Search

One-dimensional turbulence (ODT) simulations of a spatially developing planar shear layer are used to obtain the probability density function (PDF) of the concentration of a passive scalar. An asymmetry of the PDF with respect to transverse location in this self-similar flow appears in the ODT results and in experimental results obtained with planar laser-induced fluorescence of acetone. Using the ODT simulations, estimates are presented of the effect of measurement volume upon the resulting PDFs. Variable density effects on the concentration of the denser fluid within incompressible flow are also examined.

One-dimensional turbulence is a stochastic simulation method representing the time evolution of the velocity profile along a notional line of sight through a turbulent flow. In this paper, the velocity is treated as a three-component vector, in contrast to previous formulations involving a single velocity component. This generalization allows the incorporation of pressure-scrambling effects and provides a framework for further extensions of the model. Computed results based on two alternative physical pictures of pressure scrambling are compared to direct numerical simulations of two time-developing planar free shear flows: a mixing layer and a wake. Scrambling based on equipartition of turbulent kinetic energy on an eddy-by-eddy basis yields less accurate results than a scheme that maximizes the intercomponent energy transfer during each eddy, subject to invariance constraints. The latter formulation captures many features of free shear flow structure, energetics, and fluctuation properties, including the spatial variation of the probability density function of a passive advected scalar. These results demonstrate the efficacy of the proposed representation of vector velocity evolution on a one-dimensional domain.

Molecular dynamics simulations using the Lennard-Jones energy potential are compared with continuum solutions of reaction and diffusion in a dilute gas. The reaction model is a passive one in which high-energy bath atoms create a species, at dilute concentrations, which may have a very fast consumption reaction. This construction is designed based on typical fast reaction pathways involved in the fuel breakup in a hydrocarbon flame. Using reaction rates and diffusivities obtained from the molecular simulations allows the continuum solution to describe the reactive atom density spatial distribution with good accuracy. Based on this agreement, it is possible to estimate which reaction rates will produce negligible diffusive spreading, and hence, which species might be assumed to be in chemical equilibrium in continuum reacting flow calculations.

A premixed flame within a turbulent flow exhibits a decreasing enhancement of fuel consumption rate with increasing turbulence intensity, an effect known as the bending effect. Denet has shown that flow time correlations may be one cause of the bending effect. Using a Damkohler-Huygens front propagation model, we illustrate that the removal of flow components with reduced frequencies greater than unity (ω >kS L) causes a small reduction in front area but a large reduction in the flow intensity, which is the bending effect (ω is the frequency and k is the wavenumber). To be effective in producing front area, a flow mode must have a phase velocity, ω/k, smaller than the laminar burning velocity, S L.

Molecular dynamics of two- and three-dimensional liquids undergoing a homogeneous adiabatic expansion provides a direct numerical simulation of the atomization process. The Lennard-Jones potential is used with different force cutoff distances; the cluster distributions do not depend strongly on the cutoff parameter. Expansion rates, scaled by the natural molecular time unit (about a picosecond), are investigated from unity down to 0.01; over this range the mean droplet size follows the scaling behavior of an energy balance model which minimizes the sum of kinetic plus surface energy. A second model which equates the elastic stored energy to the surface energy gives better agreement with the simulation results. The simulation results indicate that both the mean and the maximum droplet size have a power-law dependence upon the expansion rate; the exponents are {minus}2d/3 (mean) and {minus}d/2 (maximum), where {ital d} is the dimensionality. The mean does not show a dependence upon the system size, whereas the maximum does increase with system size, and furthermore, its exponent increases with an increase in the force cutoff distance. A mean droplet size of 2.8/{eta}{sup 2}, where {eta} is the expansion rate, describes our high-density three-dimensional simulation results, and this relation is also close to experimentalmore » results from the free-jet expansion of liquid helium. Thus, one relation spans a cluster size range from one atom to over 40 million atoms. The structure and temperature of the atomic clusters are described. {copyright} {ital 1999} {ital The American Physical Society}« less

A premixed flame, propagating away from a point ignition source into an unlimited domain displays an increasing flame speed after the flame size has grown beyond a transition radius. Experiments by Gostintsev et al are described by the relation R = R1 + At3/2, where t is the time from ignition and, where SL is the flame burning velocity and is the thermal diffusivity. The non-dimensional function a() is determined from the experimental results to be equal to 0.0022, where is the density ratio across the flame. In the present work, two-dimensional Lagrangian simulations of flame propagation also display a radial growth with a 3/2 power-law behaviour. This is a potential flow model - no vorticity is included. Hence, the Darrieus - Landau hydrodynamic instability by itself can generate flame acceleration. The numerical results are summarized by the relation R = R1+(2/40)L(SLt/L)3/2, where L is a reference length and is the volume production ratio, = - 1. Equating the zone of velocity jump in the numerical sc...

