Showing papers on "Streamlines, streaklines, and pathlines published in 1991"

A new method for quantification of regurgitant flow rate using color Doppler flow imaging of the flow convergence region proximal to a discrete orifice. An in vitro study.

Abstract: While color Doppler flow mapping has yielded a quick and relatively sensitive method for visualizing the turbulent jets generated in valvular insufficiency, quantification of the degree of valvular insufficiency has been limited by the dependence of visualization of turbulent jets on hemodynamic as well as instrument-related factors. Color Doppler flow imaging, however, does have the capability of reliably showing the spatial relations of laminar flows. An area where flow accelerates proximal to a regurgitant orifice is commonly visualized on the left ventricular side of a mitral regurgitant orifice, especially when imaging is performed with high gain and a low pulse repetition frequency. This area of flow convergence, where the flow stream narrows symmetrically, can be quantified because velocity and the flow cross-sectional area change in inverse proportion along streamlines centered at the orifice. In this study, a gravity-driven constant-flow system with five sharp-edged diaphragm orifices (ranging from 2.9 to 12 mm in diameter) was imaged both parallel and perpendicular to the direction of flow through the orifice. Color Doppler flow images were produced by zero shifting so that the abrupt change in display color occurred at different velocities. This "aliasing boundary" with a known velocity and a measurable radial distance from the center of the orifice was used to determine an isovelocity hemisphere such that flow rate through the orifice was calculated as 2 pi r2 x Vr, where r is the radial distance from the center of the orifice to the color change and Vr is the velocity at which the color change was noted. Using Vr values from 54 to 14 cm/sec obtained with a 3.75-MHz transducer and from 75 to 18 cm/sec obtained with a 2.5-MHz transducer, we calculated flow rates and found them to correlate with measured flow rates (r = 0.94-0.99). The slope of the regression line was closest to unity when the lowest Vr and the correspondingly largest r were used in the calculation. The flow rates estimated from color Doppler flow imaging could also be used in conjunction with continuous-wave Doppler measurements of the maximal velocity of flow through the orifice to calculate orifice areas (r = 0.75-0.96 correlation with measured areas).(ABSTRACT TRUNCATED AT 250 WORDS)

Local stability conditions in fluid dynamics

Abstract: Three‐dimensional flows of an inviscid incompressible fluid and an inviscid subsonic compressible gas are considered and it is demonstrated how the WKB method can be used for investigating their stability. The evolution of rapidly oscillating initial data is considered and it is shown that in both cases the corresponding flows are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. Analyzing the corresponding transport equations, a number of classical stability conditions are rederived and some new ones are obtained. In particular, it is demonstrated that steady flows of an incompressible fluid and an inviscid subsonic compressible gas are unstable if they have points of stagnation.

Selective decay and coherent vortices in two-dimensional incompressible turbulence.

Abstract: Numerical solution of two-dimensional incompressible hydrodynamics shows that states of a near-minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the late-time similarity of the streamlines to Ewald potential contours.

Chaotic streamlines inside drops immersed in steady Stokes flows

Abstract: Motivated by the recent work of Bajer & Moffatt (1990), we investigate the kinematics of bounded steady Stokes flows. Specifically, we consider the streamlines inside a neutrally buoyant spherical drop immersed in a general linear flow. The Eulerian velocity field internal to the drop, known analytically, is a cubic function of position. For a wide range of parameters the internal streamlines, hence the fluid particle paths, may wander chaotically. Typical Poincare sections show both ordered and chaotic regions. The extent and existence of chaotic wandering is related to (i) the orientation of the vorticity vector relative to the principal axes of strain of the undisturbed flow and (ii) the magnitude of the vorticity relative to the magnitude of the rate-of-strain tensor. In the limit of small vorticity, we use the method of averaging to predict the size of the dominant island region. This yields the critical orientation of the vorticity vector at which this dominant island disappears so that particle paths fill almost the entire Poincare section. The problem studied here appears to be one of the simplest, physically realizable, bounded steady Stokes flows which produces chaotic streamlines.

