eddy simulation (LES) is conducted in a plane channel flow which is turbulent. For understanding the mechanism of the turbulent motion more efficiently, the present study is an attempt to conduct the LES using a Dynamic Smagorinsky Model (DSM) and a Differential Equation Wall Model (DEWM). DSM is a subgrid-scale model and DEWM is for approximating the near wall layer. The simulation is performed in a domain of 2 π δ × 2 δ × π δwhich is discretized by 32 × 20 × 32grid points where δ is the channel half width. The discretization techniques have been used in the simulation, are the 3rd order low storage R-K method in time and 2nd order finite difference formulation in space. To assess the performance of the LES with DSM and DEWM, the simulation results are compared with direct numerical simulation (DNS) data and LES data using Standard Smagorinsky Model (SSM). Comparing the results in the essential turbulence statistical field it has been found that DSM performs better than SSM in most of the cases and shows better agreement with the DNS results. Flow structures in the turbulent flow field are compared in isosurfaces and contour plots, and found that tube-like vortical structures are randomly distributed over the entire flow field, and the number of the vortical structures are more for the DSM case than that of SSM.

Forward and Inverse Energy Cascade in Fluid Turbulence Adhere to Kolmogorov's Refined Similarity Hypothesis.

We study fluctuations of the local energy cascade rate Φ_{ℓ} in turbulent flows at scales (ℓ) in the inertial range. According to the Kolmogorov refined similarity hypothesis (KRSH), relevant statistical properties of Φ_{ℓ} should depend on ε_{ℓ}, the viscous dissipation rate locally averaged over a sphere of size ℓ, rather than on the global average dissipation. However, the validity of KRSH applied to Φ_{ℓ} has not yet been tested from data. Conditional averages such as ⟨Φ_{ℓ}|ε_{ℓ}⟩ as well as of higher-order moments are measured from direct numerical simulations data, and results clearly adhere to the predictions from KRSH. Remarkably, the same is true when considering forward (Φ_{ℓ}>0) and inverse (Φ_{ℓ}<0) cascade events separately. Measured ratios of forward and inverse cascade probability densities conditioned on ε_{ℓ} also confirm the applicability of the KRSH to analysis of the fluctuation relation from nonequilibrium thermodynamics.

New momentum integral equation applicable to boundary layer flows under arbitrary pressure gradients

By incorporating the traditionally overlooked advective term in the wall-normal momentum equation, a new momentum integral equation is developed for two-dimensional incompressible turbulent boundary layers under arbitrary pressure gradients. The classical Kármán's integral arises as a special instance of the new momentum integral equation when the pressure gradient is weak. The new momentum integral equation's validity is substantiated by direct numerical simulation data. Unlike the classical Kármán's integral, which is limited to predicting wall shear stress within mild pressure gradients, the new momentum integral equation accurately computes wall shear stress across a broad range of pressure gradients, even in the presence of strong adverse pressure gradients that lead to flow separation. Moreover, a new pressure parameter $\beta _\kappa$ is introduced through examining terms in the new momentum integral equation. This parameter naturally quantifies the pressure gradient's influence on turbulent boundary layers and offers guidance for applying the classical Kármán's integral. Additionally, to facilitate experimental determination of wall shear stress under strong pressure gradients, an approximate integral equation is proposed that relies solely on easily measurable variables. Validation against direct numerical simulation data demonstrates that this simplified equation provides reasonably accurate estimates of wall shear stress in turbulent boundary layers experiencing strong pressure gradients.

Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ( $A = \sqrt {A_{ij}A_{ij}}$ ) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$ . The boundedness and compactness of the $b_{ij}$ -space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

Sensitivity and resolution response of optical flow-based background-oriented schlieren to speckle patterns

The degraded resolution and sensitivity characteristics of background-oriented schlieren (BOS) can be recovered by utilizing an optical flow (OF)-based image processing scheme. However, the background patterns conventionally employed in BOS setups suit the needs of the cross-correlation approach, whereas OF is based on a completely different mathematical background. Thus, in order to characterize the resolution and sensitivity response of OF-based BOS to the background generation configurations, a parametric study is performed. First, a synthetic assessment based on an analytical solution of a one-dimensional shock tube problem is conducted. Then, a numerical assessment utilizing direct numerical simulation data of density-driven turbulence is performed. Finally, the applicability of the documented conclusions in realistic scenarios is tested through an experimental assessment over a plume of a swirling heated jet.

Assessment of Laws of the Wall During Flame–Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The validity of the usual laws of the wall for Favre mean values of the streamwise velocity component and temperature for non-reacting flows has been assessed for turbulent premixed flame-wall interaction using Direct Numerical Simulation (DNS) data. Two different DNS databases corresponding to friction velocity-based Reynolds number of 110 and 180 representing unsteady head-on quenching of statistically planar flames within turbulent boundary layers have been considered. The usual log-law based expressions for the Favre mean values of the streamwise velocity and temperature for the inertial layer have been found to be inadequate at capturing the corresponding variations obtained from DNS data. The underlying assumptions of constant shear stress and the equilibrium of production and dissipation of turbulent kinetic energy underpinning the derivation of the usual log-law for the mean streamwise velocity have been found to be rendered invalid within the usual inertial layer during flame-wall interaction for both cases considered here. The heat flux does not remain constant within the usual inertial layer, and the turbulent flux of temperature exhibits counter-gradient transport within the so-called inertial layer for the cases considered in this work. These render the assumptions behind the derivation of the usual log-law for temperature to be invalid for application to turbulent flame-wall interaction. It has been found that previously proposed empirical modifications to the existing laws of the wall, which account for density and kinematic viscosity variations with temperature, do not significantly improve the agreement with the corresponding DNS data in the inertial layer and the inaccurate approximations for the kinematic viscosity compensated wall normal distance and the density compensated streamwise velocity component contribute to this disagreement. The DNS data has been utilised here to propose new expressions for the kinematic viscosity compensated wall normal distance and the density compensated streamwise velocity component, which upon using in the empirically modified law of wall expressions have been demonstrated to provide reasonable agreement with DNS data.

Prediction of turbulent energy based on low-rank resolvent modes and machine learning

A modelling framework based on the resolvent analysis and machine learning is proposed to predict the turbulent energy in incompressible channel flows. In the framework, the optimal resolvent response modes are selected as the basis functions modelling the low-rank behaviour of high-dimensional nonlinear turbulent flow-fields, and the corresponding weight functions are determined by data-driven neural networks. Turbulent-energy distribution in space and scales, at the friction Reynolds number 1000, is predicted and compared to the data of direct numerical simulation. Close agreement is observed, suggesting the feasibility and reliability of the proposed framework for turbulence prediction.

Relations between Reynolds stresses and their dissipation rates during premixed flame–wall interaction within turbulent boundary layers

A direct numerical simulation (DNS) database for head-on quenching of premixed flames propagating across turbulent boundary layers representative of friction Reynolds numbers, Reτ, of 110 and 180 has been utilized to analyze the interrelation between Reynolds stresses and their dissipation rates during flame–wall interaction. The Reynolds stresses and their dissipation rates exhibit significant deviations from the corresponding non-reacting flow profiles within the flame brush and in the burned gas region. This behavior is prominent for the components in the wall-normal direction because the mean direction of flame normal acceleration due to thermal expansion aligns with the wall-normal direction in this configuration. The anisotropy of Reynolds stresses and their dissipation rate tensors have been found to be qualitatively similar, but the anisotropic behavior weakens with increasing Reτ. However, the components of the anisotropy tensors of Reynolds stresses and viscous dissipation rate are not related according to a linear scaling, and thus, the models based on this assumption do not successfully capture the viscous dissipation rate components obtained from the DNS data. By contrast, a model, which includes the invariants of the anisotropy tensor of Reynolds stresses and satisfies the limiting conditions, has been found to capture especially the diagonal components of the viscous dissipation rate tensor more successfully for both non-reacting and reacting cases considered in this work. However, the quantitative prediction of this model suffers for the components in the wall-normal direction for lower values of Reτ, but the performance of this model improves with an increase in Reτ.

