Isotropic Flow Research Articles

Statistical Models of Clustering of Particles in Wall and Isotropic Turbulent Flows

Statistical models are given of the dispersion of inertial particles in inhomogeneous wall turbulence and homogeneous isotropic turbulence. The models are based on the kinetic equations for the one-point and two-point probability density functions of particle velocities. Comparison is made with the data of direct numerical calculations for channel and isotropic flows, known from the literature.

A Periodic Director Structure of Nematic Liquid Crystals in a High-Frequency Electric Field

We report an electrohydrodynamic instability, the prewavy instability, in nematic liquid crystals in a high-frequency electric field. This instability shows isotropic feature, zigzag flows, and constant spatial periodicity with respect to the amplitude and frequency of the applied electric field. It should be distinguished from similar instabilities such as the isotropic electrolyte mode, the inertia mode and the dielectric mode reported already.

The second order characteristic condition for plastic flow

AbstractIn this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd.

Direct numerical simulation as a tool for understanding MHD liquid metal turbulence

The method of direct numerical simulation (DNS) is applied to investigate the most general properties of turbulent flows of liquid metals in the presence of a constant magnetic field. Various aspects of the flow transformation into an anisotropic state are thoroughly examined. The flow is assumed to be homogeneous and the problem is reduced to the classical case of a turbulent flow in a 3D box with periodic boundary conditions. In the framework of this formulation, three specific types of the flow are considered, which are the forced flow, thermal convection, and freely decaying flow. To investigate the long-time evolution of an initially isotropic flow a large-scale forcing is applied to maintain the flow energy at a statistically steady level. The evolution is found to depend strongly on the magnetic interaction parameter (Stuart number). In the case of small Stuart number, the flow remains three-dimensional, turbulent, and approximately isotropic. At large Stuart number (strong magnetic field) the turbulence is suppressed rapidly and the flow becomes two-dimensional and laminar. Very interesting is the intermittent flow evolution detected at moderate Stuart number. Long periods of almost two-dimensional, laminar behaviour are interrupted by strong turbulent three-dimensional bursts. The influence of a constant magnetic field on scalar transport properties of liquid metal turbulence is investigated using the simplified formulation of a homogeneous flow driven by an imposed mean temperature gradient. The flow structure is dominated by two turbulent antiparallel jets providing an effective mechanism of heat transfer. It is shown that the magnetic field parallel to the mean temperature gradient stabilizes the jets and, thus, enhances heat transfer considerably. In the third part, freely decaying MHD turbulence is considered. Numerical simulations are applied to verify the theoretical model proposed in [J. Fluid Mech. 336 (1997) 123]. In particular, it is confirmed that the structure of viscous dissipation and evolution of perpendicular length scale are affected only slightly by the magnetic field. A simple approximation for the mean Joule dissipation is proposed.

A physical basis for calculating instrument spatial weighting functions in homogeneous systems

Starting with a streamline‐based argument, the theoretical basis for a spatial weighting function in a steady, homogenous, and isotropic flow system is developed for both compressible and incompressible flow. A physical interpretation of spatial weighting functions in terms of the ratio of steady state energy dissipation rate per unit volume of porous medium to total energy dissipation rate over the entire flow domain is formulated. Finally, applications of the spatial weighting functions are presented based on calculated gas minipermeameter mass flux fields for the conventional surface probe and a new small drill hole probe configuration. Spatial weighting function distributions indicate that with diverging flow field instruments, such as the gas minipermeameter, porous medium volumes in the inlet vicinity are heavily weighted, with volumes near the seal boundaries shown to be extremely important. The technique described allows one to quantify the size and shape of the subvolume of a domain contributing to a hydraulic conductivity or intrinsic permeability measurement. For heterogeneous systems it is suggested that the spatial weighting function for a given instrument will be heterogeneity dependent and therefore nonunique. However, extending the weighting function concept to heterogeneous and/or transient systems is an important research priority.