Eduction of swirling structure using the velocity gradient tensor

Abstract: We propose a technique for locating swirling regions of a flowfield. The technique is based on the eigenvalues of the velocity gradient tensor. We show that regions of swirling flow are characterized by complex eigenvalues for a constant velocity gradient tensor. Using results obtained in this analysis, we define an approximate parameter to indicate the tendency for the fluid to swirl about the point in question. The technique is illustrated by application to several two- and three-dimensional flowfields. In addition, the basic ideas contained here suggest the existence of a fluid property that we have termed intrinsic swirl

Self-Organization in Sheared Drift-Wave Turbulence

Abstract: Turbulent drift‐wave dynamics in a sheared magnetic field are studied using direct numerical simulations. Self‐consistent nonadiabatic electron and parallel ion dynamics are both retained in a 2‐D sheared‐slab model. Magnetic shear causes division of the system into two physically distinct regions with differing cascade dynamics. In a hydrodynamic layer centered upon the mode resonant surface, linear coupling between the density and potential is weak, and the density gradient acts to force spontaneous nonlinear alignment of density fluctuations with the turbulent flows. Further away, shear‐induced collisional dissipation constrains the density fluctuations to respond adiabatically, so that the density cannot vary on flow streamlines. The dynamics of the interregion spatial energy flow leads to strong phase coherence between modes at scales larger than the hydrodynamic layer width. Concurrently, the alignment between flows and density fluctuations at scales comparable to the layer width becomes even stronger, increasing the energy input at those scales. This self‐organizing tendency is sufficiently robust as to survive competition with a linear external drive. Because of its greater structural freedom, the full nonadiabatic system is much more likely than an adiabatic model with a linear density response to support saturated turbulence below the threshhold for linear instability.

Geostatistical characterization of groundwater flow parameters in a simulated aquifer

Abstract: An analog method is used to simulate a discrete transmissivity field free of the artifacts inherent in conventional multivariate Gaussian statistical generation methods. The simulated field provides a realistic model of a formation exhibiting the spatial continuity of extreme transmissivities which gives rise to barriers and preferential channels for flow. The heterogeneous transmissivity field and the corresponding steady-state head and discharge fields are characterized in a geostatistical framework and observed spatial statistics are compared with theoretical results from the stochastic hydrogeology literature. The simulated transmissivity field exhibits a bimodal distribution and strong directional anisotropy with nested scales of heterogeneity. Despite these significant departures from standard models, the observed head covariance and head-log-transmissivity cross-covariance agree well with theory. The spatial covariance of specific discharge is highly anisotropic reflecting preferential channeling in the mean direction of flow and the conservation of flux along streamlines. The effective transmissivity of the field is predicted more accurately by the spatial geometric average than by theoretical models despite the flow channeling and the anisotropy of heterogeneity. Tracer spreading, modeled by particle tracking, is non-Fickian at displacements of up to 13.4 times the log-transmissivity integral range because transport behavior is dominated by convection along a small number of preferential channels. The observed scale dependence of apparent longitudinal dispersivity is predicted generally well by theory. Results of this study suggest that ensemble theoretical models based on perturbation approaches can provide reasonable estimates of general flow and transport properties of single field realizations under moderate conditions of heterogeneity.

The rapid expansion of a turbulent boundary layer in a supersonic flow

Abstract: Rapid distortion approximations (RDA) may be used to simplify the Reynolds Stress equations under the satisfaction of rapid distortion criteria as suggested by Dussauge and Gaviglio (1987). The evolution of Reynolds stresses along streamlines in a boundary layer may then be calculated. This calculation was made for the distortion of a supersonic flow through a 20° expansion (Figure 1) and the results were compared with experimental observation. The rapid distortion approximations neglect diffusive and dissipative terms while retaining the production and pressure terms. The retained terms are modelled as functions of the Reynolds stress tensor and gradients of the mean flow. Models for the pressure-strain term were based on the work by Lumley (1978) and Shih and Lumley (1985). The experimental measurements revealed a boundary layer downstream of the distortion which was dramatically different from its upstream counterpart. The mean velocity profile did not possess a logarithmic region. The velocity fluctuations decreased while the mass-flux fluctuations remained initially unchanged, and the strong Reynolds analogy showed that the change in the mass-flux fluctuations seems to follow the change in the density fluctuations. Within the limits of the rapid distortion approximations, the Reynolds stress equations made surprisingly accurate predictions of the Reynolds stresses in a compressible boundary layer (Figure 2). The performance of three pressure-strain models was evaluated, and it was found that the calculation was mostly insensitive to the model chosen. The influence of dilatation alone was also investigated, and the results indicate that compressibility has a strong influence on the Reynolds stress.

