Experiments in Fluids 12, 189-199 (1992) Experimentsin Fluids 9 Springer-Verlag 1992 Flow visualization of interactions among large coherent structures in an axisymmetric jet* C.O. Pasehereit**, D. Oster***, T.A. Long, H.E. Fiedler** and I. Wygnanski Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, USA Abstract. Interactions between large coherent structures are visualized with both schlieren photography in two air jets and dye photography in a water jet. The density difference needed for the schlieren technique is provided by an electrically heated wire ring surrounding the jet. External forcing with either single axisymmetric, single non-symmetric, combined axisymmetric or combined non-symmetric modes was applied. It was found that forcing the jet with a pair of different spinning modes leads to azimuthal distortions of the mean flow. This observation confirms and explains existing hotwire data. Simultaneous excitation with two axisymmetric modes may produce structures of higher modes or even cause structurally undistinguishable development. Streamwise structures are observed both in the unforced jet and in the axisymmetrically forced jet. They do not seem to be caused by a G6rtler instability from the concave curvature of the conventional nozzle, since they were also found in a jet flow from a specially designed nozzle with only convex contraction surface. 1 Introduction Flow visualization should be utilized in concert with quantitative measurements when studying complex fluid dynamic phenomena. A primary advantage of flow visualization is the rapid and usually simple acquisition of instantaneous and spatially dense, though only qualitative, information about large regions of the flow. This information frequently provides excellent guidance for subsequent quantitative measurements of the flow. Given the large amount of information in a single photograph, it is not surprising that flow visualization led to the discovery and the conceptual formulation of large coherent structures in turbulent shear flows (Brown and Roshko 1974). The concept of large scale structures in turbulent flow would have been quite difficult * Supported in part by the National Science Foundation under Grant No. MSM 8900086 and by the Deutsche Forschungsgemeinschaft DFG, Fi178/34-1 ** Present address: Hermann-F6ttinger-Institut ffir Thermo- und Fluiddynamik, Technische Universit/it Berlin, Berlin, FRG *** Present address: Israel Aircraft Industries, Ben Gurion Airport, Israel and time-consuming to develop on the basis of hot-wire anemometry, pressure measurements, or even laser Doppler velocimetry, since these methods only provide information about the temporal evolution of the flow at a limited number of spatial locations. Image-processing techniques appear to represent the next generation of measurements by combining the spatial presentation of flow visualization with quantitative methods of data acquisition and by educing velocity information directly from optical images. Examples of such methods are found in water experiments where optically activated tracers are photographed over short time intervals. The resulting trajectories can then be converted digitally into velocity vectors (Gharib 1986). The most c o m m o n method of flow visualization is the introduction of tracers, e.g. dye or smoke, into the flow at one or more points. Whenever the fluid considered has a density inhomogeneity, optical methods such as shadowgraph and schlieren can be used to establish the location of the boundary of the inhomogeneity. Shadowgraph and schlieren techniques are most sensitive to gradients in the index of refraction which vary directly with gradients of the fluid density. Specifically, shadowgraph images are sensitive to the second spatial derivative of the density, and schlieren images are sensitive to the first spatial derivative of the density (Merzkirch 1987). In the special case of a two-dimensional shear flow between two different fluids having a Schmidt number near unity, the regions containing density gradients essentially coincide with the regions containing vorticity gradients, since for this case the vorticity equation and the mass-transport equation become identical. In general, however, the visible schlieren interfaces represent streaklines or streaksurfaces, which do not necessarily coincide with vorticity distributions. The interpretation of tracer or schlieren images in 3-D time dependent flows is, therefore, not straightforward. For example, a harmonically perturbed plane shear layer produces streaklines that roll into an array of discrete eddies, giving the impression of wave breakdown, even though the flow constitutes a linear superposition of a weak harmonic motion with a steady velocity profile (Hama 1962). Irrespective of the three-dimensionality of the turbu- 190 lent motion, the free interface apparent in a schlieren image of a flow with