Linear and nonlinear Granger causality analysis of turbulent duct flows

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

Direct numerical simulation and mode analysis of turbulent transition flow in a compressor blade channel

The separation and turbulent transition of the flow in a compressor blade channel are investigated through direct numerical simulations (DNS) at a Reynolds number of 1.367 × 105. Based on the original DNS data, both time-averaged statistics and instantaneous vortex structures of the flow field are extensively analyzed. The vortices are visualized and studied by the Liutex method, and the streaming dynamic mode decomposition (SDMD), a low-storage variant of conventional DMD, is applied to the large datasets obtained on both pressure and suction sides. The physical quantity analyzed with SDMD is the Liutex magnitude R. The DNS results indicate that flow separation occurs on both sides of the blade. On the pressure surface, the separation is weak and the flow remains in a natural transition dominated by viscous Tollmien–Schlichting instabilities. In contrast, owing to the presence of a large laminar separation bubble, the flow experiences a separation transition governed by inviscid Kelvin–Helmholtz instabilities on the suction surface. The SDMD results suggest that a broad range of vortex frequencies exist in the transition flow, and the scale of the spatial structures is negatively correlated with the frequency of the mode. On the pressure surface, the extracted SDMD modes are primarily related to Kelvin–Helmholtz rolls, whereas on the suction side, influenced by the separated boundary layer, the modal structures exhibit greater diversity.

A Combined Model of Diffusion Model and Enhanced Residual Network for Super-Resolution Reconstruction of Turbulent Flows

In this study, we introduce a novel model, the Combined Model, composed of a conditional denoising diffusion model (SR3) and an enhanced residual network (EResNet), for reconstructing high-resolution turbulent flow fields from low-resolution flow data. The SR3 model is adept at learning the distribution of flow fields. The EResNet architecture incorporates a long skip connection extending from the input directly to the output. This modification ensures the preservation of essential features learned by the SR3, while simultaneously enhancing the accuracy of the flow field. Additionally, we incorporated physical gradient constraints into the loss function of EResNet to ensure that the flow fields reconstructed by the Combined Model are consistent with the direct numerical simulation (DNS) data. Consequently, the high-resolution flow fields reconstructed by the Combined Model exhibit high conformity with the DNS results in terms of flow distribution, details, and accuracy. To validate the effectiveness of the model, experiments were conducted on two-dimensional flow around a square cylinder at a Reynolds number (Re) of 100 and turbulent channel flow at Re = 4000. The results demonstrate that the Combined Model can reconstruct both high-resolution laminar and turbulent flow fields from low-resolution data. Comparisons with a super-resolution convolutional neural network (SRCNN) and an enhanced super-resolution generative adversarial network (ESRGAN) demonstrate that while all three models perform admirably in reconstructing laminar flows, the Combined Model excels in capturing more details in turbulent flows, aligning the statistical outcomes more closely with the DNS results. Furthermore, in terms of L2 norm error, the Combined Model achieves an order of magnitude lower error compared to SRCNN and ESRGAN. Experimentation also revealed that SR3 possesses the capability to learn the distribution of flow fields. This work opens new avenues for high-fidelity flow field reconstruction using deep learning methods.