Three-dimensional turbulence simulations which include three different mean directions of passive flame propagation are analyzed for the isotropic nature of the flame shape, as given by the fluctuations in the G scalars which determine the passive Huygens propagation. When the turbulence intensity is greater than the flame burning velocity, the fluctuations appear to be isotropic as assumed in the analysis of Peters (1992)

Flame propagation through an array of vortices was studied with a model which incorporated the variation of the local burning velocity with stretch. Assuming incompressible flow, the mean burning velocities were calculated and compared to those of the Huygens limit. It was found that stretch causes a decrease in the mean burning velocity, and a mechanism which explains this trend was identified. The study also demonstrated that, as expected, stretch only has a significant effect on the mean burning velocity for vortices whose size is of the same order as that of the flame thickness.

Flame propagation into a swirling flow allows the creation of burnt gas vorticity which may enhance the forward motion of the flame. This baroclinic push on the flame differs from the axial pressure model suggested by Chomiak (1976). In particular, the baroclinic enhancement will depend upon the location of the burnt gas with respect to the flame, as shown by two vortex configurations: straight and curved. Additionally, the baroclinic effect, depending upon the flame density gradient and the swirling flow radial pressure gradient, will provide an enhancement that is proportional to the ambient pressure.

A flame ball growing into a turbulent mixture exhibits a speed which is proportional to its size - this effect is a consequence of the distorted flame surface: the inner flame regions “push” the outer regions, the magnitude of this velocity depends upon the flame surface density distribution. A simple two-dimensional, zero-thickness flame model interacting with defined eddies illustrates how rapidly this flame distortion occurs after a spark ignition. This distributed volume source effect is also the functional form of Groffs modified entrainment model of flame propagation. A result of this size dependent growth is exponential growth of flame area which is an essential feature of spark-ignition internal combustion engines.

The mean passage rate of a propagating interface, subject to random advection or random variation of the local propagation speed, is investigated analytically and computationally. A model representing the longitudinal propagation of two points of the interface separated by a fixed transverse distance is formulated and analyzed. In the limit of weak random perturbations, the model predicts several parameter dependences of the mean passage rate. These predictions are evaluated by performing two-dimensional and three-dimensional numerical simulations of interface propagation. The analysis addresses broadband (i.e., multiscale, as in turbulent flow) as well as narrow-band perturbations. In the broadband case, scaling laws governing transient as well as statistically steady propagation are derived. The numerical simulations span a sufficient range of perturbation amplitudes to exhibit the complete amplitude dependence of the mean passage rate, including scaling behaviors governing the weak and strong perturbation limits.

The structure of a nonpremixed methane-air flame interacting with avortex is described by a two-step reduced mechanism. The mixture-fraction field Z for the flamelet is approximated by a stretched parabola. This synthetic mixture-fraction field is used to relate the vortex swirl velocity to the tangential velocity along the flamelet and to identify a rate of scalar dissipation χ appropriate for parabolically shaped flame tongue. The flame temperature and χ along the tongue are calculated in the context of rate-ratio asymptotics. It is found that the peak temperatures, and hence the smallest χ, occur at the flame tip. In addition, analytical estimates are made to evaluate the importance of the transverse convective effects in the reaction zone relative to the usually assumed diffusive-reactive balance. Away from the tip of the flame tongue but near it, the influences of transverse convection are important, but the relative magnitude of these effects is dependent on the curvature κ of the flamelet as well as on the spacing l between the mixture-fraction contour of the oxidizer stream (Z = 0) and that of the fuel stream (Z = 1); the convective influence becomes more pronounced as κ and/or l is increased. However, the estimates show that the importance of transverse convection is not as large as would be indicated using activation-energy asymptotics.

