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DOE OSTI2015

Numerical Simulations of Subscale Wind Turbine Rotor Inboard Airfoils at Low Reynolds Number

New blade designs are planned to support future research campaigns at the SWiFT facility in Lubbock, Texas. The sub-scale blades will reproduce specific aerodynamic characteristics of utility-scale rotors. Reynolds numbers for megawatt-, utility-scale rotors are generally above 2-8 million. The thickness of inboard airfoils for these large rotors are typically as high as 35-40%. The thickness and the proximity to three-dimensional flow of these airfoils present design and analysis challenges, even at the full scale. However, more than a decade of experience with the airfoils in numerical simulation, in the wind tunnel, and in the field has generated confidence in their performance. Reynolds number regimes for the sub-scale rotor are significantly lower for the inboard blade, ranging from 0.7 to 1 million. Performance of the thick airfoils in this regime is uncertain because of the lack of wind tunnel data and the inherent challenge associated with numerical simulations. This report documents efforts to determine the most capable analysis tools to support these simulations in an effort to improve understanding of the aerodynamic properties of thick airfoils in this Reynolds number regime. Numerical results from various codes of four airfoils are verified against previously published wind tunnel results where data at those Reynolds numbers are available. Results are then computed for other Reynolds numbers of interest.

17 WIND ENERGY↗

DOE OSTI2024

Towards accelerating particle-resolved direct numerical simulation with neural operators

In this paper, we present our ongoing work aimed at accelerating a particle-resolved direct numerical simulation model designed to study aerosol–cloud–turbulence interactions. The dynamical model consists of two main components—a set of fluid dynamics equations for air velocity, temperature, and humidity, coupled with a set of equations for particle (i.e., cloud droplet) tracing. Rather than attempting to replace the original numerical solution method in its entirety with a machine learning (ML) method, we consider developing a hybrid approach. We exploit the potential of neural operator learning to yield fast and accurate surrogate models and, in this study, develop such surrogates for the velocity and vorticity fields. We discuss results from numerical experiments designed to assess the performance of ML architectures under consideration as well as their suitability for capturing the behavior of relevant dynamical systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Numerical simulation of evaporating wavy falling liquid films in laminar gas streams

Numerical simulations are performed to investigate the interfacial heat and mass transfer from evaporating wavy falling liquid films in interaction with laminar gas streams. The OpenFOAM solver has been used to conduct the simulations where the liquid-gas interface is resolved using the Volume of Fluid method of solving for three phases, i.e., liquid, vapor, and air. The configuration considered is a falling liquid (water) film on a heated vertical plate with a confined laminar moist air (gas) flow that is either (a) co-current or (b) counter-current to the downward liquid flow. The evaporation at the liquid-gas interface is driven by the interfacial gradient of the vapor mass fraction. Interfacial waves are triggered using a monochromatic forcing disturbance that leads to sinusoidal or solitary waves forming at the liquid-gas interface under respective forcing frequencies. Further, the numerical model is validated with the available experimental data. The results show nearly a 15% enhancement in time-averaged Sherwood number (Sh) due to film waviness (sinusoidal or solitary) at the lower volumetric gas flow rate, Q g = +50 (co-current) and Q g = -50 (counter-current). This enhancement in the Sh for both the waves further increases by 11% with Q g = +800 and 196% with Q g = -800. A closer examination of the mass transfer process over a wave demonstrates that with Q g = +50, the concentration of the gas side streamlines at the trough locations of the wave leads to higher values of Sh at these locations. However, with Q g = +800, although the overall Sh increases, vortices appear at the wave trough locations, leading to a corresponding decrease in the local Sh values. Correlations are proposed for predicting Sh under co-current and counter-current gas flow effects.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Direct Numerical Simulations of Autoignition in Stratified Dimethyl-ether (DME)/Air Turbulent Mixtures

