Methods of measuring vorticity in turbulent flows
TL;DR: Experimental methods which have been developed over the last three decades to measure one or more components of the vorticity vector are described and assessed in this article, where they include methods which estimate the velocity gradients comprising the various VV components, methods which sense fluid rotation directly, and methods which senses other fluid properties which can be related to VV.
Abstract: Experimental methods which have been developed over the last three decades to measure one or more components of the vorticity vector are described and assessed. These include methods which estimate the velocity gradients comprising the various vorticity components, methods which sense fluid rotation directly, and methods which sense other fluid properties which can be related to vorticity.
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TL;DR: In this article, a general scheme for educing coherent structures in any transitional or fully turbulent flow is presented, based on smoothed vorticity maps in convenient flow planes, which recognizes patterns of the same mode and parameter size, and then phase-aligns and ensembles them to obtain coherent structure measures.
Abstract: This is a personal statement on the present state of understanding of coherent structures, in particular their spatial details and dynamical significance. The characteristic measures of coherent structures are discussed, emphasizing coherent vorticity as the crucial property. We present here a general scheme for educing structures in any transitional or fully turbulent flow. From smoothed vorticity maps in convenient flow planes, this scheme recognizes patterns of the same mode and parameter size, and then phase-aligns and ensemble-averages them to obtain coherent structure measures. The departure of individual realizations from the ensemble average denotes incoherent turbulence. This robust scheme has been used to educe structures from velocity data using a rake of hot wires as well as direct numerical simulations and can educe structures using newer measurement techniques such as digital image processing. Our recent studies of coherent structures in several free shear flows are briefly reviewed. Detailed data in circular and elliptic jets, mixing layers, and a plane wake reveal that incoherent turbulence is produced at the ‘saddles’ and then advected to the ‘centres’ of the structures. The mechanism of production of turbulence in shear layers is the stretching of longitudinal vortices or ‘ribs’ which connect the predominantly spanwise ‘rolls’; the ribs induce spanwise contortions of rolls and cause mixing and dissipation, mostly at points where they connect with rolls. We also briefly discuss the role of coherent structures in aerodynamic noise generation and argue that the structure breakdown process, rather than vortex pairing, is the dominant mechanism of noise generation. The ‘cut-and-connect’ interaction of coherent structures is proposed as a specific mechanism of aerodynamic noise generation, and a simple analytical model of it shows that it can provide acceptable predictions of jet noise. The coherent-structures approach to turbulence, apart from explaining flow physics, has also enabled turbulence management via control of structure evolution and interactions. We also discuss some new ideas under investigation: in particular, helicity as a characteristic property of coherent structures.
1,117 citations
TL;DR: In this article, the multifractal formalism is extended to more than one variable, and applied to simultaneous measurements in several classical turbulent flows of the joint distribution of a component of the dissipation of kinetic energy.
Abstract: A high-Reynolds-number turbulent flow subsumes several intermittent fields; some examples are the rates of dissipation of turbulent energy and scalar variance, square of turbulent vorticity and rate of strain, etc. These intermittent fields display different degrees of correlation among them. Motivated by the need for characterizing such coexisting distributions of intermittent fields in fully developed turbulence, the multifractal formalism---which we have already found useful in describing such intermittent distributions singly---is extended to more than one variable. The formalism is first illustrated by studying joint log-normal as well as joint binomial distributions. It is then applied to simultaneous measurements in several classical turbulent flows of the joint distribution of a component of the dissipation of kinetic energy, the dissipation rate of passive scalar variance, as well as the square of a component of turbulent vorticity. This allows simple but realistic models of simultaneous cascades of more than one variable to be developed.
226 citations
TL;DR: Detailed descriptions of the transition to turbulence and of the spatial and temporal variation of the wall shear stress, particularly near the reattachment point, have not been previously reported for pulsatile flow through constricted tubes.
