Feature Article

74 July/August 2006 Published by the IEEE Computer Society 0272-1716/06/$20.00 © 2006 IEEE

T he study of coherent structures in turbu-lent boundary layers is an active area of

research. Driven by applications including the reduc-tion of turbulent skin-friction drag over aircraft,researchers have long been interested in developing adeeper understanding of the key physical features with-in turbulent flows. One application of interest is theanalysis of multiple scalar and vector distributions andhow the interaction of variables contributes to theoriesof drag and the formation of vortex packets within aturbulent boundary layer. A second application involvesexamining the correlation between different layerswithin a numerical simulation of a turbulent channel

flow. The analysis of these applica-tions can be greatly facilitated by abetter understanding of the compli-cated interactions that occurbetween the vortices that make upthe motion.

Important research conducted inthe computational physics fieldfocuses on modeling 3D magneto-hydrodynamic light supersonic jetsin the context of astrophysical jets ingalaxy clusters. These high-speedjets propagate distances of over650,000 light years from theirsources, transporting energy andmagnetic fields to their surrounding

environments. The jet magnetic field is advected alongwith the flow and is expected to reflect properties of theevolving velocity field. Of particular interest is the extentto which the magnetic and velocity vector fields are spa-tially aligned and/or orthogonal to one another and theinterplay between magnetic field strength and the cor-responding velocity structures.

Our research explores strategies for developing effec-tive methods for the visual representation of multiplecolocated vector and scalar fields to allow understand-ing and analyses of each field, both individually and inthe context of the other. Mining the knowledge base ofprevious visualization research yields important find-ings and insights to assist the research of our specificapplications. Using these insights, we can reconstruct,

manipulate, and expand upon the existing state of theart to further the knowledge-discovery process relatedto specific tasks and conditions. Our present efforts focusprimarily on the investigation of methods for effective-ly visualizing multiple fields defined over a 2D domain;the problem of effectively visualizing multiple fieldsdefined over a 3D domain is even more challenging, andan important area for future work. The “Classifying andCombining Visualization Techniques” sidebar presentsprevious and related work.

Dual vector fieldsWhile it would be possible to compare the orientation

between two vector fields by deriving a scalar field basedon the dot product of corresponding vectors, it’s alsocritical for our applications to understand the local mag-nitude, direction, and gradients of each vector field inde-pendent of the other. For this reason, we considertechniques for the multiple representation of 2D vectorfields.

Considering one sample from each of the three visual-ly distinct methods for vector field visualization—texture,glyph, and line (discussed in the sidebar)—we explorethe range of effects achievable using layered combina-tions of these approaches to visualize two colocated vec-tor fields (see Figure 1 on page 76). For the texture-basedsample, we use line integral convolution (LIC)—the mostwidely used texture-based approach. For the glyph-basedsample, we create an image by repeatedly texture map-ping a comet-like glyph along thick, equally spacedstreamlines. This results in a glyph sequence that is con-tinuous in the direction of the flow. We create the line-based sample using the source code supplied by theauthors of an equally spaced streamline technique.1

One primary goal for each application is to depict thekey physical structures of one vector field in the contextof the key physical structures in another. Therefore, ahighly desirable ability is to easily differentiate betweenthe visual representations of each field and to identifyeach distribution. This process becomes more compli-cated when we apply the same representational tech-nique (for example, texture, glyph, or line) to each field.While we could use a supplemental visual variable, suchas color, to distinguish the two representations, we

Strategies for effectivelyvisualizing colocated 2D vectorfields enable understanding ofkey physical structures of onevector field within the contextof a related vector field. Thisarticle describes the range ofeffects possible by combiningseveral existing flowvisualization techniques foranalyzing multiple vector fields.

Timothy UrnessDrake University

Victoria Interrante, Ellen Longmire, Ivan Marusic,Sean O’Neill, and Thomas W. JonesUniversity of Minnesota

Strategies for the Visualization of Multiple 2DVector Fields

would prefer to reserve the use of color for the commu-nication of related, colocated scalar quantities.

The problem of differentiating between two vectorfields is illustrated in Figures 1a, 1b, and 1c. The combi-nation of two texture-based techniques (see Figure 1a)provides a rich representation in which both vectorfields are often visible, particularly in regions where thevector field orientations are not aligned. However, itbecomes challenging to distinguish the two data sets inregions where the orientations are aligned, as it’s diffi-cult to determine which field is being represented bywhich texture at any given location. Both the glyph andline techniques use an inherently sparse streamline spac-ing that leaves empty space in the image. Combiningtwo sparse techniques creates a large amount of nega-

tive space, which can result in a lost opportunity to rep-resent the vector fields’ fine details.