Mathematical Modeling of Epitaxial Silicon Growth in Pancake Chemical Vapor Deposition Reactors

Abstract: Here, a mathematical model of the gas flow, transport phenomena, and growth rate profiles of epitaxial silicon in a pancake reactor is presented and the resulting modeling equations are solved. Two-dimensional conservation equations of momentum, energy, and mass developed in cylindrical coordinates along with appropriate boundary conditions are solved numerically with finite element methods. Streamlines of the gas flow in the reactor show that the shearing force of the inlet flow yields a recirculation zone inside the reactor and a separation point on the susceptor. As the inlet volumetric flow rate increases, the gas flow direction over the susceptor changes from inwards to outwards, resulting in another reverse circulating flow above the susceptor. The temperature and concentration profiles obtained show that steeper thermal and concentration boundary layers develop above the susceptor at higher volumetric flow rates. Under the assumption of a first-order deposition reaction on the substrate, growth rate profiles are calculated along the radial direction. The effects of total gas mixture flow rates, magnitude of the deposition rate constant, susceptor temperature, and thermal diffusion upon growth rate profiles are investigated. The agreement between observed and predicted growth rates at various temperatures is seen to be satisfactory

The strong nonlinear interaction of tollmien-schlichting waves and taylor-gortler vortices in curved channel flow

Abstract: It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

Fluid Flow Patterns Around a Well Bore or an Underground Drift With Complex Skin Effects

Abstract: A semianalytic solution is given for steady state flow around a well bore or a drift with a complex skin. The hydraulic conductivity of the skin may vary continuously as a function of the radial distance from the well (or drift) and may also be radially anisotropic. Such configurations can be found around damaged or acidized well bores or around a drift near which the stress redistribution induces changes in hydraulic conductivity. Purely radial flow, regional flow around an open or cemented hole without pumping or injection, and combined regional and radial flow are considered. Variations of hydraulic potential and Darcy velocity in various radial directions are studied for several cases and are found to be strongly affected by a complex skin. It is shown that the convergence of the streamlines toward the borehole, which is used in applications involving the point dilution method of measuring regional flow velocity, is significantly enhanced by a complex negative skin. Negative skin values may also reduce the size of the capture zone of a withdrawal well. Head distribution and tracer transport in combined radial and regional flow around a drift have also been modeled. It is demonstrated that tracer breakthrough curves from an experiment of tracer transport from an injection zone in the rock to the drift can be significantly affected by the fluid flow pattern around the drift, so the commonly used radial pattern may lead to erroneous results for tracer dispersivity.

The momentum flux in turbulent submerged jets

Abstract: Although the jet momentum flux has been traditionally accepted as constant, this is not in general true because a weak pressure field is induced in the ambient fluid with positive gradient and because the induced flow field carries momentum flux to the jet. The angle ϕ, at which the induced flow streamlines enter the jet, is the basic parameter which determines whether the jet momentum flux increases, remains constant or decreases. A theoretical solution is presented for the variation of the jet momentum flux in turbulent submerged jets in stationary ambient fluid. The solution presented in this paper generalizes previous theoretical solutions and is in good agreement with existing experimental results. The contribution of the induced pressure field relative to the induced velocity field in varying the jet momentum flux is investigated. The induced flow streamlines are calculated using non-constant jet momentum flux and are compared with Taylor's solution (where constant jet momentum flux was assumed).

Quantitative study of steady flow using color Doppler ultrasound.