Shock‐capturing with natural high‐frequency oscillations

AbstractThis paper explores the potential of a newly developed conjugate filter oscillation reduction (CFOR) scheme for shock‐capturing under the influence of natural high‐frequency oscillations. The conjugate low‐ and high‐pass filters are constructed based on the principle of the discrete singular convolution (DSC), a local spectral method. The accuracy and resolution of the DSC basic algorithm are accessed with a one‐dimensional advection equation. Two Euler systems, the advection of an isotropic vortex flow and the interaction of shock–entropy wave are utilized to demonstrate the utility of the CFOR scheme. Computational accuracy and order of approximation are examined and compared with the literature. Some of the best numerical results are obtained for the shock–entropy wave interaction. Numerical experiments indicate that the CFOR scheme is stable, conservative and reliable for the numerical simulation of hyperbolic conservation laws. Copyright © 2003 John Wiley & Sons, Ltd.

Greenland glacial history, borehole constraints, and Eemian extent

We examine the extent to which observations from the Greenland ice sheet combined with three‐dimensional dynamical ice sheet models and semi‐Lagrangian tracer methods can be used to constrain inferences of the Eemian evolution of the ice sheet, of the extent and frequency of summit migration during the 100 kyr ice age cycle, and of the deep geothermal flux of heat from the Earth into the base of the ice sheet. Relative sea level, present‐day surface geometry, basal temperature, and age and temperature profiles from the Greenland Ice Project (GRIP) are imposed as constraints to tune ice sheet model and climate forcing parameters. Despite the paucity of observations, model‐based inferences suggest a significant northeast gradient in geothermal heat flux. Our analyses also suggest that during the glacial cycle, the contemporaneous summit only occupied the present‐day location during interglacial periods. On the basis of the development and use of a high‐resolution semi‐Lagrangian tracer analysis methodology for δ18O, we rule out isotropic flow disturbances due to summit migration as a possible source of the high Eemian variability of the GRIP δ18O record. Finally, in contrast with results obtained in some recent attempts to infer the extent to which Greenland may have contributed to the anomalous highstand of Eemian sea level, we find that conservative bounds for this contribution are 2–5.2 m, with a more likely range of 2.7–4.5 m.

Stability of Rossby waves in the β-plane approximation

Floquet theory is used to describe the unstable spectrum at large scales of the β-plane equation linearized about Rossby waves. Base flows consisting of one to three Rossby waves are considered analytically using continued fractions and the method of multiple scales, while base flows with more than three Rossby waves are studied numerically. It is demonstrated that the mechanism for instability changes from inflectional to triad resonance at an O(1) transition Rhines number, Rh= U/( βL 2), independent of the Reynolds number. For a single Rossby wave base flow, the critical Reynolds number Re c for instability is found in various limits. In the limits Rh→∞ and k→0, the classical value Re c = 2 is recovered. For Rh→0 and all orientations of the Rossby wave except zonal and meridional, the base flow is unstable for all Reynolds numbers; a zonal Rossby wave is stable, while a meridional Rossby wave has critical Reynolds number Re c = 2 . For more isotropic base flows consisting of many Rossby waves (up to 40), the most unstable mode is purely zonal for 2≤ Rh<∞ and is nearly zonal for Rh=1/2, where the transition Rhines number is again O(1), independent of the Reynolds number and consistent with a change in the mechanism for instability from inflectional to triad resonance.