Laser diagnostics and flow simulation techniques are now providing information that, if available 50 years ago, would have allowed Damkohler to show how turbulence generates flame area. In the absence of this information, many turbulent flame speed models have been created, most based on Kolmogorov concepts that ignore the turbulence vortical structure. Over the last 20 years, the vorticity structure in mixing layers and jets has been shown to determine the entrainment and mixing behavior, and these effects need to be duplicated by combustion models. Turbulence simulations reveal the intense vorticity structure as filaments and simulations of passive flamelet propagation show how this vorticity creates flame area and defines the shape of the expected chemical reaction surface. Understanding how volume expansion interacts with flow structure should improve experimental methods for determining turbulent flame speed. Since the last decade has given us such powerful new tools to create and see turbulent combustion microscopic behavior, it seems that a solution of turbulent combustion within the next decade would not be surprising in the hindsight of 2004.

Computed flame motion through and between swirling eddies exhibits a maximum advancement rate which is related to the time duration of flame motion between eddies. This eddy spatial structure effect upon the apparent turbulent flame speed appears to be similar to the square-root dependence observed in wrinkled flamelet data. The rate-limiting behavior at one eddy length-scale can be removed by inclusion of smaller eddies which reside between the larger eddies. This large-eddy, small-eddy concept yields a recursion relation and repeated functional iteration can be done to approximate a desired flame speed relation. As an example, an iteration to produce ST In ST = u' is given for the range of u' observed in liquid flames. Currently, the iteration process is a post-diction of flame speed, but if a universality can be developed, then a predictive theory of turbulent flame propagation might be achieved.

Molecular mechanics simulations of liquid water in a shear-driven cavity flow have been presented by Greenspan [Fluid Dyn. Res. 25 (1999) 37]. The selected parameter values in these calculations require cautionary comments, for example, the presented turbulent flow results involve atomic motion with a kinetic temperature exceeding a million degrees Kelvin

The overall propagation rate of growing interfaces subject to weak random stirring is investigated, based on a variant of the Kardar-Parisi-Zhang equation. Scaling analysis, supported by computations, indicates that random stirring increases the overall propagation rate in proportion to 4/3 power of the ratio of stirring rate to growth rate. The generally assumed quadratic dependence on this ratio is valid only for special cases such as periodic flow. On this basis, a modified turbulent-flame speed formula is proposed. Implications concerning interpretation of measurements are noted.

Experimental and numerical determinations of flame front curvature and orientation in premixed turbulent flames are presented. The experimental data is obtained from planar, cross sectional images of stagnation point flames at a high Damkohler number (80) and turbulent Reynolds number of 60. A direct numerical simulation of constant energy turbulent flow is combined with a zero-thickness, constant density flame model to provide the numerical results. The two-dimensional curvature distributions of the experiments and numerical simulations compare well at q′ / S L =0.5 with mean values close to zero and significant negative skewness. At higher turbulence levels the simulations show that the distributions become symmetric about zero. These features are also found in the three dimensional distributions of curvature. The simulations support assumptions which make it possible to estimate the true mean direction cosine from two-dimensional images. The effect of these assumptions on the flame surface area density is a 12% reduction in comparison with the value determined directly from the planar data.

Marble's problem of a vortex winding up a diffusion flame sheet is simulated (Marble, 1985, with the effects of variable density and vorticity generation included. The initial flame is straight and passes through the vortex core, but not through the center of the vortex as in Marble's work. During the first eddy turn-over time, the swirling flow forms a flame tip region, and the amount of tip rotation around the vortex depends on the diffusion coefficient. During the next eddy turn-over time, the flame shape is quasi-steady with minor differences due to heat release and vorticity production over the parameter range examined. The gradient of mixture fraction at the flame sheet determines the amount of reaction in this Burke-Schumann flame model. This swirling flow maintains a uniform gradient along most of the flame surface, with the exception of a low-gradient region at the flame tip. If finite-rate chemistry is considered, then the tip region would likely be at higher temperature than the rest of the flame surface.

Computed vorticity-flame interactions in two-dimensions suggest that a wrinkled flame is a common occurrence in reacting turbulent flow and that these wrinkles are formed in a small fraction of an eddy turn-over time. An experiment in which the Tsuji porous-cylinder burner is spinning may be a way to achieve a steady, wrinkled diffusion flame under laboratory conditions. The wrinkled flame differs from the previously studied stagnation, counterflow flame in that the former has a large spatial variation in diffusive gradients near the wrinkle. These gradient variations may explain the extinction observed in unsteady, pulsed jets by Lewis et al

M\"uller-Plathe [Phys. Rev. E 59, 4894 (1999)] gives a velocity exchange method that creates a shear momentum flux. Measurement of the mean velocity gradient allows the determination of the shear viscosity. Low gradients are achieved when the time interval between exchanges is large (low frequency). We show that low frequency does not produce a steady shear flow while a weaker, but continuous exchange, does have a steady flow.