In our paper, two- and three-dimensional direct numerical simulations (DNS) of autoignition phenomena in stratified dimethyl-ether (DME)/air turbulent mixtures are performed. A reduced DME oxidation mechanism, which was obtained using rigorous mathematical reduction and stiffness removal procedure from a detailed DME mechanism with 55 species, is used in the present DNS. The reduced DME mechanism consists of 30 chemical species. This study investigates the fundamental aspects of turbulence-mixing-autoignition interaction occurring in homogeneous charge compression ignition (HCCI) engine environments. A homogeneous isotropic turbulence spectrum is used to initialize the velocity field in the domain. Moreover, the computational configuration corresponds to a constant volume combustion vessel with inert mass source terms added to the governing equations to mimic the pressure rise due to piston motion, as present in practical engines. DME autoignition is found to be a complex three-staged process; each stage corresponds to a distinct chemical kinetic pathway. The distinct role of turbulence and reaction in generating scalar gradients and hence promoting molecular transport processes are investigated. Then, by applying numerical diagnostic techniques, the different heat release modes present in the igniting mixture are identified. In particular, the contribution of homogeneous autoignition, spontaneous ignition front propagation, and premixed deflagration towards the total heat release are quantified.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2015

Picosecond lasing in ytterbium fibre laser with nonlinear optical loop mirror: experiment and numerical simulation

The operation regimes of a pulsed all-normal-dispersion polarisation-maintaining fibre laser with a nonlinear optical loop mirror are studied. The use of polarisation-maintaining fibres ensures polarisation and temperature stability of output radiation. The lasing and instability thresholds of the pulsed laser are determined experimentally. A spectral filter placed in the cavity makes it possible to change the centre wavelength of laser radiation within the range 1.02 – 1.05 μm with a spectral full width at half maximum of 2 nm. The average output power is 7 mW, which corresponds to a pulse energy of 0.8 nJ. The autocorrelation function width of the output pulse is 50 ps. The minimum pulse duration achieved after compression by an external pair of diffraction gratings is 1.8 ps. The dynamics of the temporal and spectral parameters of laser pulses is studied using mathematical simulation based on numerical solution of the nonlinear Schrödinger equation. The simulation results coincide with experimental data with a high accuracy. (lasers)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Direct numerical simulations for hybrid rocket boundary layers: Performance modeling and scaling

This paper presents a comprehensive performance and scaling analysis of direct numerical simulations for reacting boundary layers, focusing on slab burner configurations. Using a PETSc-based finite volume CFD framework, the study evaluates the scalability and computational cost of flow, chemistry, and radiation evaluations across 2D and 3D simulations. Polymethyl methacrylate (PMMA) is the fuel with pure O 2 as the oxidizer, modeled using a detailed chemical kinetics mechanism with 113 species and 660 reactions. A ray-tracing-based radiation solver, designed for distributed memory applications, is implemented to model radiation heat transfer. Parallel scalability is analyzed for the coupled flow, chemistry, and radiation heat transfer processes. Weak and strong scaling studies are conducted on up to 15,000 computational ranks, revealing robust performance when flow cells exceed 200 per rank. Chemistry evaluations dominate the computational cost in large 3D simulations, accounting for approximately 40% of the total runtime, while flow processes contribute around 35%, and radiation solver contributions remain below 10% due to reduced evaluation frequencies. GPU accelerated chemistry evaluation, implemented with Zero-RK, demonstrates significant promise, achieving up to a 4x speedup for workloads exceeding 30,000 cells per GPU. However, diminishing returns are observed for smaller workloads due to CPU-GPU communication overhead. This study identifies key challenges, including memory bottlenecks and the effects of domain partitioning on flow scalability, while highlighting the potential of GPU-accelerated chemistry to reduce computational costs. In conclusion, these findings provide realizable run configurations for 2D, 3D, and GPU-accelerated cases, offering insights for optimizing reactive flow solvers.

CFD Scalability↗

DOE OSTI2021

Direct Numerical Simulation of Flow Over a Wall-Mounted Cube with the Nek5000 Spectral Element Code: DNS at Re h = 3900

The direct numerical simulation (DNS) of the canonical wall-mounted unit cube subjected to two distinct incident velocity profiles is performed at a Reynolds number where the bulk flow characteristics are known to become relatively Reynolds number insensitive. The aim of this work is to highlight the sensitivity of such bluff-body flows to mean shear and to provide a representative set of data for such flow scenarios where common turbulence modeling techniques often fail. Simple boundary conditions and a small domain are selected to allow for cost-effective and easy comparisons for model development purposes. In addition to mean velocity profiles, select turbulence statistics are presented in detail. Further, the basic efficacy of eddy viscosity models is evaluated and found to be adequate only for the shear stress components for the bluff-body flows examined here. Other failure mechanisms for RANS are proposed.