Une classification des flots solutions d'une EDS

Under general hypotheses, we show that the flows of kernels can be associated to a stochastic differential equation (SDE). We also show a classification theorem of the solutions of the SDE: they can be obtained through filtering the coalescing solution with respect to a sub-noise containing the white noise driving the SDE. The example of the isotropic flows is studied. To cite this article: Y. Le Jan, O. Raimond, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Parametric study on sound radiation from an infinite fluid-filled/semi-submerged cylindrical shell

This work presents the parametric study on the far-field sound pressure radiated from an infinite fluid-filled/semi-submerged cylindrical shell excited by a radial point load. Here, the exterior fluid is non-viscous, isotropic and irrotational coaxial flow. The formula of the radial velocity of the shell in wave-number domain is developed by using the wave-number domain approach (WDA). Then, the analytic expressions are derived for the far-field sound pressure radiating from the shell by using the same method presented in Salaün [Journal of the Acoustical Society of America 90 (1991) 2173]. The influences of parameters such as fluid velocity, structural damping, position of the force, and structural thickness on the far-field sound pressure are investigated. The sound pressure is shown to be very different from the one in the case of a fluid-filled/full-submerged cylindrical shell. Furthermore, it is shown that the pressure and the resonance frequency would increase with the fluid velocity increasing for downstream propagation. The reverse is true for upstream propagation. Moreover, the far-field sound pressure is related to the position and frequency of the excited force. In addition, the influences of structural damping and thickness are shown to be very important.

Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence

Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.

Large eddy simulation of heat and mass transport in turbulent flows. Part 1: Velocity field

Localized residual or subgrid-scale (SGS) models are presented for use in large eddy simulation of heat and mass transport in turbulent flows. In part (1) (this paper), we discuss the SGS stress models for the velocity field. The models for the scalar field are presented in part (2). The new SGS stress closures are compared with the dynamic-Smagorinsky model (DSM) and the dynamic two-parameter mixed model (DTMM). All models are applied “locally” and their performances are assessed via both a priori and a posteriori analyses with detailed comparisons against data obtained from direct numerical simulation of homogeneous isotropic, homogeneous shear and temporal mixing layer flows. The results of a priori assessments indicate that the new closures predict the SGS stresses better than both DSM and DTMM in all simulated flows. The results of a posteriori assessments also show that the SGS stresses and the statistics of the filtered velocity are more accurately predicted with the new models.

Effects of crustal stresses on fluid transport in fractured rock: case studies from northeastern and southwestern USA

The link between stress and hydrologic properties was examined at two sites that are distinguished by different rock types and different stress states. This investigation is based upon the analysis and interpretation of geophysical logs obtained in water wells at the two locations. At the northeast site (Newark Basin), the hydrologic characteristics of sedimentary rocks are dependent upon the relationship to the current regional stress field of two primary types of orthogonal features that serve as preferential pathways for fluid flow. Subhorizontal bedding-plane partings are highly transmissive near the surface and delineate transversely isotropic fluid flow at shallow depths. With increasing depth, the subhorizontal planes become less dominant and steeply dipping fractures become more influential hydrologically. These high-angle features define anisotropic flow pathways that are preferentially oriented along strike. At the southwest site (west Texas), extrusive rocks are subjected to topographically modified tectonic and gravitational stresses that vary spatially within a valley setting. The attendant changes in stress invariants cause fracture connectivity within the rock mass to systematically increase with depth along the valley flanks, but to remain relatively low in the central valley. The degree of fracture connectivity predicted within this valley configuration is consistent with variations in transmissivity determined at several well locations. In each of these cases, the idealized understanding of the hydrologic system is enhanced by considering the effects of regional and local stresses that act upon the fractured-rock aquifer.

Classification of limiting shapes for isotropic curve flows

A complete classification is given of curves in the plane which contract homothetically when evolved according to a power of their curvature. Applications are given to the limiting behaviour of the flows in various situations.

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the Kármán–Howarth equation, that arises due to lack of mirror-reflection-symmetry in isotropic flows. The main equation we obtain is consistent with the results of Chkhetiani [JETP 63 (1996) 768] and L’vov et al. [Exact result for the 3rd order correlations of velocity in turbulence with helicity, 1997. http://xxx.lanl.gov/abs/chao-dyn/9705016] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling exponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov prediction for the scaling exponents of velocity structure function.