Schmidt number (or Prandtl number in the case of temperature inhomogeneities) of approximately unity corresponds to the vorticity boundary, i.e., the interface between turbulent and potential flow. The purpose of this study was to visualize the patterns ensuing from secondary interactions of helical and axisymmetric modes in a forced axisymmetric jet. Although previous theoretical analysis and quantitative data provide a considerable amount of detailed information about this flow (Cohen and Wygnanski 1987; Long and Petersen 1990; Paschereit and Wygnanski 1990), an integrated knowledge of the ensuing overall flow pattern is missing. Flow visualization was used as a learning tool to understand the mechanisms affecting the large scale structures and perhaps to identify new flow phenomena. The results reported here stem from both schlieren photography in two air jets with different contractions shapes and dye visualization in a water jet. 2 Description of the facilities 2.1 The air j e t facilities Most of the experiments were carried out in an existing axisymmetric air jet facility. A cross section of the plenum chamber and the jet nozzle is shown in Fig. 1 a. The plenum chamber includes perforated plates, two air filters, a honeycomb, and three screens for reducing the turbulence level of the flow prior to the contraction. The area ratio of the contraction is 36:1 with an exit diameter of 50.8 mm and a contour of two tangent arcs. The nozzle exit is extended by a parallel section of one diameter (50.8 ram) length after the end of the contraction. The air flow for the jet is supplied by a blower with a Toshiba VF Pack P1 speed controller which provides for a stable air source. The jet can be operated at exit speeds up to Uo=25.0m/s, which corresponds to a Reynolds number, based on the nozzle diameter, of Re o = 78,000. At 16.0 m/s the mean velocity is maintained to within 1% of its nominal value, with a free stream turbulence level of 0.15%. The jet emerges from the nozzle with a "top hat" velocity profile surrounded by a very thin shear layer. Both jet and measuring apparatus are enclosed in a large cage of I/6 mm mesh screen to minimize the effect of room drafts. External excitation of the jet was accomplished by two different methods. Axisymmetric disturbances (mode 0) were produced with a loudspeaker used as a compression driver located in the bottom of the plenum chamber. Asymmetric disturbances were produced using a circumferential array of compression drivers located at the nozzle exit, equally spaced in polar angle. The drivers in the azimuthal array were adjusted to equal amplitudes at zero velocity using a microphone located on the jet centerline near the nozzle exit plane. The type of asymmetric disturbance was controlled by varying the phase difference between speakers. A 45 ~ phase Experiments in Fluids 12 (1992) difference between adjacent speakers results in a helical, or mode 1, disturbance, while a 90 ~ phase lag between adjacent speakers results in a double helical, or mode 2, disturbance. The sign of the mode number refers to the direction in which the helices are coiling, positive mode numbers being counter-clockwise and negative mode numbers being clockwise when looking towards the nozzle. For both methods of forcing, the excitation signals were generated on the laboratory computer and passed from digital to analog converters to a network of amplifiers, and then to the speakers. A sketch of the nozzle of a second air jet facility is shown in Fig. 1 b. The diameter of this nozzle was reduced to 25.4 mm to enable us to investigate different regimes of the flow in each facility. In contrast to conventional contractions which have both convex and concave sections, the contraction in the second air jet facility has only convex and concave sections, the contraction in the second air jet facility has only convex curvature. An adjustable bypass vent was provided in the plenum chamber downstream of the contraction entrance to eliminate separation upstream of the contraction. One of the purposes of this design is to eliminate the generation of streamwise vortices along the contraction walls through the G6rtler instability. The contraction, however, still allows for control of the boundary layer thickness at the nozzle exit. The plenum chamber of this air jet also contained screens for turbulence management and a compression driver for the generation of axisymmetric disturbances. 