Abstract: The use of color Doppler flow mapping systems for quantitative in vitro studies of flow fields is examined and illustrated. A 5-MHz color Doppler system was used, and the resolution was determined by comparing the results of flow-field measurement for steady parabolic pipe flow with calculated values. The velocity accuracy was about 6% of the velocity corresponding to half the pulse repetition frequency, and the spatial resolution was better than 1 mm. Frame frequency limitations permitted only partial tracking of fast temporal changes in the flow field. However, detection of vortices downstream from a small cylinder placed in the flow tube was significantly enhanced by synchronizing the frame frequency with the vortex shedding frequency and using a velocity-variance mode. Color Doppler aliasing was found to be useful to define streamlines and determine whether the flow was laminar or turbulent. The color Doppler system clearly imaged Poiseuille, transitional and turbulent flow and vortex shedding in vitro. It is concluded that color Doppler ultrasound flow mapping can enable large, complex flow fields to be quantitatively studied in vitro.

Reaction-driven convection in a porous medium

Abstract: The onset of three-dimensional reaction-driven convection in a porous medium is investigated using linear stability theory. The geometries investigated include a finite cylinder and a rectangular parallelepipped of arbitrary aspect ratios. The analysis determines, among other things, the likely modes (flow patterns) to emerge first as a function of reaction parameters and aspect ratios. The flow fields corresponding to three-dimensional modes are described in detail. Important qualitative differences are found between reaction-driven convection and the standard Lapwood or Benard convection due to a temperature gradient applied to the boundaries of the system. The second part of the work examines numerically reaction-driven natural convection in a porous two-dimensional rectangular box. Orthogonal collocation and continuation techniques are used to determine the conduction and convection branches of solutions as a function of the Rayleigh number (Ra), the Frank-Kamenetskii number (δ) and the aspect ratio (α). The convective solutions (streamlines and isotherms) corresponding to primary, secondary and tertiary bifurcations are presented. The effect of natural convection (Ra) on the ignition point (critical δ value) is determined for three different aspect ratios.

Mass arrival of reactive solute in single fractures

Abstract: Transport of reactive solute in individual fractures is investigated. Solute advection is coupled with matrix diffusion that is assumed perpendicular to the fracture plane. Fluid advection in the fracture is viewed as intersecting flow paths, whereby the advection velocity of a solute particle varies along individual streamlines. Solute mass arrival at a fixed position averaged in the direction perpendicular to the mean flow is examined. The dispersion in the solute breakthrough arises because of the different advection travel times and varying mass flux along individual streamlines. The fracture is conceptualized as a two-dimensional porous medium with a statistically anisotropic, spatially varying transmissivity with a given correlation structure; the assumed anisotropy condition is consistent with elongated, channel-like flow paths that have been observed in single fractures. Approximate expressions for the first two moments of solute travel time are used to illustrate the sensitivity to different correlation models for the fracture transmissivity. In particular, the finite correlation scale model, the self-similar (fGn) model, and the channel model are considered. The expected cumulative mass arrival is more sensitive to the assumed correlation model for lower rates of matrix diffusion. The derived expression for the mass arrival can also be used for analyzing the effect of nonequilibrium sorption-desorption reactions in single fractures.

Fast dynamo action in a steady chaotic flow

Abstract: THE observation of rapid variations in the Sun's magnetic field motivates the search for 'fast dynamos'1–3—flows of highly conducting fluid that amplify magnetic fields on the typically rapid timescales of convection, rather than the longer timescales of diffusion. Certain helical flows4–6 have been proposed as possible fast dynamos, but numerical studies7,8 of such flows have shown no conclusive evidence for this. Here I examine the evolution of a magnetic field in one such flow, which possesses a web of chaotic streamlines mingled with tubes of regular streamlines9. In the case of no magnetic diffusion, I observe intense stretching and folding of the magnetic field in the chaotic regions of the flow. The folding brings together field that is largely aligned in the same direction, and the average field in a chaotic region therefore grows exponentially with time. This provides evidence for fast dynamo action, the main effect of weak diffusion being to average the field locally10–13, and indicates that smooth, steady chaotic flows can be fast dynamos.