Large eddy simulation of flow over a circular cylinder with a neural-network-based subgrid-scale model

A neural-network-based large eddy simulation is performed for flow over a circular cylinder. To predict the subgrid-scale (SGS) stresses, we train two fully connected neural network (FCNN) architectures with and without fusing information from two separate single-frame networks (FU and nFU, respectively), where the input variable is either the strain rate (SR) or the velocity gradient (VG). As the input variables, only the grid-filtered variables are considered for the SGS models of G-SR and G-VG, and both the grid- and test-filtered variables are considered for the SGS models of T-SR and T-VG. The training data are the filtered direct numerical simulation (fDNS) data at $Re_d=3900$ based on the free-stream velocity and cylinder diameter. Using the same grid resolution as that of the training data, the performances of G-SR and G-VG (grid-filtered inputs) and T-SR-FU and T-VG-FU (grid- and test-filtered inputs with fusion) are better than those of the dynamic Smagorinsky model and T-SR-nFU and T-VG-nFU (grid- and test-filtered inputs without fusion). These FCNN-based SGS models are applied to untrained flows having different grid resolutions from that of training data. Although the performances of G-SR and G-VG are degraded, T-SR-FU and T-VG-FU still provide good performances. Finally, T-SR-FU and T-VG-FU trained at $Re_d = 3900$ are applied to higher-Reynolds-number flows ( $Re_d = 5000$ and 10 000) and their results are also in good agreements with those of fDNS and previous experiment, indicating that adding the test-filtered variables and fusion increases the prediction capability even for untrained Reynolds number flows.

Multiscale Modeling of Flow in Rod Bundles: From Direct Numerical Simulation and Subchannel to Coarse-Mesh CFD

Fast and accurate evaluation of flow and heat transfer phenomena in rod bundles is a problem of long-standing interest in nuclear engineering. Computational fluid dynamics (CFD) can provide accurate but relatively time-intensive estimates, such that simulations of very long transients with high spatial detail are infeasible. On the other hand, subchannel codes require relatively low computational time and can provide pin-level estimates, but have substantial empiricism in evaluating aspects such as crossflows and turbulent mixing coefficients. A multiscale method (SC+) for bridging this accuracy/speed gap, based on the Subchannel CFD (SubChCFD) method of Liu et al. [Nucl. Eng. Design, Vol. 355, paper 110318 (2019)], is demonstrated and developed here with a focus on a 5 × 5 square rod bundle geometry. The method has been newly implemented into the commercial code STAR-CCM+ and benchmarked against Liu et al.’s data. The 5 × 5 geometry was chosen in part due to the availability of direct numerical simulation (DNS) data at a relevant Reynolds number of a similar configuration for comparison. The SC+ results are variously compared against results from DNS, large eddy simulation, wall-resolved Reynolds-averaged Navier-Stokes, and coarse-mesh CFD methods. As an expansion to the original SubChCFD approach, a simple Hi2Lo approach is demonstrated using the DNS data as a correction to the original friction factor correlations employed. This is verified to improve the predictions. Additional test cases with geometric perturbations are pursued, illustrating the flexibility of SC+. The potential of this method for modeling the narrow gap vortex instability, which would represent an advancement over standard subchannel approaches, is also assessed. The method is expanded to include transverse flow losses, which was found to improve the results for modeling the gap instability. Initial extensions of SC+ for hexagonal rod bundles are also presented; some inaccuracies for the coarsest meshes prompted a detailed investigation of the mesh convergence behavior of the method. Geometric correction factors were devised that provided substantial improvement on these very coarse meshes, improving the prospects of SC+ for wider usage. Future work plans are to expand the methodology to wire-wrapped rod bundles and to implement the method into Pronghorn, with a unified pipeline via the Cardinal wrapper between the codes NekRS, Pronghorn, and BISON, to solve fuel performance problems of direct interest to industry.