42 ENGINEERING↗

DOE OSTI2022

A micromorphic filter for determining stress and deformation measures from direct numerical simulations of lower length scale behavior

A micromorphic filter is presented for the extraction of stress and deformation measures from underlying direct numerical simulation (DNS) of microstructural mechanical response. The filter is consistent with the micromorphic continuum theory of Eringen and Suhubi (1964), and allows the interrogation of a DNS to generate higher order constitutive models. The filter adopts aspects of the overlap coupling techniques for atomistic-continuum scale-bridging in order to update the nodal degrees of freedom of the finite-element-based filter. Here, two methods for the extraction of quantities of interest from the underlying DNS are presented. The first is a least squares fitting technique which is appropriate for finite-element-style macro-scale domains, and the second is a variationally based approach which generalizes the method to any macro-scale domain which has a variational form. No restrictions on the form of the micro-scale simulation are inherent to the approach, provided that the required quantities (stress, position, etc.) can be provided. The filter is applied to a simple homogeneous medium undergoing homogeneous deformation to demonstrate the recovery of a classical continuum response, what we call the null case. We then apply the framework to the same homogeneous medium with a central and edge penny-shaped crack to show micromorphic effects. We demonstrate that varying the size of the filter causes the micromorphic behaviors to arise and then dissipate as the filter becomes smaller than the crack's length scale. Additionally we show the effect of filter size on a chiral element network along with a plate perforated with evenly spaced and perturbed holes through the thickness. The micromorphic effects are shown to be present for the chiral elements under any loading but become most pronounced when a single element is located within each averaging domain. Micromorphic effects become pronounced for the plate upon the onset of localization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to $4096^3$ points. The Reynolds and Froude numbers are respectively equal to $Re=5.4\times 10^4$ and $Fr=0.0242$. The ratio of the Brunt-V\"ais\"al\"a to the inertial wave frequency, $N/f$, is taken to be equal to 5, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number $R_B=ReFr^2=32$, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, and a large-scale enhancement of energy is also observed, directly attributable to the effect of rotation.

Bolgiano-Obukhov↗

DOE OSTI2014

Estimating uncertainties in statistics computed from direct numerical simulation

Rigorous assessment of uncertainty is crucial to the utility of direct numerical simulation (DNS) results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier–Stokes equations. Due to the presence of non-trivial sampling error, standard techniques for estimating discretization error (such as Richardson extrapolation) fail or are unreliable. This work provides a systematic and unified approach for estimating these errors. First, a sampling error estimator that accounts for correlation in the input data is developed. Then, this sampling error estimate is used as part of a Bayesian extension of Richardson extrapolation in order to characterize the discretization error. These methods are tested using the Lorenz equations and are shown to perform well. These techniques are then used to investigate the sampling and discretization errors in the DNS of a wall-bounded turbulent flow at Reτ ≈ 180. Both small (Lx/δ × Lz/δ = 4π × 2π) and large (Lx/δ × Lz/δ = 12π × 4π) domain sizes are investigated. For each case, a sequence of meshes was generated by first designing a “nominal” mesh using standard heuristics for wall-bounded simulations. These nominal meshes were then coarsened to generate a sequence of grid resolutions appropriate for the Bayesian Richardson extrapolation method. In addition, the small box case is computationally inexpensive enough to allow simulation on a finer mesh, enabling the results of the extrapolation to be validated in a weak sense. For both cases, it is found that while the sampling uncertainty is large enough to make the order of accuracy difficult to determine, the estimated discretization errors are quite small. This indicates that the commonly used heuristics provide adequate resolution for this class of problems. However, it is also found that, for some quantities, the discretization error is not small relative to sampling error, indicating that the conventional wisdom that sampling error dominates discretization error for this class of simulations needs to be reevaluated.