Stably stratified rotating flow through a group of obstacles

Abstract: A linear calculation is presented of uniform stably stratified flow (velocity U 0, Brunt-Vaisala frequency N) through a region of resistance on a rigid plane with vertical scale Hand horizontal scale Dwhen the Froude number F = U 0/HNis much less than unity, and when the velocity perturbation is small compared with U 0. It is shown that that largest vertical perturbation occurs to the streamlines within a “summit layer”, of thickness O(U 0/N), at the top of the region and that this perturbation is transmitted upwards and downwards by internal waves. This calculation is a model of the flow through groups of hills (which is illustrated with some small laboratory experiments) and it helps explain some unsolved problems about strongly stratified flow over a single hill. The first-order correction, below the summit layer, to flow through and around groups of hills can be larger than the O(F2) term given by Drazin (1961). On extending the theory, it is found that the effect of a rotation with angular v...

An upper-bound solution for axisymmetric extrusion of composite rods through curved dies

Abstract: The study is concerned with an analysis of forward extrusion of composite rods through curved dies. A kinematically admissible velocity field is derived by assuming proper streamlines and applying the flow function concept to each material region of plastic deformation. Two kinds of flow functions are chosen in order to compare the effect of the choice of the flow functions. The effect of work-hardening is incorporated approximately by calculating the strains at the exit of both materials. The upper-bound method is then employed to determine the extrusion pressure for various process variables. The experiments are carried out with commercially pure aluminum and copper billets for various reductions of area and cone angles at room temperature. The experimental results are then compared with the theoretical calculations. The comparison shows that the second-order flow function is in better agreement with the experimental observation both in extrusion loads and in deforming regions.

Numerical Analysis of Heat Transfer by Natural Convection and Radiation in Participating Fluids Enclosed in Square Cavities

Abstract: The influence of thermal radiation on natural convection in a participating fluid contained in a square cavity is studied numerically. The radiative transfer process is solved from the PI approximation. The Navier-Stokes equations are solved by a finite difference scheme integrated over control volumes. A numerical study of the so-called window problem (thermally driven cavity) shows the influence of thermal radiation on this reference problem for Rayleigh numbers in the range of 103-107 and Planck numbers varying from 1 to 0.05. The isotherms, streamlines, and heat lines show an increase of the dynamical effects in the central part of the cavity and a significant modification of the boundary layers. Results obtained from the simulation of an isotropically scattering medium are given.

Dipolar electric field induced by a vortex moving in an anisotropic superconductor

Abstract: The dipolar electric field induced by an isolated vortex aligned along a principal axis and moving at constant velocity in an anisotropic type-II superconductor is investigated. It is shown that the standard dipolar-field case can be extended by the inclusion of a mass-anisotropy parameter \ensuremath{\beta}. It is shown that the streamlines of the electric field can be easily calculated analytically. In addition, an inertial mass tensor per unit length of vortex is found.

Streamlines, vorticity lines, and vortices

Abstract: The properties of vortical flows are studied using both theoretical analysis and computational flow fields. The consequences of two definitions of the vortex core, a minimum in the streamline curvature and a maximum in the normalized helicity, are examined. Analysis indicates that several criteria must be met if the cores defined by these two methods are to coincide. In certain regions of the flow, computational flow fields indicate that these two definitions are coincident, that the velocity and vorticity fields are aligned at the core, and that extrema in the velocity magnitude, vorticity magnitude, pressure, and density occur at the core.

A Numerical Method of Flow through a Cross-Flow Runner

Abstract: The flow inside a cross-flow runner is analyzed two dimensionally. The unsteady flow along streamlines in the relative systems of the runner is calculated numerically and the flow along the runner periphery is investigated. Additionally, calculated results are compared with experimental data

Aerodynamic design of gas and aerosol samplers for aircraft

Abstract: The aerodynamic design of airborne probes for the capture of air and aerosols is discussed. Emphasis is placed on the key parameters that affect proper sampling, such as inlet-lip design, internal duct components for low pressure drop, and exhaust geometry. Inlet designs that avoid sonic flow conditions on the lip and flow separation in the duct are shown. Cross-stream velocities of aerosols are expressed in terms of droplet density and diameter. Flow curvature, which can cause aerosols to cross streamlines and impact on probe walls, can be minimized by means of a proper inlet shape and proper probe orientation, and by avoiding bends upstream of the test section. A NASA panel code called PMARC was used successfully to compute streamlines around aircraft and probes, as well as to compute to local velocity and pressure distributions in inlets. A NACA 1-series inlet with modified lip radius was used for the airborne capture of stratospheric chlorine monoxide at high altitude and high flight speed. The device has a two-stage inlet that decelerates the inflow with little disturbance to the flow through the test section. Diffuser design, exhaust hood design, valve loss, and corner vane geometry are discussed.