When two glyph-based techniques are overlaid (see Fig-ure 1b), maintaining good visual continuity or good con-tinuation in the flow direction in each field becomes achallenge, particularly when the glyphs are separated bya nontrivial amount of empty space. Overlaying two line-based techniques (see Figure 1c) maintains the continu-ity of streamlines; however, the accidental patterns ofintersections between streamlines in different vector fieldscan lead to visual artifacts that might cause an inaccurateperception of the data (see Figure 2 on the next page).

Combining different visualization techniques allowsfor the ability to easily identify and distinguish each dis-tribution (see Figures 1d, 1e, and 1f). When we use a

IEEE Computer Graphics and Applications 75

Classifying and Combining VisualizationTechniques

Many techniques exist for 2D flow visualization. Weexplore how several of these techniques can be classifiedand combined for the visualization of multiple relatedvector and scalar fields.

Classification Different visual techniques have characteristics that allow

different flow components to be more visually salient.1 Weclassify existing 2D vector field visualization techniques intoone of three visually distinct categories: texture, line, orglyph based.

Texture-based techniques are characterized by a consistent,highly detailed, and dense representation of a vector field.Many texture-based techniques exist for the visualization of2D flow, as it allows for easy display and analysis of a vectorfield’s fine details. The pioneering technique of spot noiseproduces a texture from weighted and randomly positionedspots deformed in accordance with flow direction.2 Lineintegral convolution (LIC)—a widely used technique—involves convolving a white noise input texture alongcalculated streamlines.3 We can resolve ambiguous flowdirection in LIC images by animating the texture.

Line-based techniques involve the display of elongatedstreamlines—segments completely tangent to the vectorfield. These images are fundamentally different than theimages created with texture-based techniques asstreamlines can be visually traced over a long distance, andline-based images are more sparse than textures (as emptyspace exists between the lines). While streamlines give aglobal sense of flow by depicting paths along the vectorfield, flow direction is not always apparent.

Glyph-based techniques are characterized by the use ofrepeatable icons that can express various types ofinformation about the flow, including flow orientation. Themost basic technique is the use of hedgehogs (sometimesknown as vector plots), which are short line segments orarrows aligned with the flow direction at regularly orrandomly distributed locations. Glyphs provide the ability todepict flow direction by using the glyph shape or aluminance ramp.4 We also include in this category techniquesthat involve placing glyphs along calculated streamlines.

Combining multiple imagesTransparency or layering is one of the most effective

methods to portray relationships between overlayingcomponents. Kirby, Marmanis, and Laidlaw introduced amethod inspired by the layering techniques used in oilpaintings to visualize components of 2D flow data.5 Weigleet al. demonstrated a texture-generation technique, basedon the layering of oriented slivers, using orientation andluminance to encode multiple overlapping scalar fields.6

Hotz et al. vary the input texture density and spot size inaddition to kernel length and overlay sparse LIC images tovisualize tensor field features.7

Wong et al. developed a technique that combineselements of alpha channel manipulation, filigreed graphics,and elevation terrain mapping, along with colormapenhancement to visualize a multivariate climate data set.8

Our research is inspired by these techniques, and seeks toexpand the applications of layering in the visualization ofmultiple related vector and scalar fields.

References1. D.H. Laidlaw et al., “Comparing 2D Vector Field Visualization

Methods: A User Study,” Trans. Visualization and Computer Graph-ics, vol. 11, no. 1, 2005, pp. 59-70.

2. J.J. van Wijk, “Spot Noise—Texture Synthesis for Data Visualiza-tion,” Proc. Siggraph, ACM Press, 1991, pp. 309-318.

3. B. Cabral and L. Leedom, “Imaging Vector Fields Using Line Inte-gral Convolution,” Proc. Siggraph, ACM Press, 1993, pp. 263-269.

4. R. Wegenkittl, E. Gröller, and W. Purgathofer, “Animating Flow-fields: Rendering of Oriented Line Integral Convolution,” Proc.IEEE Computer Animation, IEEE CS Press, 1997, pp. 15-21.

5. R.M. Kirby, H. Marmanis, and D.H. Laidlaw, “Visualizing Multival-ued Data from 2D Incompressible Flows Using Concepts fromPainting,” Proc. IEEE Visualization, IEEE CS Press, 1999, pp. 333-340.