Revisiting Tensor Basis Neural Network for Reynolds stress modeling: Application to plane channel and square duct flows

Recent advances in computing power devoted to Computational Fluid Dynamics (CFD) have opened up a new avenue for addressing the turbulence closure problem through Machine Learning (ML). Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence Reynolds-Averaged Navier–Stokes (RANS) modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However, persistent ambiguities remain regarding the physical adequacy of applying the General Eddy Viscosity Model (GEVM) within these frameworks. This work aims at investigating this aspect in an a priori stage for better predictions of the Reynolds stress anisotropy tensor, while preserving the Galilean and rotational invariances. In particular, we propose a general framework providing optimal tensor basis models for two types of canonical flows with increasing complexity: Plane Channel Flow (PCF) and Square Duct Flow (SDF). Subsequently, deep neural networks based on these optimal models are trained using state-of-the-art strategies to achieve a balanced and physically sound prediction of the full anisotropy tensor. A priori results obtained by the proposed framework are in very good agreement with the reference Direct Numerical Simulations (DNS) data. Notably, our shallow network with three layers excels in providing accurate predictions of the anisotropy tensor for PCF at unobserved friction Reynolds numbers, both in interpolation and extrapolation scenarios. The learning of the SDF case is more challenging because of its physical nature but also due to a lack of training data at various regimes. We propose a numerical strategy to alleviate this problem based on Transfer Learning (TL). In order to more efficiently generalize to an unseen intermediate Reτ regime, we take advantage of our prior knowledge acquired from a training with a larger and wider dataset. Our results indicate the potential of the developed network model, and demonstrate the feasibility and efficiency of the TL process in terms of training data size and training time. Based on these results, we believe there is a promising future by integrating these neural networks into an adapted in-house RANS solver.

Modelling of the Flame Surface Density Transport During Flame-Wall Interaction of Premixed Flames within Turbulent Boundary Layers

ABSTRACT A priori Direct Numerical Simulation (DNS) analysis of the modelling of the generalised flame surface density (FSD) transport equation in the framework of Reynolds Averaged Navier-Stokes (RANS) simulations has been conducted with a focus on flame-wall interaction (FWI) within turbulent boundary layers. The analysis was performed using two different scenarios: one involving the unsteady head-on interaction of a statistically planar premixed flame as it propagates through a turbulent boundary layer, and the other addressing statistically stationary oblique-wall interaction of a V-shaped premixed flame within a turbulent channel flow. Flame-wall interaction has been observed to exert a significant influence on the statistical behavior of the terms in the FSD transport equation. Throughout all phases of flame-wall interaction in both configurations, the primary source and sink terms in the FSD transport equation are consistently associated with the tangential strain rate and curvature terms. The relative importance of the contributions of the propagation and turbulent transport terms in the FSD transport equation have been found to be influenced by the flame-wall interaction configuration. Existing models for the tangential strain rate term in the FSD transport equation have been identified as inadequate based on a priori DNS assessment. Hence, adjustments to these models have been proposed to address the impact of flame orientation and near-wall effects specifically in the context of flame-wall interaction within turbulent boundary layers. The alignment between the flame normal vector and the wall normal vector has been identified as a crucial factor in modelling the contributions of unresolved dilatation rate and unresolved normal strain rate to the FSD transport equation. New models for these terms have been demonstrated to exhibit satisfactory agreement with the corresponding terms extracted from DNS data.

Multiscale analysis of turbulence in horizontal pipes: Liquid and particle-liquid flow investigation

An experimental–theoretical methodology is developed to investigate the characteristics of turbulence in horizontal particle-liquid pipe flows. Using a discrete wavelet transform, the three-dimensional Lagrangian trajectories of the liquid phase experimentally determined by positron emission particle tracking are decomposed into their deterministic and stochastic sub-trajectories, which are then utilized to construct profiles of local fluctuating velocity components and turbulent kinetic energy. The results for a single-phase flow are independently validated using computational fluid dynamic simulation and the analysis parameters are fine-tuned using direct numerical simulation data from the literature. In a particle-liquid flow, the investigation explores the influence of various factors including particle size, density, and concentration on turbulence intensity. Remarkably, the results demonstrate significant effects of the particle size and density on liquid turbulence. The enhanced understanding gained regarding turbulence intensity helps to advance our fundamental interpretation of the dynamics of particle-liquid flows, thus potentially aiding the rational design of such complex flows and associated equipment.