Stretching in duct flows

Abstract: Duct flows are steady three‐dimensional isochoric velocity fields composed of a recirculating two‐dimensional cross‐sectional flow and a unidirectional axial flow, both flows being independent of the axial distance. It is shown that lineal stretch in such flows increases linearly in time. In particular, length stretch in bounded steady two‐dimensional flows is linear as well.

Assessment of modeling and discretization accuracy for high-speed afterbody flows

Abstract: The accuracy of Reynolds-aver aged Navier-Stokes calculations of axisymmetric high-speed afterbody flows is investigated. An approximate truncation error analysis is used to identify specific regions where discretization errors are large, and grid refinement is used to evaluate global solution accuracy. Good alignment of grid lines with streamlines in the shear layer at the nozzle exit is found to be important for obtaining solutions at high nozzle pressure ratios. Solution-adapted grids are used, and solutions that are essentially grid-independent are obtained. Modifications to the k- model for Mach number and streamline curvature effects are presented and validated in flows unrelated to base flows. In base flow calculations, these model modifications produce changes hi base drag in excess of 20%. Computed solutions agree well with experiment for base pressure and flow structure.

High‐Reynolds‐number thermocapillary flows in shallow enclosures

Abstract: Steady thermocapillary flows of low‐Prandtl‐number fluids in shallow rectangular enclosures under an imposed‐heat‐flux configuration are studied in the absence of gravitational forces. The Navier–Stokes equations are solved numerically for Reynolds numbers up to 104. The pressure correction method is used to treat the pressure‐velocity coupling, in particular, the SIMPLEC approximation is considered. In the numerical simulation, the free surface is assumed flat. This hypothesis is justified a posteriori; free surface deformations are computed by domain perturbation for small capillary numbers. The numerical results show the existence of a boundary layer along the free surface and the existence of a strong vortex close to the vertical wall. The characteristic velocity in the boundary layer responds to Ostrach’s scaling of thermocapillary boundary layers, and the wall vortex responds to Batchelor’s model for steady laminar flows with closed streamlines at large Reynolds numbers. The calculated surface defor...

On the Instability of Wall-Boundary Layers Close to Separation

Abstract: The inviscid instability of wall-bounded velocity profiles with an inflexion point has been investigated numerically. The growth rates and phase velocities of the disturbances have been calculated for profile types ranging from that found in free shear layers to those in wall boundary layers close to separation. It is found that the presence of the wall has a stabilizing influence. For a special case, the distribution of the fluctuating velocity, the streakline pattern and the instantaneous velocity and pressure profiles are shown. The effect of finite, but large Reynolds number has been studied by comparing the inviscid results with that of the Orr-Sommerfeld equation and with measured values.

Defining the zonal structure of turbulence using the pressure and invariants of the deformation tensor

Abstract: A set of objective criteria based on the local strain rate, vorticity and pressure have been found to describe regions in which the streamlines circulate, converge or diverge, and form streams of high velocity flow. The homogeneous and sheared turbulent flow fields are made up of characteristic flow zones — eddy, shear, convergence and streaming zones. These are studied in turbulent velocity fields produced by different methods of simulation, including the novel method of Kinematic Simulation of homogeneous isotropic turbulence are summarised. We derive and explain the zonal algorithm to classify structures and then use this classification to compare the results of two different numerical simulations (DNS, KS) both qualitatively (turbulence structure, physical processes) and quantitatively (turbulence statistics) for homogeneous isotropic turbulence and then we apply the zonal algorithm to a turbulent shear flow. New conclusions are reached about the significant regions in turbulent flows for dynamical and kinematical processes.