6. C. Weigle et al., “Oriented Sliver Textures: A Technique for LocalValue Estimation of Multiple Scalar Fields,” Graphics Interface,Lawrence Erlbaum Assoc., 2000, pp. 163-170.

7. I. Hotz et al., “Physically Based Methods for Tensor Field Visualiza-tion,” Proc. IEEE Visualization, IEEE CS Press, 2004, pp. 123-130.

8. P.C. Wong et al., “Multivariate Visualization with Data Fusion,”Information Visualization, vol. 1, nos. 3-4, 2002, pp. 182-193.

different representational approach for each field, theprimary challenge is to appropriately balance the visu-al prominence of each representation, so that neitheroverwhelms the other in the combined presentation.Figure 3 illustrates how we can make different repre-sentations more or less prominent by altering the con-trast and luminance values prior to layering the twoimages. Similarly, we can use differences in line thick-ness to make one vector field more prominent when dis-played with another (see Figure 4).

In our experience, we can achieve particularly goodresults by layering a relatively sparser, higher contrast,glyph- or line-based representation of one field over a rel-atively denser, lower contrast, texture-based representa-tion of the other field. The high contrast between the glyphor line elements and the background or empty spaceenables them to maintain their visibility when superim-posed over the textured background; the glyph or line ele-ments’ relatively sparse distribution in the top-layer flowhelps enable the simultaneous, effortless appreciation ofthe flow that the underlying layer portrays.

Next we illustrate methods that allow for two differentrepresentations to be combined in such a way that eachrepresentation remains distinct and visually separable.

OverlayIn Figure 5, we’ve combined two representations

using a screen overlay method. This method is similarto a standard image multiplication operation but oper-ates on the additive inverse of each input image. Specif-ically, if D(x, y) is the output image and A(x, y) and B(x,y) are the respective input images, and we assume thateach pixel intensity is between 0.0 and 1.0, we definethe screen overlay operation as D(i, j) = 1.0 − (1.0 −A(i, j)) ∗ (1.0 − B(i, j)).

Applying this formula allows the underlying textureimage’s intensities to show through in the places wherethe overlying glyph image contains empty (black) space.This technique is most effective when using an imagewith a black background as the resulting image is high-lighted only in regions where the glyph or line is placed.In Figure 5, you can easily distinguish the two vectorfields not only where their orientations are nearly orthog-onal, but also in the places (such as the upper right cor-ner) where their orientations are nearly aligned. It’sprecisely to enable these sorts of comparisons of the rel-ative alignments of the two fields that we pursue inves-tigating these methods for their combined portrayal.

Embossing In the overlay method, we primarily rely on lumi-

nance differences to distinguish the overlying glyph orline elements from the underlying texture image.Embossing is an alternative technique that we canemploy to distinguish an overlaid image from an under-lying image.2 In this method, we give each element ofthe overlaying image a distinct 3D visual appearance toenable the elements to perceptually group preferential-ly with each other and at the same time jointly segre-gate from the background.

Embossing algorithms simulate a standard lightingequation with a single-point light source. While thismethod is highly effective in many situations, artifacts

Feature Article

76 July/August 2006

1 Different 2D vector visualization techniques appliedto two colocated vector fields: (a) combination of twotexture-based techniques, (b) two glyph-based tech-niques overlaid, (c) two line-based techniques overlaid,(d) glyph- and texture-based techniques overlaid, (e)line- and glyph-based techniques overlaid, and (f) line- and texture-based techniques overlaid.

(a) (d)

(b) (e)

(c) (f)

2 Combiningstreamlinerepresentationscan lead tovisual artifacts.(a) Two streamlineimages arecombined. (b)The artifact(highlighted inred) caused byintersectingstreamlines.

(a)

(b)

can arise when attempting to emboss vector fields, par-ticularly when the vectors are oriented in the same direc-tion as the light source. To sidestep this problem, weimplemented the embossing using two different lights inthe plane: one from a source directly above the image,and one from a source above and to the right of theimage—that is, at a 45-degree angle. The combinationof these directions gives the impression of a broad lightcoming from above. This produces the visual effect ofthe embossed image being raised from the surface. Wecreate the composited image on a pixel-by-pixel basis bysampling from the appropriate input image, dependingon the flow orientation at each point (taking care toalways sample from an image created using a lightsource direction not aligned with the vector field).Regions of transition are alpha blended between the twoimages (see Figure 6 on the next page).