One-dimensional turbulence (ODT), a method for one-dimensional stochastic simulation of turbulent flow, is generalized to incorporate variable-density effects. This formulation is used to investigate variable-density effects in planar mixing layers. Computed results are compared to direct numerical simulations of temporally developing mixing layers and to measurements performed in spatially developing mixing layers. Dependencies of mean flow structure and fluctuation statistics on the free-stream density ratio s are examined, including s values beyond the range of previous experimental and computational studies. For temporally developing mixing layers, the previously noted decrease of the layer growth rate as s deviates from unity is reproduced. For spatially developing mixing layers, dependence on s is sensitive to whether the high-speed or the low-speed stream is denser; by convention, the latter case corresponds to s>1. Experimental results indicating that layer growth is an increasing function of s have previously been interpreted on the basis of models that imply the continuation of this monotonic trend for all s. ODT reproduces the observed trend within the experimentally accessible range, but predicts a reversal of the trend slightly beyond that range and a subsequent decrease of the growth rate as s increases. This and related results suggest a closer analogy between the behaviors of temporally and spatially developing mixing layers than has previously been recognized. An experimental test of the predicted trend reversal in spatially developing mixing layers is proposed.

An experimental and numerical study of the three-dimensional transition of plane wakes and shear layers behind a flat plate is presented. Flow visualization techniques are used to monitor the response of laminar flows at moderate Reynolds numbers (≈100) to perturbations periodically distributed along the span. In this way, the formation and evolution of streamwise vortex tubes and their interaction with the spanwise vortices are analyzed. The flow was studied numerically by means of three-dimensional inviscid vortex dynamics. Assuming periodicity in the spanwise and the streamwise direction, we discretize the vorticity field into two layers of vortex filaments with finite core diameter. Comparison between experiment and visualization indicates that important features of the three-dimensional evolution can be reproduced by inviscid vortex dynamics. Vortex stretching in the strain field of the spanwise rollers appears to be the primary mechanism for the three-dimensional transition in this type of flows.

A discrete vortex dynamics time-dependent simulation of a premixed wrinkled laminar flame shows that the computed turbulent shear stress in the flame brush region based on unconditioned velocities is substantial. By comparison, the computed shear stresses in the burnt and in the unburnt flow are negligible. Thus, it is the intermittent flame motion that gives the appearance of counter-gradient fluxes in a turbulence model based on unconditioned velocities. The flame is considered to be of zero thickness and the flame location is described in terms of arc length from the flame holder. Two-dimensional V-shaped and bunsen burner flames have been simulated in planar geometry. A flame speed relation is used which depends on flame curvature and in some calculations on flame stretch. Discrete volume sources are distributed along the flame location to represent the volume expansion at constant pressure combustion in this open system. The estimated vorticity production due to fluctuating pressure gradients combine...

The evolution of the two- and three-dimensional structures in a temporally growing plane shear layer is numerically simulated with the discrete vortex dynamics method. We include two signs of vorticity and thus account for the effect of the weaker boundary layer leaving the splitter plate which is used to create a spatially developing mixing layer. The interaction between the two layers changes the symmetry properties seen in a single vorticity-layer calculation and results in closer agreement with experimental observations of the interface between the two streams. Our calculations show the formation of concentrated streamwise vortices in the braid region between the spanwise rollers, whereas the spanwise core instability is observed to grow only initially. Comparison with flow visualization experiments is given, and we find that the processes dominating the early stages of the mixing-layer development can be understood in terms of essentially inviscid vortex dynamics.

With a Biot-Savart model of vortex filaments to provide initial conditions, a finite difference scheme for the incompressible Navier-Stokes equation is used in the region of closest approach of two vortex rings. In the Navier-Stokes solution, we see that the low pressure which develops between the interacting vorticity regions causes the distortion of the initially circular vortex cross section and forces the rearrangement of vorticity on a convective time scale which is much faster than that estimated from viscous transport.