2.2 The water j e t .facility The water jet facility was built as a companion experiment to the first air jet discussed above and therefore designed to operate in the same parameter ranges as the first air jet, having also the same exit diameter. Except for the nozzle extension and the forcing mechanisms, both of which were redesigned for the current work, the water jet facility is described in great detail elsewhere (Clough 1989). The details of the redesigned nozzle extension are shown in Fig. 1 c. The extension provides a settling chamber with four entry ports for the dye. The settling chamber is large compared to the circumferential exit slit, allowing the dye to distribute evenly around the nozzle circumference. The inside edge of the nozzle extension has a slightly larger diameter than the developing shear layer so that it does not interfere with the shear layer. A new forcing mechanism was designed and built for the current work in the water jet. The device, shown in Fig. 1 d, was used for combined fundamental and subharmonic forcing. A single motor, along with the proper choice of gears (having a 2 : 1 ratio) was used to drive two plungers in the rear of the jet plenum chamber, one for the fundamental frequency and one for the subharmonic frequency. Taking both forcing frequencies from a single motor ensured that the relative phase between the fundamental and the subharmonic disturbances did not drift during the experiment. The C. O. Paschereit et al.: Flow visualization of interactions among large coherent structures in an axisymmetric jet 191 'action 1 Nozzle ~ Screen -- --~-:[~7Scrc I Air supply _ _ & i Plenum speaker j., Plenum speaker L/ ~er Motor Dye injection stot [] Settling injector [] Nozzle e: [ ] Water ta [ ] Nozzle Gear 2 Gear 1 = 2 Gear 2 a d Fig. 1 a-d. A schematic sketch of the apparatus; a the conventional air jet facility; b the convergent nozzle facility; c detailed sketch of the dye injection; d the forcing mechanism in water amplitude ratio of the two waves could be varied independently of the forcing frequency by adjusting the stroke length of the plungers. In addition, the relative phase between the fundamental and the subharmonic perturbations could be adjusted by changing the relative position of the two plungers. 3 Flow visualization techniques 3.1 Schlieren system Flow visualization using schlieren photography is feasible whenever gradients in the index of refraction, and therefore gradients in density, exist. When a shear flow consists of two 192 Experiments in Fluids 12 (1992) fluids of different density, such as a helium jet in air or a hot jet in a cold environment, the interface between the two fluids is clearly visible with an optical technique such as schlieren or shadowgraph. A schlieren picture integrates along the light rays and produces a 2-D projection of the interface between the two fluids. Heating a thin sheet of fluid for the purpose of using schlieren is analogous to marking it with dye in a bleaching medium. One observes streaklines which fade and eventually disappear in the direction of the flow as the heated fluid becomes mixed with unheated fluid. When the original sheet of the heated fluid is thin and uniform, circumferential convolutions of the sheet appear as streamwise streaks in a schlieren photograph. Visualization of the flow patterns in air was accomplished by a double-pass schlieren system. Two different configurations were required to visualize both r-q~ cross-sectional views (Fig. 2b) and r-x streamwise views (Fig. 2a) of the shear layer. Density differences were induced in the flow by a thin (0.15 m m diameter), electrically heated, stainless steel wire which surrounded the jet. The wire could be moved to different downstream locations, and the diameter of the circle which it described could be adjusted so that the warm air was generated in the ambient region outside of the jet and then entrained by the shear layer. Since the wire was outside of the jet, the density variations were produced with minimal disturbance of the flow. Streamwise views of the jet were obtained using the system shown in Fig. 2 a. Light from the source (a) was focused by a collimator lens (b) on a pinhole (c) of 1 mm diameter. This diameter provided a reasonable compromise between brightness of the image and the sensitivity of the schlieren system. An achromatic lens was chosen for the collimator to allow for the use of a polychromatic light source without chromatic aberration. The pinhole was located at the focal point of a 108 m m diameter spherical mirror (d) with a 1.2 m focal length which produced parallel light. The parallel light was then directed through the test section by plane mirror (e) and reflected back along the same path by plane mirror (f). The incident and reflected beams were then separated with a beam splitter (9)- The image of the focal point of the spherical mirror, and thus the pinhole, was then formed in the plane of the adjustable knife edge (h), which was used to produce the schlieren effect. A length scale was included in the streamwise pictures by placing string on plane mirror ( f ) at one diameter intervals downstream from the nozzle. The string appears in the pictures as horizontal dark lines. In order to view a cross section of the jet, the system of mirrors was slightly modified (Fig. 2b). The parallel light was directed