Abstract: A photochromic tracer method has been used to record pulsatile flow velocity profiles simultaneously at three axial locations along a flow channel. Two major advantages of this multiple-trace method are that it enables velocity data to be acquired in an efficient non-invasive manner and that it provides a detailed description of the spatial relationship of the flow field. The latter is found to be particularly useful in the investigation of transitional type flows; for example, in describing coherent flow structures. Studies of the flow patterns in tubes with mild to moderate degrees of vessel constriction were performed using a 2.9 Hz sinusoidal flow superimposed on a steady flow (frequency parameter of 7.5; mean and modulation Reynolds numbers of 575 and 360, respectively). With mild constrictions (< 50% area reduction), isolated regions of vortical and helical structures were observed primarily during the deceleration phase of the flow cycle and in the vicinity of the reattachment point. As expected, these effects were accentuated when the constriction was asymmetric. For moderate constrictions (50%–80%), transition to turbulence was triggered just before peak flow through the breakdown of waves and streamwise vortices that were shed in the high-shear layer. During this vortex generation phase of the flow cycle, the wall shear stress fluctuated quite intensely, especially in the vicinity of the reattachment point, and its instantaneous value increased by at least a factor of eight. Such detailed descriptions of the transition to turbulence and of the spatial and temporal variation of the wall shear stress, particularly near the reattachment point, have not been previously reported for pulsatile flow through constricted tubes. The observed wall shear stress variations support a proposal by Mao & Hanratty (1986) of an interaction of the imposed flow oscillation with the turbulent fluctuations within the viscous sublayer.
191 citations
TL;DR: In this article, the authors describe a quantitative study of the three-dimensional nature of organized motions in a turbulent plane wake and detect coherent structures from the instantaneous, spatially phase-correlated vorticity field using certain criteria based on size, strength and geometry of vortical structures.
Abstract: This paper describes a quantitative study of the three-dimensional nature of organized motions in a turbulent plane wake. Coherent structures are detected from the instantaneous, spatially phase-correlated vorticity field using certain criteria based on size, strength and geometry of vortical structures. With several combinations of X-wire rakes, vorticity distributions in the spanwise and transverse planes are measured in the intermediate region (10d [les ] x [les ] 40d) of the plane turbulent wake of a circular cylinder at a Reynolds number of 13000 based on the cylinder diameter d. Spatial correlations of smoothed vorticity signals as well as phase-aligned ensemble-averaged vorticity maps over structure cross-sections yield a quantitative measure of the spatial coherence and geometry of organized structures in the fully turbulent field. The data demonstrate that the organized structures in the nominally two-dimensional wake exhibit significant three-dimensionality even in the near field. Using instantaneous velocity and vorticity maps as well as correlations of vorticity distributions in different planes, some topological features of the dominant coherent structures in a plane wake are inferred.
117 citations
TL;DR: In this article, a nine-sensor hot-wire probe is described which is capable of simultaneously measuring the velocity and vorticity vectors with a spatial resolution of about six Kolmogorov microscales just above the viscous sublayer in a thick turbulent boundary layer at a Reynolds number of Rθ = 2685.
Abstract: A nine-sensor hot-wire probe is described which is capable of simultaneously measuring the velocity and vorticity vectors with a spatial resolution of about six Kolmogorov microscales just above the viscous sublayer in a thick turbulent boundary layer at a Reynolds number of Rθ = 2685. Results from tests of the probe performance are presented to show that the three velocity components at each of its three arrays are measured with sufficient accuracy to allow determination of velocity gradients and from them the vorticity vector. Measurements with this probe of statistical properties of the velocity and vorticity fields of the turbulent boundary layer are given in Part 2 of this paper. When compared to the results of others, they further demonstrate the capability of this probe to measure simultaneously the velocity and vorticity vectors in turbulent flows of low to moderate Reynolds numbers.
108 citations
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TL;DR: In this article, a definition of coherent structures in turbulent shear flows is proposed and its implications discussed, and the characteristic coherent structure properties are identified and the analytical and experimental constraints in the eduction of coherent structure are examined.
Abstract: The nature and significance of large‐scale coherent structures in turblent shear flows are addressed. A definition for the coherent structure is proposed and its implications discussed. The characteristic coherent structure properties are identified and the analytical and experimental constraints in the eduction of coherent structures are examined. Following a few comments on coherent motions in wall layers, the accumulated knowledge from a number of recent and ongoing coherent structure investigations in excited and unexcited free shear flows in the author’s laboratory is reviewed. Also briefly addressed are effects of initial conditions, the role of coherent structures in jet noise production and broadband noise amplification, the feedback effect of coherent structures, the use of the Taylor hypothesis in coherent structure description, negative production, turbulence suppression via excitation, validity of the Reynolds number similarity hypothesis, etc. From the detailed quantitative results, a picture of the state of the art in coherent structure studies emerges. While coherent structures are highly interesting characteristic features of (perhaps all) turbulent shear flows, it is argued that their dynamical significance has been overemphasized. These are predominant only in their early stages of formation following instability, or in resonant situations and excited flows, or in regions adjacent to a wall of a turbulent boundary layer. The coherent Reynolds stress, vorticity, and production are comparable to (and not an order of magnitude larger than) the time‐average Reynolds stress, vorticity, and production, respectively, in fully developed states of turbulent shear flows, where incoherent turbulence is also important and cannot be ignored. The concept and importance of coherent structures are here to stay; understanding and modeling of turbulent shear flows will be incomplete without them; but they are not all that matter in turbulent shear flows.