Oliver, Todd A.↗

DOE OSTI2017

Computational Flame Diagnostics for Direct Numerical Simulations with Detailed Chemistry of Transportation Fuels

The goal of the proposed research is to create computational flame diagnostics (CFLD) that are rigorous numerical algorithms for systematic detection of critical flame features, such as ignition, extinction, and premixed and non-premixed flamelets, and to understand the underlying physicochemical processes controlling limit flame phenomena, flame stabilization, turbulence-chemistry interactions and pollutant emissions etc. The goal has been accomplished through an integrated effort on mechanism reduction, direct numerical simulations (DNS) of flames at engine conditions and a variety of turbulent flames with transport fuels, computational diagnostics, turbulence modeling, and DNS data mining and data reduction. The computational diagnostics are primarily based on the chemical explosive mode analysis (CEMA) and a recently developed bifurcation analysis using datasets from first-principle simulations of 0-D reactors, 1-D laminar flames, and 2-D and 3-D DNS (collaboration with J.H. Chen and S. Som at Argonne, and C.S. Yoo at UNIST). Non-stiff reduced mechanisms for transportation fuels amenable for 3-D DNS are developed through graph-based methods and timescale analysis. The flame structures, stabilization mechanisms, local ignition and extinction etc., and the rate controlling chemical processes are unambiguously identified through CFLD. CEMA is further employed to segment complex turbulent flames based on the critical flame features, such as premixed reaction fronts, and to enable zone-adaptive turbulent combustion modeling.

42 ENGINEERING↗

DOE OSTI2016

Characterisation of two-stage ignition in diesel engine-relevant thermochemical conditions using direct numerical simulation

With the goal of providing a more detailed fundamental understanding of ignition processes in diesel engines, this study reports analysis of a direct numerical simulation (DNS) database. In the DNS, a pseudo turbulent mixing layer of dimethyl ether (DME) at 400 K and air at 900 K is simulated at a pressure of 40 atmospheres. At these conditions, DME exhibits a two-stage ignition and resides within the negative temperature coefficient (NTC) regime of ignition delay times, similar to diesel fuel. The analysis reveals a complex ignition process with several novel features. Autoignition occurs as a distributed, two-stage event. The high-temperature stage of ignition establishes edge flames that have a hybrid premixed/autoignition flame structure similar to that previously observed for lifted laminar flames at similar thermochemical conditions. In conclusion, a combustion mode analysis based on key radical species illustrates the multi-stage and multi-mode nature of the ignition process and highlights the substantial modelling challenge presented by diesel combustion.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In this paper, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.

42 ENGINEERING↗

DOE OSTI2017

A direct numerical simulation study of flame structure and stabilization of an experimental high Ka CH 4 /air premixed jet flame

In the present work, a direct numerical simulation (DNS) of an experimental high Karlovitz number (Ka) CH 4 /air piloted premixed flame was analyzed to study the inner structure and the stabilization mechanism of the turbulent flame. A reduced chemical mechanism for premixed CH 4 /air combustion with NO x based on GRI-Mech3.0 was used, including 268 elementary reactions and 28 transported species. The evolution of the stretch factor, I 0 , indicates that the burning rate per unit flame surface area is considerably reduced in the near field and exhibits a minimum at x /D = 8. Downstream, the burning rate gradually increases. The stretch factor is different between different species, suggesting the quenching of some reactions but not others. Comparison between the turbulent flame and strained laminar flames indicates that certain aspects of the mean flame structure can be represented surprisingly well by flamelets if changes in boundary conditions are accounted for and the strain rate of the mean flow is employed; however, the thickening of the flame due to turbulence is not captured. The spatial development of displacement speeds is studied at higher Ka than previous DNS. In contrast to almost all previous studies, the mean displacement speed conditioned on the flame front is negative in the near field, and the dominant contribution to the displacement speed is normal diffusion with the reaction contribution being secondary. Further downstream, reaction overtakes normal diffusion, contributing to a positive displacement speed. The negative displacement speed in the near field implies that the flame front situates itself in the pilot region where the inner structure of the turbulent flame is affected significantly, and the flame stabilizes in balance with the inward flow. Notably, in the upstream region of the turbulent flame, the main reaction contributing to the production of OH, H+O 2 ⇌O+OH (R35), is weak. Moreover, oxidation reactions, H 2 +OH⇌H+H 2 O (R79) and CO+OH⇌CO 2 +H (R94), are influenced by H 2 O and CO 2 from the pilot and are completely quenched. Hence, the entire radical pool of OH, H and O is affected. Furthermore, the fuel consumption layer remains comparably active and generates heat, mainly via the reaction CH 4 +OH⇌CH 3 +H 2 O (R93).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as well as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.