down the axis of the jet using plane mirrors (e) and (i). The light was reflected back along the same path by a plane mirror (j) which had a 58.9 m m diameter hole milled in its center, so that it could sit flush with the nozzle exit. Two types of light source were used. For single snapshots, continuous light was supplied by a 50 W halogen light bulb. The snapshots were taken with a 35 mm camera at a fast shutter speed (1/2,000 s). Phase-averaged photographs were obtained by illuminating the flow with an externally triggered stroboscope in place of the halogen light. The total exposure time for the phase averaged pictures varied from 0.5 to 4 s. In the systems described above, the axis of the spherical mirror was tilted by an angle ~k (Fig. 2 a) to the light source and to the image source. Thus, the line connecting the light source with the image source does not coincide with the axis of the spherical mirror. Such a system is referred to as "off-axis" and results in coma and astigmatism aberrations. The effect of the aberrations was reduced by keeping the angle ~ as small as possible. In both configurations, however, the off-axis optical alignment produced a slightly distorted image. 3.2 D y e injection system For the experiments carried out in the water jet facility, blue-green food coloring was used to mark the shear layer. /.Plane mirror(i) / Planemirror(f) / / ~_._.~Ze.t ~ ./ Planemirror(e) Lightsource(a) Electrical[y Co[[imater heatedwire ~ \Pinhole (c) Mirrorwith/J \ Sphericalmirror(d) .~Beom splitter.(g) bhOte(J) ~ Camera~-~ Knifeedge(h) \ Sphericalmirror(d)Plane / mirror(e) (c) a Fig. 2a and b. The schlieren apparatus; a visualization in the r-x plane; b visualization in the r-q~ plane (b) C. O. Paschereit et al.: Flow visualization of interactions among large coherent structures in an axisymmetric jet t 93 Fig. 3a-d. A side view of a jet forced by a single mode; a mode m=0 forcing a snapshot; b mode m= 1 forcing - a snapshot; c mode m=0 forcing an ensemble averaged picture; d mode m = 1 forcing - an ensemble averaged picture The dye reservoir was located above the test section of the jet. It was connected to the nozzle extension with four tubes which entered the settling chamber of the nozzle extension at locations spaced 90 ~ apart around the circumference of the extension. The dye was then injected through a circumferential slit into the nozzle boundary layer by static pressure from the elevated dye reservoir. 4 Results 4.1 Single mode Jbreing By forcing a jet column in an axisymmetric mode, the vortex sheet coinciding with the boundary of the jet is rolled into a large "ring-vortex" which is also axisymmetric in the mean. The coherent structures seen in Fig. 3 a were obtained by forcing the jet with mode 0 and taking a snapshot of the schlieren image. The photograph represents an instantaneous image of the flow. This picture shows the projection of the ring vortices and of the interconnecting sheet of vorticity. The distance between adjacent vortices can be deduced from the horizontal lines on the photograph which mark intervals of one nozzle diameter. The longitudinal streaks observed in Fig. 3 a correspond to the instantaneous convolutions of the heated sheet of fluid. The snapshot of the jet forced with mode 1, shown in Fig. 3 b, is not as sharp as the corresponding snapshot taken of the jet forced with mode 0. The reduction in contrast, and therefore in clarity, is attributed to two factors. First, the incident light in the case of the axisymmetric forcing passes through regions of similar density gradients twice, once as it penetrates the ring vortex in the front of the jet, and once as it leaves the ring vortex in the rear of the jet. For the helically forced jet, however, the incident light only intersects the core of a helical vortex filament once as it passes through the jet. Second, the density gradients generated by the heated wire degrade in the direction of streaming. Since the image of the helical mode starts out at approximately half the strength of the image of the axisymmetric mode, the helical vortex core is not visible as far downstream as the axisymmetric structures. Using stroboscopic illumination, ensemble-averaged photographs were taken of the predominant structures in the forced jet. Figs. 3 c and d represent phase-averaged images of the jet forced with axisymmetric and helical modes, respeclively. The striations visible in Fig. 3 c indicate that streamwise vortices reside in preferred azimuthal locations under axisymmetric mode of forcing. The streamwise structures may have been triggered by slight imperfections in the nozzle surface, initiating a secondary, azimuthal instability of the vortex rings (Widnall et al. 1974). Another possibility is that 194 Experiments in Fluids 12 (1992) 4.2 Combined axisymmetric forcing Fig. 4a-c. A side view of an axisymmetrically forced air jet; a forced at the fundamental