772 citations
01 Jan 1955
TL;DR: In this paper, an experimental and theoretical study made of the instantaneously sharp and irregular front which is always found to separate turbulent fluid from contiguous "nonturbulent" fluid at a free-stream boundary is presented.
Abstract: Report presents the results of an experimental and theoretical study made of the instantaneously sharp and irregular front which is always found to separate turbulent fluid from contiguous "nonturbulent" fluid at a free-stream boundary. This distinct demarcation is known to give an intermittent character to hot-wire signals in the boundary zone. The overall behavior of the front is described statistically in terms of its wrinkle-amplitude growth and its lateral propagation relative to the fluid as functions of downstream coordinate.
460 citations
TL;DR: An analysis of the spatial resolution of the Kovasznay vorticity meter and arrays for measuring velocity derivatives in isotropic turbulence is presented in this article, where Pao's three-dimensional spectrum is used, allowing calculations of the measured values of the one-dimensional VOR spectrum and mean-square velocity derivatives to be compared with their predicted values.
Abstract: Analyses of the spatial resolution of the Kovasznay vorticity meter and of arrays for measuring velocity derivatives in isotropic turbulence are presented. Pao's three-dimensional spectrum is used, allowing calculations of the measured values of the one-dimensional vorticity spectrum and mean-square velocity derivatives to be compared with their predicted values. It is found that for accurate measurement the array size should be of the order of the Kolmogorov microscale of the turbulence field.
165 citations
Additional excerpts
...In the boundary layer flow in which this probe has been used to date, with a momentum thickness Reynolds number of Ro ~ 2,600, the distance over which the velocity gradients are estimated is about 9.7 viscous lengths (1.5 mm) which is about five times the estimation of the flow's Kolmogorov microscale of 1.7 viscous lengths at y+= 20. This is only slightly larger than the size recommended by Wyngaard (1969) for good spacial resolution....
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TL;DR: In this article, it was found that simple signal shapes describe the turbulence structures on the average, i.e., a gradual deceleration from a local maximum followed by a strong acceleration.
Abstract: It is now well established that coherent structures exist in turbulent shear flows. It should be possible to recognize these in the turbulence signals and to program a computer to extract and ensemble average the corresponding portions of the signals in order to obtain the characteristics of the structures. In this work only the u-signal patterns are recognized, using several simple criteria; simultaneously, however, the v or w signals as well as uv or uw are also processed. It is found that simple signal shapes describe the turbulence structures on the average. The u-signal pattern consists of a gradual deceleration from a local maximum followed by a strong acceleration. This pattern is found in over 65% of the total sample in the region of high Reynolds-stress production. The v signal is found to be approximately 180° out of phase with the u signal. These signal shapes can be easily associated with the coherent structures that have been observed visually. Their details have been enhanced by quadrant truncating. These results are compared with randomly generated signals processed by the same method.
112 citations
TL;DR: An optical system for direct measurement of vorticity in a flowing fluid is disclosed in this article, where spherical particles suspended in the flow rotate with an angular velocity that is accurately equal to half the local vortivities.
Abstract: An optical system for direct measurement of vorticity in a flowing fluid is disclosed. Spherical particles suspended in the flow rotate with an angular velocity that is accurately equal to half the local vorticity; thus, measurements of the rotation rates of such particles indicate the vorticity. The particles are transparent, and preferably are less than 50 μm diameter, and each contains embedded planar crystal mirrors. The particles are suspended in a refractive index matched liquid. Measurement of the particle rotation rate and thus the vorticity of the fluid is preferably accomplished by measuring the rotation rates of reflections of one or more light beams from the planar mirrors. The measurements may be carried out using any system of position sensitive optical detectors such as photo sensitive devices screened by suitable slits or photo diode arrays.
70 citations