Where it’s relatively straightforward to embossstreamlines and glyphs, dense textures typically do notemboss well. Embossing is most effective when appliedto sparse textures that contain a sufficient amount ofempty space within the image. This allows us to portraythe shading equation’s result (see Figure 7).

We can overlay an embossed image on another imageby adding the intensities in the two images on a pixel-by-pixel basis and then subtracting the value that thebackground color takes in the embossed image. This isequivalent to increasing the intensity in the nonem-bossed image at the points where the intensity in theembossed image is above average, and decreasing theintensity in the nonembossed image at the points wherethe intensity in the embossed image is below average(see Figure 8). The embossing, in effect, gives a visualdistinction of an applied 3D lighting equation and isvisually separable from the nonembossed image.

As the initial results of layering a relatively sparse(glyph-like or streamline representation) of one vectorfield over a denser texture-based representation of theother vector field appear particularly promising, we usethis approach to demonstrate the effective representa-tion of two different, related vector fields in three scien-tific applications.

Application 1: experimental turbulentflow

Stereoscopic particle image velocimetry (PIV) canhelp experimentally measure instantaneous compo-

nents of a velocity field in a turbulent boundary layerplane in a moderate to high Reynolds number flow. Inaddition to the experimentally generated velocity field(v), we can numerically calculate and analyze the vor-ticity vector field (w = ∇ × v) with the velocity vectorfield. While this data is sampled on a 2D plane, theresulting multivariate data’s footprint gives insight intothe 3D flow’s structure and behavior. Because the knowl-edge discovery process related to this application is

IEEE Computer Graphics and Applications 77

3 We can emphasize different representations by altering luminance properties of individual representations prior to image com-positing. In this sequence of images, from left to right, the glyphs become brighter while the texture becomes darker. When theglyphs are subtle (left image), the vector field represented by the texture is more prominent. When the contrast between the whiteglyphs and the darkened texture is more obvious (right image), the vector field represented by the glyphs is more prominent.

4 Differences inline thicknesscause one vec-tor field toappear moreprominentlythan the other.

5 Glyph texturemappedstreamlinesoverlaid on aline integralconvolutiontexture mappedbackground.

predicated on achieving an integratedunderstanding of each variable’s individ-ual contribution and how the variablesinterrelate, developing effective, multi-variate visualization methods is criticallyimportant to the understanding andanalysis of PIV experiment results.

Many investigators are interested inunderstanding the coincidence of thevelocity and vorticity fields, particularlyin conjunction with the visualization ofvortex core locations. These visualiza-tions allow for the analysis of severalterms such as (v × w), the Lamb vector,and (v ⋅ w), which is proportional tohelicity, both of which researchers havesuggested as possible vortex tube descrip-tors.3 By visualizing multiple quantities,we can better develop theories about theintegrated system, not just individualcomponents of the data.

We use the methods described here tovisualize data acquired from experimen-tally generated dual plane PIV experi-ments. Our goal is to further understandthe relationship among the vorticity vec-tor field, velocity vector field, and 2D and

3D swirl strength scalar distributions.

Swirl strengthTo understand and identify the subtle components of

fluid dynamics, researchers have developed several vor-tex identification methods. Zhou et al. suggested the useof the imaginary part of the complex eigenvalue (λci) ofthe velocity gradient tensor to visualize vortices.4 Thisvalue is referred to as the local swirl strength of the vor-tex. We can compute a simplified version of swirlstrength using only in-plane velocity gradients to iden-tify vortex cores. This quantity is referred to as 2D swirlstrength and is limited to identifying vortex cores ori-ented in a position normal to the sampling plane. Dualplane PIV is an extension of single plane PIV in whichvelocity components are measured in two planes simul-taneously. This allows us to calculate all 3D velocity gra-dient measurements. The corresponding 3D swirlstrength is a measure of the existence of a vortex corein any orientation.

We can use the size, strength, and orientation of vor-tex cores, which can be elucidated from vorticity and 2Dand 3D swirl, in theories designed to reduce skin-fric-tion drag in turbulent flow.

Vorticity, velocity, and swirl strengthWe first analyze the in-plane velocity vector along

with the 2D and 3D swirl fields. We visualize the veloc-ity vector field using a LIC texture and encode the 2Dand 3D swirl variables in color using a technique thatmaps each color to alternating streamlines to avoid theambiguity that occurs when colors are mixed.5 The LICtexture serves as a method to convey the underlying vec-tor field while simultaneously providing the means todistribute the color representing additional scalar fields.