frequency; b forced at the subharmonic frequency; c combined forcing at the two frequencies the streamwise structures are remnants of G6rtler instabilities in the concave portion of the contraction. When the jet is forced with a helical mode, the vortex ring is replaced by a helical vortex filament (Fig. 3 d). The secondary streamwise vortices which are expected to be superposed on the primary helical structure are not as clearly visible in either the snapshot or the ensemble-averaged picture. These secondary vortices might be inclined in different directions across the jet, they might also rotate or oscillate in the azimuthal direction and are thus obliterated in the phase-locked, ensemble-averaged photograph. One may examine the visible effects on the structure of the jet excited simultaneously with two axisymmetric modes at different frequencies, a fundamental and its subharmonic. In Fig. 4 a, the jet is forced with a single frequency corresponding to St = f D/U = 2.3. Three ring vortices are observed at x/D < 1 which are separated by a distance equivalent to 0.2 diameters of the nozzle. Breakdown to turbulence under these conditions (Re=13,000) occurs approximately one diameter downstream of the nozzle. Forcing the jet at half the frequency (St=l.15; Fig. 4b) while maintaining all other parameters unchanged elongates both the distance between adjacent ring vortices and the distance from the nozzle at which breakdown occurs by a factor of 2, as seen in Fig. 4a and b. Combined forcing under these circumstances (Stfund = 2.30, Stsu b = 1.15 ; Fig. 4 c) generates eddies which are similar to the eddies generated by the subharmonic frequency alone (Fig. 4 b). These similarities are not sensitive to the initially imposed amplitude ratio, R = A J A s = 1.0. Quantitative measurements (Paschereit and Wygnanski 1990) have also shown that the relative forcing amplitude has only little effect on the structure of the jet over the range 0.1 _<R _<1.6. The number of ring vortices observed remains unaltered and the predominant distance between adjacent vortices remains 0.4 diameters. An interaction between adjacent ring vortices can be seen approximately 0.6 diameters from the nozzle exit. In addition, the ring vortex at x/D "~ 1.6 is clearly turbulent. Both observations are attributed to forcing the jet with a combination of fundamental and subharmonic axisymmetric modes. Since the three pictures shown in this figure were not synchronized with the phase of the forcing, one cannot compare the absolute distances from the nozzle at which roll-up occurs. The large coherent structures resulting from axisymmetric forcing of a jet were also examined in water by dye visualization. Figures 5 a and b are side views of the water jet with simultaneous forcing of fundamental and subharmonic modes (Re = 5,000; Stfund = 1.0, Stsu b = 0.5). One may observe the streakline pattern just before (Fig. 5a) and just after (Fig. 5 b) a vortex interaction. The first three vortices in both pictures are laminar. Note in Fig. 5 a that the second vortex, which is being drawn through the center of the preceding vortex, has developed large amplitude azimuthal variations. The azimuthal waviness is also visible on the preceding vortex buth with smaller amplitude (see also Fig. 6c). As the second vortex is pulled through the center of the third (Fig. 5 b), the strain field causes the amplitude of the azimuthal variations to increase drastically while the streamwise extent of the second vortex more than doubles. The interaction rapidly destabilizes the eddies which become turbulent shortly thereafter. It should be noted that beyond the region of interaction, the dye marking of the eddies no longer has a toroidal shape. In addition, Figures 6a c demonstrate that in spite of the axisymmetric forcing, the preferred structure of the jet further downstream need C.O. Paschereit et al.: Flow visualization of interactions among large coherent structures in an axisymmetric jet 195 Fig. 5a and b. A side view of an axisymmetrically forced water jet at two frequencies; a before vortex interaction; b after vortex interaction not be axisymmetric. The jet may develop a helical mode of either positive or negative sense (Figs. 6 a and b) or the jet may have no distinguishable mode at all (Fig. 6 c). Viewing the air jet axially, as shown in Fig. 7, reveals the existence of streamwise structures in the flow. The dark region in the centers of Figs. 7 a e is due to the hole cut in the mirror to allow it to sit flush with the nozzle exit. A schlieren image of the unforced jet photographed at Re= 13,000 is shown in Fig. 7a. The notable feature in this figure is the existence of streamwise vortices around the circumference of the shear layer, which appear as "horse-shoe" shapes, located between the nozzle and the heated wire. These structures bear a strong resemblance to the azimuthal instability of a