On the higher order mixed structure functions in laboratory shear flow

Structure functions to order 8 are determined from the longitudinal and transverse velocity fluctuations measured at a single point in high Reynolds number laboratory shear flow. We examine the relationship between mixed structure functions (which are explicitly zero in isotropic flow), and those of the longitudinal and transverse structure functions. Our results confirm recent findings using SO(3) symmetry decomposition [S. Kurien and K. R. Sreenivasan, Phys. Rev. E 62, 2206 (2000)] that show that the mixed structure functions have larger scaling exponents than those of the single component structure functions, i.e., the j=2 anisotropic sector structure function scaling exponent is greater than that of the j=0 isotropic sector. However, we also show that the ratio of the j=2 to j=0 sector scaling exponents systematically decreases with increasing order, suggesting that at higher orders there is persistence of anisotropy at the smallest scales. Difficulties in the analysis due to the difference in scaling exponents of the transverse and longitudinal structure functions are addressed.

Double scaling and intermittency in shear dominated flows.

The nature of intermittency in shear dominated flows changes with respect to homogeneous and isotropic conditions since the process of energy transfer is affected by the turbulent kinetic energy production associated with the Reynolds stresses. For these flows, a new form of refined similarity law is able to describe the increased level of intermittency. Ideally a length scale associated with the mean shear separates the two ranges, i.e., the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. In the present paper we give evidence of the coexistence of the two regimes and we support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data. The analysis shows that the larger anisotropic scales of shear turbulence display universality, and determines the modality by which the dissipation field fixes the properties of turbulent fluctuations in the shear dominated range.

Color image enhancement via chromaticity diffusion

A novel approach for color image denoising is proposed in this paper. The algorithm is based on separating the color data into chromaticity and brightness, and then processing each one of these components with partial differential equations or diffusion flows. In the proposed algorithm, each color pixel is considered as an n-dimensional vector. The vectors' direction, a unit vector, gives the chromaticity, while the magnitude represents the pixel brightness. The chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals. This theory deals with the regularization of vectorial data, while satisfying the intrinsic unit norm constraint of directional data such as chromaticity. Both isotropic and anisotropic diffusion flows are presented for this n-dimensional chromaticity diffusion flow. The brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement. We present the underlying theory, a number of examples, and briefly compare with the current literature.

The structure of weakly compressible grid-generated turbulence

A decaying compressible nearly homogeneous and nearly isotropic grid-generated turbulent flow has been set up in a large scale shock tube research facility. Experiments have been performed using instrumentation with spatial resolution of the order of 7 to 26 Kolmogorov viscous length scales. A variety of turbulence-generating grids provided a wide range of turbulence scales with bulk flow Mach numbers ranging from 0.3 to 0.6 and turbulent Reynolds numbers up to 700. The decay of Mach number fluctuations was found to follow a power law similar to that describing the decay of incompressible isotropic turbulence. It was also found that the decay coefficient and the decay exponent decrease with increasing Mach number while the virtual origin increases with increasing Mach number. A possible mechanism responsible for these effects appears to be the inherently low growth rate of compressible shear layers emanating from the cylindrical rods of the grid. Measurements of the time-dependent, three dimensional vorticity vectors were attempted for the first time with a 12-wire miniature probe. This also allowed estimates of dilatation, compressible dissipation and dilatational stretching to be obtained. It was found that the fluctuations of these quantities increase with increasing mean Mach number of the flow. The time-dependent signals of enstrophy, vortex stretching/tilting vector and dilatational stretching vector were found to exhibit a rather strong intermittent behaviour which is characterized by high-amplitude bursts with values up to 8 times their r.m.s. within periods of less violent and longer lived events. Several of these bursts are evident in all the signals, suggesting the existence of a dynamical flow phenomenon as a common cause.

The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence

The variational multiscale method is applied to the large eddy simulation (LES) of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation (DNS) data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model (the least accurate model!) except for removal of the eddy viscosity from a very small percentage of the lowest modes.