42 ENGINEERING↗

DOE OSTI2015

A mass conserving level set method for detailed numerical simulation of liquid atomization

An improved mass conserving level set method for detailed numerical simulations of liquid atomization is developed to address the issue of mass loss in the existing level set method. This method introduces a mass remedy procedure based on the local curvature at the interface, and in principle, can ensure the absolute mass conservation of the liquid phase in the computational domain. Three benchmark cases, including Zalesak's disk, a drop deforming in a vortex field, and the binary drop head-on collision, are simulated to validate the present method, and the excellent agreement with exact solutions or experimental results is achieved. It is shown that the present method is able to capture the complex interface with second-order accuracy and negligible additional computational cost. The present method is then applied to study more complex flows, such as a drop impacting on a liquid film and the swirling liquid sheet atomization, which again, demonstrates the advantages of mass conservation and the capability to represent the interface accurately.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Tracing the Rain Formation Pathways in Numerical Simulations of Deep Convection

Quantifying the microphysical process contributions to surface precipitation in numerical simulations can be challenging. This is due to the fact that many microphysical processes contribute to the formation and depletion of rain drops and there is almost always a spatial/temporal mismatch between where/when rain is formed and where/when it strikes the surface. In this work, we develop a tracing method that tracks the sources and sinks of raindrop mass and number as they are advected by the Weather Research and Forecasting model. Applying the method to an idealized squall line confirms that convective precipitation is dominated by warm rain processes (autoconversion and accretion) while stratiform precipitation is dominated by the melting of rimed and unrimed ice crystals. Sensitivity experiments in which the prescribed cloud drop number concentration is increased confirm the conventional wisdom that weakened autoconversion increases the fraction of raindrops originating from cold rain processes. The method also reveals that when applied to deep convection the Khairoutdinov and Kogan autoconversion scheme produces an excessive number of raindrops which are subsequently clipped in P3 microphysics to keep the rain size distribution within prescribed limits. This problem can mostly be mitigated by increasing the assumed radius for raindrops created by autoconversion.

58 GEOSCIENCES↗

DOE OSTI2015

Direct numerical simulation of Taylor-Couette flow subjected to a radial temperature gradient

Direct numerical simulations have been performed to study the Taylor-Couette (TC) flow between two rotating, coaxial cylinders in the presence of a radial temperature gradient. Specifically, the influence of the buoyant force and the outer cylinder rotation on the turbulent TC flow system with the radius ratio η = 0.912 was examined. For the co-rotating TC flows with Re{sub i} (inner cylinder) =1000 and Re{sub o} (outer cylinder) =100, a transition pathway to highly turbulent flows is realized by increasing σ, a parameter signifying the ratio of buoyant to inertial force. This nonlinear flow transition involves four intriguing states that emerge in sequence as chaotic wavy vortex flow for σ = 0, wavy interpenetrating spiral flows for σ = 0.02 and 0.05, intermittent turbulent spirals for σ = 0.1 and 0.2, and turbulent spirals for σ = 0.4. Overall, the fluid motion changes from a centrifugally driven flow regime characterized by large-scale wavy Taylor vortices (TVs) to a buoyancy-dominated flow regime characterized by small-scale turbulent vortices. Commensurate changes in turbulence statistics and heat transfer are seen as a result of the weakening of large-scale TV circulations and enhancement of turbulent motions. Additionally, the influence of variation of the outer cylinder rotation, −500 < Re{sub o} < 500 in presence of buoyancy (σ = 0.1) with Re{sub i} = 1000, has been considered. Specifically, it is demonstrated that this variation strongly influences the azimuthal and axial mean flows with a weaker influence on the fluctuating fluid motions. Of special interest, here are the turbulent dynamics near the outer wall where a marked decrease of turbulence intensity and a sign inversion of the Reynolds stress R{sub rz} are observed for the strongly counter-rotating regimes (Re{sub o} = − 300 and −500). To this end, it has been shown that the underlying flow physics for this drastic modification are associated with the modification of the correlation between the radial and axial fluctuating motions. In turn, the intriguing effects of this modification on the mean axial flow, turbulent statistics, force balance, and dynamic processes such as turbulence production and dissipation are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