Feature Article

78 July/August 2006

6 Embossing with different light source angles on streamlines (top row) and glyphs(bottom row). (a–b) Light source from directly above (90 degrees). Vectors verticallyoriented aren’t illuminated well. (c–d) Light source from 45 degrees. In this case, therepresentation of the diagonally oriented vectors suffers. (e–f) Both light sources combined.

(a) (c) (e)

(b) (d) (f)

7 Embossing atexture. (a) Asparse texturein which theeffects of anembossingalgorithm canbe perceived.(b) Anembossedsparse texturecombined witha line integralconvolutiontexture.

(a)

(b)

8 Distinguish-ing differentfields byembossing. (a)Embossed tex-ture compositedwith glyphs. (b) Embossedstreamlinescompositedwith texture. (c) Embossedglyphs compositedwith texture.

(a)

(b)

(c)

We obtain the velocity vector field by sub-tracting the mean streamwise velocity from thein-plane velocity component. Thus, the loca-tions of critical points are subject to the relativevelocity of the observer and are not germane tothe analysis in this example. Swirling stream-lines in the vicinity of the area of high swirlstrength will only occur in the vicinity of theparticular vortex cores that convect at a ratesimilar to the mean streamwise velocity.

Analyzing the relationship between the 3Dswirl and 2D swirl components leads to a valu-able understanding of the orientation of a vor-tex core. As 3D swirl is calculated using allgradient components, it can accurately measurethe existence of a vortex core at any orientationto the referencing plane. The 2D swirl distribu-tion measures only the swirl of a vortex corewith significant orientation orthogonal to theplane. Accordingly, 2D swirl is present onlywhere there is also significant 3D swirl.

To develop an understanding of how the vor-ticity vector field contributes to the phenome-non of swirl strength and the existence of avortex core, we screen overlay the velocity vec-tor field LIC image with a glyph image repre-senting the vorticity vector field (see Figure 9).Using the result of this image, we can analyzethe relationships between the velocity and vor-ticity vector fields in a way that lends insight tohow these two components interrelate.

The glyphs’ thickness is directly proportional to thein-plane vorticity magnitude. The two vector fields dis-played in Figure 9 reveal zones where velocity and vor-ticity are nearly perpendicular (regions within a square)and nearly parallel (regions within an oval) for the par-ticular convection velocity being visualized. The regionin the center of the image exhibiting strong 2D swirl(red) also contains strong in-plane vorticity, as evi-denced by thick glyphs, and additional 3D swirl (blue),suggesting a vortex core inclined at a significant angleto the measurement plane. The remaining zones of 3Dswirl that lack a prominent indication of 2D swirl rep-resent cores whose vorticity is more closely aligned withthe measurement plane. The glyphs give the core’s pre-dominant vorticity direction.

The integrated visualization of these componentsallows us to correlate the vorticity direction and magni-tude with the direction of a vortex core delineated byswirl strength. Effectively combining techniques formultiple vector and scalar field visualization allows fora better understanding of vortex frequency, strength,and orientation, as well as the 3D interactions amongand caused by vortices. This technique can be particular-ly useful in the analysis of large fields characterized bythe occurrence of multiple interactions.

Application 2: astrophysical jetsThe modeling of magnetohydrodynamic light super-

sonic jets in the context of astrophysical galaxy clustersis an area of active research in computational physics.6

In addition to the velocity field, physicists are concerned

with the magnetic vector field advected by these super-sonic jets and with analyzing the relationship betweenboth vector fields. Developing a deeper understandingof the relationship between the vector fields’ topology,magnetic field strength, and corresponding velocitystructures results in a greater understanding of howkinetic and magnetic energy distributions evolve inthese systems and contributes to the explanation ofradio emissions that can be physically observed.

In addition to understanding the relationship of thetopology of both vector fields, astrophysicists are inter-ested in the interplay between magnetic field strengthand the corresponding velocity structures as magneticfield enhancement naturally results from shear andcompression in the flow.