vortex ring (Didden 1979; Glezer 1988). One should remember, however, that the image shown in Fig 7 a corresponds to an integrated view of the potential core of the jet rather than a single vortex ring. It was ascertained, by using the purely convergent nozzle described above, that the azimuthal struc- ture in an unforced jet need not to be triggered by the G6rtler instability associated with the concave section of a conventional contraction. The azimuthal structure is, therefore, a manifestation of a secondary instability of the large coherent structures in the jet. Schlieren images of the jet forced at the fundamental frequency (Stfuna=2.30), and with the combination of the fundamental and the subharmonic frequencies (Stfuna-- 2.30, Sts,b= 1.15), are shown in Figs. 7b and c, respectively. The subharmonic case is indistinguishable from the fundamental case shown in Fig. 7 b and is thus not presented. When comparing Figures 7 a - c , it is seen that axisymmetric forcing acts to stabilize the position of the streamwise vortices. Since the fundamental and subharmonic forcing reveals essentially identical secondary azimuthal structures, it can be concluded that, in the range of frequencies tested in this experiment, the streamwise vortices do not depend on the frequency of forcing. With this in mind, it is not surprising to find that 196 E x p e r i m e n t s in F l u i d s 12 (1992) Fig. 6 a - c . T h e e m e r g e n c e of helical m o d e in the jet despite a x i s y m m e t r i c forcing; a m = 1 ; b m = -- 1 ; e n o distinct lower m o d e C.O. Paschereit et al.: Flow visualization of interactions among large coherent structures in an axisymmetric jet 197 Fig. 7 a - f . A top view of the air jet; a no forcing; b axisymmetric forcing at the fundamental frequency; e axisymmetric forcing at two frequencies, a fundamental and a subharmonic; d forcing simultaneously at mode rn1=2 and m2 = - - 1 ; e forcing simultaneously at mode m 1=2 and rn2 = - 2 ; f contours of u'2 while the jet was simultaneously forced with m= _+2 mode forcing the jet with a c o m b i n a t i o n of axisymmetric modes, as in Fig. 7 c, has little or no effect on the azimuthal structure of the jet, although the amplitude of the structures appears to have increased with the increased forcing level of the combined forcing case. One m a y conclude from Figs. 5, 6, and 7 a - c , that the p r i m a r y vortex structure is d o m i n a t e d by the s u b h a r m o n i c frequency while the streamwise vortex structure is stabilized by axisymmetric forcing although it does not scale with the Strouhal n u m b e r based on nozzle diameter. 4.3 Azimuthal distortion of the mean flow Azimuthal distortion of the mean flow can be accomplished by forcing the jet at a single frequency with a pair of different spinning modes, m 1 and m 2. The triad resonance conditions predict that the resulting p e r t u r b a t i o n on the axisymmetric mean flow will have the form cos [(ml-m2) ~b], where q5 is the azimuthal angle. Cohen and Wygnanski (1987) calculat- ed these distortions under inviscid parallel flow conditions and d e m o n s t r a t e d their existence in an axisymmetric jet. Long and Petersen (1990) refined this prediction, showing that the pattern can be rotated at will by changing the phase between the two forced modes. The azimuthal distortion was visualized by taking schlieren pictures of r-~b cross sections of the jet. W h e n the flow was excited with modes m 1--2 and m z = - 1, Figure 7d, the mean flow had the predicted 3 azimuthal lobes. Forcing the jet with m l = - m 2 = 2 , Figure 7 e, p r o d u c e d the expected 4 lobe pattern of the mean flow. Quantitative measurements by Petersen and Long (1990) confirm the visual observations (Figs. 7 d and e), suggesting that the small scale turbulent m o t i o n is primarily contained within the large azimuthal lobes. The m o d u l a t i o n of b r o a d b a n d turbulence by the coherent structures in the jet is both a novel and a technologically significant effect. A sample of the {u '2} fluctuations measured by Petersen and Long for the 4 lobe case is shown in Fig. 7 f. The plot represents contours of equal turbulence intensity measured at x/D=2.0. This 198 Experiments in Fluids 12 (1992) layer. The two waves intersect at two azimuthal locations, 180 ~ apart because of symmetry, during each cycle of forcing. The intersecting non-coplanar vortices produce 3-D vorticity fluctuations which lead to the increased turbulence levels and thus locally increased spreading rates. 