By a molecular-dynamics simulation of a three-dimensional system of 4000 particles, we show that the long-time tail of the velocity autocorrelation function has the form ${\ensuremath{\alpha}}_{0}{t}^{\ensuremath{-}\frac{3}{2}}$, where $t$ is the time and ${\ensuremath{\alpha}}_{0}$ a coefficient depending on the kinematic viscosity and on the diffusion coefficient.

A numerical simulation of the response of a premixed flame to various randomly defined two-dimensional flow fields is performed in order to obtain an insight into Lewis number effects in turbulent premixed combustion. A one-step reaction with a large, but finite, activation energy in the limit of zero heat release is assumed.The numerical simulation uses vortex dynamics to describe the velocity field, while the scalar field is computed on a mesh.The flow field integral length scale is typically ten times the flame thickness, and the r.m.s. velocity fluctuation is of the order of the flame velocity. Ensemble averages are taken over a total number of 30 realization for Le of 1/2 and 37 realizations for Le of 2, where the Lewis number is Le = λ/(ρcpD). Since the density is kept constant, there is no feedback from the reacting scalar field to the velocity field. For the Le of 1/2 case, there is a clear manifestation of the thermo-diffusive instability mechanism leading to a cellular flame front struc...

We show asymptotically and numerically that a constant-density flame will exhibit different geometrical shapes which depend on the flow time-scales. In particular, a frozen flow may yield a flame surface composed of bulges connected by cusps, whereas a pulsating flow may dampen the flame motion to the extent that only a flat, laminar flame surface will be possible. The cusp nature disappears when the eddy frequency becomes comparable to uLk, where uL is the laminar flame speed and k is a characteristic wave number of the flow. Flame shapes obtained with a sheet of laser light within a spark-ignited engine show a cusp nature only at low engine RPM, in agreement with the frequency criteria given above.

The mathematical analogy between the elastic stress due to particle displacements in Hooke's law solids and the viscous stress due to velocity gradients in incompressible fluids correlates two interesting phenomena. In a two‐dimensional crystal the elastic restoring force opposing particle displacements approaches zero with increasing crystal size, leading to a logarithmically diverging rms displacement in the large‐system limit. The vanishing of the solid‐phase force is mathematically analogous to the lack of viscous damping for a particle moving slowly through a two‐dimensional incompressible fluid. These two continuum results are compared with discrete‐particle computer simulations of two‐dimensional solids and fluids. The divergence predicted by macroscopic elasticity theory agrees quantitatively with computer results for two‐dimensional harmonic crystals. These same results can also be correlated with White's experimental study of the viscous resistance to a cylinder (a falling wire) moving slowly th...

Numerical simulation of premixed flame propagation through a two-dimensional vorticity distribution exhibits the coupling between combustion heat release and fluid dynamics. Effects of both thermal expansion and vorticity generation via baroclinic torques are considered. The rotational part of the velocity field is described by discrete vorticity. The irrotational velocity. given by a velocity potential. is determined by a Poisson equation where the chemical reaction determines the spatial distribution of volume expansion. The transport of a single reacting scalar is computed on an Eulerian mesh with a small-Mach-number flow assumption so that the density gradient is nonzero only within the reaction zone. The vector cross product of density gradient and pressure gradient defines the baroclinic generation of vorticity. With a single initial vortical region-the monopole interacting with a premixed flame-the baroclinic effect produces opposite circulation, and thus. creates a dipole configuration. W...

(mkT)112/a 2 , at strain rates of 0.0253,0.0408, and 0.0724 a fit is shown in our own fig. 1. The sinh 1 function (kT/m)ll2/a. The straight-line intercept of 11.7 considerably is smooth at the origin and also has been confirmed exceeds the (solid-line) Ree-Eyring value of 9.4 (mkT)1I2/a2. experimentally, for some materials, over many decades The Ree-Eyring extrapolation corresponds to a viscous rela­ of strain rate [6]. Its use in fitting the hard-sphere data xation time of 30 a(m/kT)1/2. The 500-particle Alder-Gass·· significantly reduces 1/(0), from 11.7 to 9.4 in units Wainwright viscosity is 7.2 (mkT)1/2/a 2 .

Nonequilibrium molecular dynamic simulation of liquid argon yields the strain-rate dependence of shear viscosity. Near the triple point the apparent viscosity decreases with increasing strain rate; the extrapolated zero-gradient viscosity is consistent with the equilibrium Green-Kubo viscosity calculated by Levesque, Verlet, and Kurkijarvi. At higher temperatures along the saturated vapor pressure line, our results are insensitive to the strain rate and agree well with experimental data for liquid argon.