Magnetic induction Given a magnetic field B, and a vector field v, we can

calculate changes in magnetic field from the ideal mag-netic induction equation:

(1)

Equation 1 describes how motions of a perfectly con-ducting fluid change the magnetic fields containedtherein. By examining this vector’s magnitude, weexamine correlations between increases in magneticfield strength and anticipated shear or compressionregions in the velocity field. Simultaneous visualizationof all velocity field components and the rate of changeof the magnetic field strength enables us to locate

∂∂

= ∇× ×( )BB

tv

IEEE Computer Graphics and Applications 79

9 Visualization of multiple scalar and vector fields from a dualplane, particle image velocimetry experiment. The underlying lineintegral convolution texture represents the velocity vector field.The glyph field represents the vorticity vector field. The figureshows 2D swirl strength (red) and 3D swirl strength (blue). Theregions within each square box depict areas where the velocityfield and vorticity field are orthogonal. The areas within each ovaldepict regions where both fields are parallel. The combination ofvariables within a single image allows for the determination ofvortex core location, orientation, and convection.

regions of active field enhancement, distinguish newlymagnetized fields from those advected along with theplasma, and identify velocity structures that generateenhanced fields.

Multivariate visualization Through simultaneous visualization of the simulat-

ed velocity and magnetic fields, we have identified sev-eral regions of magnetic field enhancement and theirantecedent velocity structures. We first visualize thevelocity field using a high-frequency LIC texture withthe magnitude of the magnetic field’s rate of changerepresented in color. Next, we apply the magnetic vec-tor field’s streamlines using the embossing techniqueintroduced previously. We visualize the magnetic field’smagnitude using the line thickness. Figure 10 showsthe result.

Careful analysis of Figure 10 reveals regions of highmagnetic field strength obviously correlated with partic-ular velocity structures such as high-speed flows, flowcompression, and shearing between flow structures.Areas in which there exist positive regions of magneticinduction

indicate regions of magnetic field amplification. Regionsof alignment of the magnetic vector field and the veloc-ity field result from shear enhancement of the magnet-ic field. There are, however, additional magnetic

enhancements with which the velocity field isnot obviously causally connected. Moreover, inmany instances the magnetic field is unalignedor even orthogonal to the velocity field. Thisobservation runs contrary to theoretical expec-tations, assuming shear is the dominant formof magnetic field amplification.

Astronomers find an understanding of mag-netic field amplification processes and theirrelationship to flow velocity valuable becausethese magnetic structures are responsible forthe observed radio emission characteristic ofthese systems. Through simulations andadvanced visualization techniques, we expectto learn more about what observations of radiogalaxies can tell us about the physics govern-ing their evolution.

Application 3: direct numericalsimulation of turbulent channelflow

Fluid dynamics researchers are interested inmodeling turbulent channel flow because thesimulation allows for the analysis of large,energetic features in the flow and correlationof flow structures in different layers within the3D model. Developing a deeper understand-ing between the different regions within achannel flow results in a better understandingof the formation of vortical structures and thekey physical features that cause skin-friction

drag. In this application, we consider wall-bounded tur-bulent flow data from a direct numerical simulation(DNS) of the full Navier-Stokes and continuity equa-tions.7

Numerical simulation The great value of DNS data is that it’s fully resolved

and provides full 4D (space and time) data. However,the difficulty with DNS is that it’s expensive and limitedin Reynolds number. This is because the cost of simulat-ing wall-bounded turbulent flows scales nominally with

, where represents the importance of inertia rel-ative to viscous forces. Thus, larger, faster flows havehigher . The simulation involved 2.7-billion gridpoints (3,072 × 2,304 × 385), with each resulting timestep producing a raw (unprocessed) field of 9 Gbytes.The Reynolds number for the simulation is .

The numerical technique involved the integration ofthe Navier-Stokes equations in the form of evolutionproblems for the wall normal vorticity and the Lapla-cian of the wall normal velocity. For spatial discretiza-tion, Chebychev polynomials were used in the wallnormal direction, while dealiased Fourier expansionswere used in wall parallel planes. A third-order, semi-implicit Runge-Kutta scheme was used for temporal dis-cretization. Because a large streamwise extent is neededto capture the longest energy containing motions of theflow, the simulation employed a computational domainof 8πδ units in the streamwise direction and 3πδ unitsin the spanwise direction, where δ is the channel halfwidth.

Reτ = 934

Reτ

ReτReτ3

∂∂

⎛

⎝⎜

⎞

⎠⎟

Bt

Feature Article

80 July/August 2006

10 Visualization of multiple scalar and vector fields within amagnetohydrodynamic light supersonic jet. The underlying lineintegral convolution texture depicts the velocity vector field.The embossed streamlines represent the magnetic vector field.Purple (negative) and orange (positive) colors represent themagnitude of the magnetic field’s rate of change. The circledarea in the center is a region of significant magnetic field ampli-fication where the magnetic field lines change orientation to beoriented perpendicular to the flow. The regions within therectangles highlight an orthogonal correlation between flowstructures and magnetic field lines.