Modeling of high-speed, methane–air, turbulent combustion, Part I: One-dimensional turbulence modeling with comparison to DNS

The ability of the one-dimensional turbulence (ODT) model to serve as a surrogate direct numerical simulation (DNS) is assessed for highly turbulent flames. The ODT model is applied to freely propagating premixed methane–air flames at Karlovitz numbers 10, 102, 103, and 104, and results are compared with DNS. The ODT model solves the conservation equations for momentum, energy, and species on a one-dimensional domain, which corresponds to a streamwise line of sight spanning the DNS domain. The effects of turbulent advection are modeled via a stochastic process, in which the Kolmogorov and reactive length and time scales are explicitly resolved. Molecular transport and chemical kinetics are concurrently advanced in time. Both the ODT and DNS simulations use a 21-species skeletal chemical model for methane combustion. The accuracy of the ODT model is assessed by comparing its predictions of several key characteristics of the flames for each Karlovitz number tested, including the turbulent flame speed and width and the joint probability density functions (jPDFs) of major and selected minor species as well as the heat release rate conditioned on temperature with the results of DNS under comparable conditions. The ODT model is shown to yield qualitative and quantitative agreement with the DNS data for most of the above flame characteristics. Discrepancies are observed primarily for the jPDFs of several minor species examined. Overall, the ODT approach is shown to be an effective surrogate of DNS, potentially useful for guiding chemical reaction model reduction and for assessing the sensitivities of the flame structure and the burning rate to chemistry under highly turbulent conditions.Novelty and Significance:The direct numerical simulations (DNS) of premixed turbulent methane–air flames presented in this work span a uniquely wide range of turbulent intensities, from relatively modest corresponding to Karlovitz number Ka=10 to ultra-high intensities at Ka=104. This represents virtually the entire range of turbulent intensities that could be encountered in any realistic situation. This is also the first time that such a wide range of conditions is probed for methane in high-fidelity, fully resolved simulations, which use a fully compressible set of flow equations. The one-dimensional turbulence (ODT) model utilizes the same forcing that is present in the DNS enabling a direct comparison between the ODT and DNS. The results show that ODT captures the key features of the DNS results. ODT is shown to be an effective surrogate for DNS and may be useful in guiding chemical reaction model reduction, where many simulations are required.

Robust relation of streamwise velocity autocorrelation in atmospheric surface layers based on an autoregressive moving average model

We construct an autoregressive moving average (ARMA) model consisting of the history and random effects for the streamwise velocity fluctuation in boundary-layer turbulence. The distance to the wall and the boundary-layer thickness determine the time step and the order of the ARMA model, respectively. Based on the autocorrelation's analytical expression of the ARMA model, we obtain a global analytical expression for the second-order structure function, which asymptotically captures the inertial, dynamic and large-scale ranges. Specifically, the exponential autocorrelation of the ARMA model arises from the autoregressive coefficients and is modified to logarithmic behaviour by the moving-average coefficients. The asymptotic expressions enable us to determine model coefficients by existing parameters, such as the Kolmogorov and the Townsend–Perry constants. A consequent double-log expression for the characteristic length scale is derived and is justified by direct numerical simulation data with $Re_\tau \approx 5200$ and field-measured neutral atmospheric surface layer data with $Re_\tau \sim O(10^6)$ from the Qingtu Lake Observation Array site. This relation is robust because it applies to $Re_\tau$ from $O(10^4)$ to $O(10^6)$ , and even when the statistics of natural ASL deviate from those of canonical boundary-layer turbulence, e.g. in the case of imbalance in energy production and dissipation, and when the Townsend–Perry constant deviates from traditional values.