Coherent flow patterns, also known as eddy structure or large eddy flow, are observed in many situations. Recently, the discrete vortex dynamics method has been used to simulate these flows. The method is a Lagrangian tracking of discrete fluid vorticity from which the velocity fleld can be calculated a t any point. A modest review of these calculations is given with emphasis on flow patterns obtained and the level of agreement with experiment. Two-dimensional flows discussed include free and wall-bounded shear layers and wake type flows. Scalar transport and chemical reaction are also described. Several three-dimensional applications are mentioned and details are presented for a cylindrical shear layer. While the vortex method is computationally expensive and not yet on completely firm mathematical footing, it does produce results not accessible by other techniques. Thus, its value as a research tool will continue to expa.nd with the computer hardware expansion and more comparison with well-characterized experiments. *Work supported by U. S. Department of Energy, OEce of Basic Energy Sciences.

Convection and diffusion of a conserved scalar is calculated in a two-dimensional mixing layer using the discrete vortex method. Scalar dissipation, the square of the scalar gradient, is calculated along various scalar isolines. The dissipation distribution is found to be approximately lognormal with parameters that can be described by a laminar diffusion model which has lognormally-distributed stretching of the mixing layer interface.

In theoretical equation-of-state investigations an important goal is to obtain the Helmholtz free energy, from which other thennod)lnamic properties can be obtained. The Helmholtz free energy is hard to cal­ culate directly. A less ambitious goal is to relate the free energy for the system of interest to the properties of a simpler, well-understood system. The simplest example of such a "perturbation" calculation considers the effect on the free energy when attractive forces are added to a purely repulsive hard-sphere system. This idea that attractive forces can be treated as a perturbation, with the distribution of particles being determined by short-range repulsive forces goes back to van der Waals and Boltzmann. Zwanzig1 formulated the corresponding perturbation theory precisely, show­ ing that the change in Helmholtz free energy caused by adding an attractive potential to a repulsive hard-core interaction could be expressed as a high-temperature series in liT, where T is the temperature. Until recently it had been relatively unnoticed that the first tenn in Zwanzig's series provides a rigorous upper bound on the Helmholtz free energy

The alignment between vorticity and eigenvectors of the strain‐rate tensor in numerical solutions of Navier–Stokes turbulence is studied. Solutions for isotropic flow and homogeneous shear flow from pseudospectral calculations using 1283 grid points have been examined. The Taylor Reynolds number is 83 or greater. In both flows there is an increased probability for the vorticity to point in the intermediate strain direction and at three‐fourths of the sample points this strain is positive (extensive). This propensity for vorticity alignment with a positive intermediate strain is a consequence of angular momentum conservation, as shown by a restricted Euler model of the coupling between strain and vorticity. Probability distributions for intermediate strain, conditioned on total strain, change from a symmetric triangular form at small strain to an asymmetric one for large strain. The most probable value of the asymmetric distribution gives strains in the ratios of 3:1: −4. The evolution of the distribution from a symmetric to an asymmetric form as the strain magnitude increases is essentially the same in both flows, indicating a generic structure of intense turbulence. The alignment between the gradient of a passive scalar and eigenvectors of the strain‐rate tensor for Prandtl numbers of 0.1, 0.2, 0.5, and 1.0 has also been studied. There is an increased probability for the scalar gradient to align in the most compressive strain direction, and the average gradient is larger when it is pointing in that direction. Estimates for the scalar dissipation from the turbulent kinetic energy, its dissipation, and the root‐mean‐square scalar value are in reasonable agreement with calculated scalar dissipation if no explicit Prandtl number dependence is used in the estimate. Statistical analysis of scalar dissipation conditioned on energy dissipation yields a power‐law relation between conditioned mean values. Both simulated flows are found to obey the qualitative predictions of the Gurvich–Yaglom (lognormal) intermittency model. Energy and scalar intermittency exponents are estimated and compared to measured values.

In a simulated turbulent shear flow the pressure gradient caused by velocity fluctuations alone has increased probability for alignment with the most compressive strain direction, which is similar to passive scalar-gradient behavior. The pressure-gradient component depending on the mean shear indicates no correlation with the strain directions.