Regions of flowDNS data allows for the investiga-

tion of large-scale energetic featuresand how these might interactbetween different regions in theflow. Conventional approachesdescribe wall turbulence in terms ofthree predominant regions: an innerregion, immediately next to thewall, dominated by viscous process-es; an outer region, far from thewall, with negligible viscous effects;and an intermediate region, theoverlap of the inner and outerregions. This middle region is alsoreferred to as the log region or theinertial wall region. Most existingtheoretical approaches regard theinner region to scale universallywith inner-wall viscous variables and to be independentof the log region and beyond. Recent studies, however,have shown evidence that the inner region is influencedby outer region parameters.8

PIV experimental studies have consistently shown thelog region to contain packets of hairpin vortices, withlong streamwise regions of momentum deficit and withhigh-speed fluid seeming to fill the separation betweenneighboring motions. However, the PIV fields are some-what limited in length (approximately 2δ). Researchershave recently discovered that the structures can exist upto 20δ in length and may have a tendency to meanderin the spanwise direction.9 The tendency of the low-speed region to meander across the flow explains whysuch long length scales have not been observed previ-ously from single-point measurements in boundarylayer flows.

Visualization of multiple layersThe discovery of the long superstructures is partic-

ularly significant as it indicates an outer-layer scaledphenomena might have influence all the way down tothe wall in the inner layer. The DNS data is useful forinvestigating this conjecture; Figure 11 shows someresults.

Figure 11 shows two planes simultaneously from theDNS data set. The embossed glyphs data represents aplane in the log region (z+ = 150) and the underlyingtexture data is in the viscous buffer zone (z+ = 15) at thewall normal location of maximum turbulent energy pro-duction. The luminance values for the texture and theglyph size show the instantaneous streamwise valuesfor each plane. Dark, long, low-speed structures are vis-ible in the viscous buffer zone, and careful examinationindicates that the footprints of these structures extendto the log region based on the presence of large glyphsin coincident locations. The long superstructuresdescribed previously are approximately outlined in red.These results indicate that near-wall regeneration mech-anisms are not independent of the slow dynamics asso-ciated with structures on the order of the externaldimension of the flow, as has always been previouslybelieved.

Discussion and conclusion We have explored the development of visualization

methods that can provide a deeper and more compre-hensive understanding of the key interrelated featuresin coincident vector fields, augmented with the simulta-neous display of related coincident scalar quantities.The needs of fundamental fluids research problems havedriven our investigations: investigations by aerospaceengineers into the physics of turbulence, and the com-putational modeling and simulation by astrophysicistsof the behavior of supersonic jets in galactic clusters. Ineach of these application areas, we have demonstratedhow our developed techniques facilitate the process ofscientific inquiry.

This interaction between visualization researchers anddomain scientists has proven extremely beneficial to bothparties. Through our collaboration we have advancedour ability to create effective visualizations and madeimportant discoveries that further the development ofimportant theories related to the applications. The appli-cation scientists played a critical role in defining the spe-cific needs that the visualization techniques presentedhere were developed to address. In addition, they pro-vided an objective assessment of the functionality of themethods, in terms of how well they meet their goals ofgaining greater insight into their data.

The focus of our research so far has been the explo-ration of different visualization methods, and we havenot yet honed our code into a production quality tool.However, we eventually intend to package our variousutilities into a user-friendly application—using currentgraphics hardware—that the application scientists canuse on a routine basis for the analysis of coincident mul-tiple vector fields. Future work will also include expand-ing our investigations to consider a wider variety oftexture patterns beyond LIC. Finally, we are also consid-ering techniques to explore the potential effectiveness ofvarious alternative methods for simultaneously portray-ing multiple colocated vector and scalar fields in 3D.■

AcknowledgmentsWe thank Bharathram Ganapathisubramani for the

collection of the dual plane PIV data, Robert Moser for

IEEE Computer Graphics and Applications 81

11 Visualization of two separate layers of the numerically generated wall-bounded turbulentflow. The underlying texture displays a layer in the viscous buffer zone where luminance valuesdepict streamwise flow speed; the dark regions represent slow-moving fluid. The embossedglyphs represent another plane in the log region where glyph size depicts the streamwise flowspeed; the large glyphs represent slow-moving fluid. The red lines indicate some examples ofelongated regions where the streamwise velocity is highly correlated in both layers.

the use of the DNS data, and Nicholas Hutchins for hisanalysis and assistance with the DNS data. We alsothank the anonymous reviewers for their valuable com-ments and suggestions. This research was supported bythe Digital Technology Center at the University of Min-nesota and by grants from the US National Science Foun-dation (AST03-07600, CTS-0324898, ACI-9982274)and the David and Lucile Packard Foundation.

References1. G. Turk and D. Banks, “Image-Guided Streamline Place-

ment,” Proc. Siggraph, ACM Press, 1996, pp. 453-460. 2. T. Urness et al., “Techniques for Visualizing Multi-Valued

Flow Data,” Proc. Eurographics/IEEE TCVG Symp. DataVisualization, Eurographics Assoc., 2004, pp. 165-172.

3. H.K. Moffatt, “Magnetostatic Equilibria and AnalogousEuler Flows of Arbitrarily Complex Topology. Pt. 1: Fun-damentals,” J. Fluid Mechanics, vol. 159, 1985, pp. 359-378.

4. J. Zhou et al., “Mechanisms for Generating Coherent Pack-ets of Hairpin Vortices in Channel Flow,” J. Fluid Mechan-ics, vol. 387, 1999, pp. 353-396.

5. T. Urness et al., “Effectively Visualizing Multi-Valued FlowData Using Color and Texture,” Proc. IEEE Visualization,IEEE CS Press, 2003, pp. 115-121.

6. S.M. O’Neill et al., “Three-Dimensional Simulations ofMHD Jet Propagation through Uniform and StratifiedExternal Environments,” The Astrophysical J., vol. 633, no.2, 2005, pp. 717-732.

7. J.C. del Álamo et al., “Scaling of the Energy Spectra of Tur-bulent Channels,” J. Fluid Mechanics, vol. 500, 2004, pp.135-144.

8. B. Ganapathisubramani et al., “Investigation of Large-ScaleCoherence in a Turbulent Boundary Layer Using Two-PointCorrelations,” J. Fluid Mechanics, vol. 524, 2005, pp. 57-80.

9. N. Hutchins, W. T. Hambleton, and I. Marusic, “InclinedCross-Stream Stereo PIV Measurements in TurbulentBoundary Layers,” J. Fluid Mechanics, vol. 541, 2005, pp.21-54.

Timothy Urness is an assistantprofessor in the Department of Math-ematics and Computer Science atDrake University. His research inter-ests include developing techniques forthe effective visualization of multidi-mensional flow data. Urness has aPhD in computer science from the Uni-

versity of Minnesota. Contact him at timothy.urness@drake.edu.

Victoria Interrante is an associ-ate professor in the Department ofComputer Science and Engineering atthe University of Minnesota. Herresearch interests include the applica-tion of insights from visual perceptionto the design of techniques for moreeffectively conveying information

through images. Interrante has a PhD in computer sciencefrom the University of North Carolina at Chapel Hill. Con-tact her at interran@cs.umn.edu.

Ellen Longmire is a professor in theDepartment of Aerospace Engineeringand Mechanics at the University ofMinnesota. Her research interestsinclude experimental fluid mechanicsincluding turbulent, multiphase, bio-medical, and microscale flows. Long-mire has a PhD in mechanical

engineering from Stanford University. Contact her atellen@aem.umn.edu.

Ivan Marusic is an associate pro-fessor in the Department of AerospaceEngineering and Mechanics at theUniversity of Minnesota. His researchinterests include experimental andtheoretical fluid mechanics, with anemphasis on turbulence. Marusic hasa PhD in mechanical engineering from

the University of Melbourne, Australia. Contact him atmarusic@aem.umn.edu.

Sean O’Neill is a PhD student in theastronomy department at the Univer-sity of Minnesota. His research inter-ests include numerical studies inhigh-energy astrophysics, specificallythe simulation and analysis of super-sonic jets in realistic galaxy clusterenvironments. Contact him at

soneill@astro.umn.edu.

Thomas Jones is a professor ofastronomy at the University of Min-nesota. His research interests includecomputational fluid dynamics, high-energy astrophysics, and cosmology.Jones has a PhD in physics from theUniversity of Minnesota. Contact himat twj@umn.edu.

Article submitted: 25 Aug. 2005; revised: 4 Jan. 2006;

accepted: 28 Feb. 2006.

Feature Article

82 July/August 2006