5 Conclusions Fig. 8a and b. A side view of the air jet undergoing model interaction; a ~b=0 (minor axis); b q~=~/2 (major axis) effect is accentuated by the flow visualization method because the schlieren image produced by the system shown in Fig. 2 b integrates along the beam of light which, in this case, coincides with the jet axis. The effect of modal interaction on the streamwise evolution of the jet is seen in the streamwise views shown in Fig. 8. In this case the jet was forced with m~ = + 1 and m 2 = - 1 to produce a cos (2 ~b) distortion. Consequently, the characteristic width of the jet depends on the angle from which it is viewed. The photographs shown in Figs. 8 a and b represent views of the jet along minor (q~=qSo) and major (~b=~bo+ n/2) axes of the cos (2q~) distortion, respectively. The large structures viewed in this manner appear as if they were triggered by an axisymmetric excitation. These large eddies, however, are not toroidal and many also appear while the flow is contracting towards the center (Fig. 8 a) and not only during divergence (e.g. Fig. 3a). The jet viewed along the minor axis is narrower at 1 < x/D < 2, and at x/D -~ 2 downstream it is approximately 2 0 - 2 5 % wider along the major axis than on the minor axis of the distorted flow. One may also notice that the shear layer spreads into the core of the jet at a much smaller downstream distance in Fig. 8b as compared to Fig. 8 a. This effect results from the interaction of the two helical disturbances of opposite sign in the shear A thin sheet of locally heated fluid was used in conjunction with schlieren photography to visualize both large coherent structures and small scale turbulence in a jet. In unsteady flows both schlieren and the dye images must be interpreted carefully, since both methods show streaklines rather than the interface between the jet and the surrounding fluid. Nonetheless, both schlieren and dye photographs have led to an increased understanding of known phenomena, and have suggested new directions of research. An instability manifested by an array of streamwise vortices was observed in an unforced jet as well as in an axisymmetrically forced jet. Although the streamwise structures are affected by the forcing, they did not appear to scale with the Strouhal number based on the forcing frequency and the conditions at the nozzle (i.e. St=f D/U). While the streamwise striations observed in the various photographs could be triggered by a G6rtler instability associated with the concave curvature of a conventional nozzle design, the latter is probably not the leading mechanism for their appearance. Streamwise striations were also seen in a flow emerging from a strictly convex contraction, in which the G6rtler instability does not exist. This proves that the streamwise vortices observed represent a secondary instability inherent to the perturbed shear layer surrounding the jet column. Exciting the jet simultaneously with two axisymmetric modes did not affect the azimuthal structure of the forced flow over the observed range of Strouhal numbers. The streamwise development of the flow, however, was altered due to interaction between neighboring vortices. Mean flow distortion of the jet column resulting from simultaneous excitation with two different azimuthal modes at the same frequency was observed by this technique. Since schlieren images are sensitive to the first derivatives of the density with respect to space, the azimuthal modulation of the "small scale turbulence" residing inside the large coherent eddies was also observed. Since the bulk of the small scale motions in the shear layer were contained inside the large scales, the mixing process, which depends strongly on small scale activity, may be significantly manipulated through control of the large eddies alone. Acknowledgements The authors would like to acknowledge the assistance of Professor Ari Glezer of the Aerospace and Mechanical Engineering Department at the University of Arizona for the loan of the spherical mirror and the video camera used in the schlieren system. Professor C. O. Paschereit et al.: Flow visualization of interactions among large coherent structures in an axisymmetric jet Glezer also provided assistance in the design of the optical system. The authors would also like to acknowledge the assistance of Mr. Eli Horev, Visiting Research Scientist, for the design and construction of the forcing mechanism used for the water jet visualization. Mr. Horev also assisted in the photography of the dye visualizations. References Brown, G. L.; Roshko, A. 1974: On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775 816 Clough, R. C. 1989: Vortex interactions in an axisymmetric water jet. University of Arizona (Masters Thesis) Cohen, J.; Wygnanski, I. J. 1987: The evolution of instabilities in the axisymmetric jet. Part 2: The flow resulting from the interaction between two waves. J. Fluid Mech. 176, 221-235 Didden, N. 1979: On the formation of vortex rings: rolling-up and production of circulation. J. Appl. Math. Phys. (ZAMP) 30, 101116 199 Gharib, M. 1986: Flow velocity measurements by image processing of optically modulated tracers. AGARD-CP-413, 22 Glezer, A. 1988: The formation of vortex rings. Phys. Fluids 30, 3532-3542 Hama, E R. 1962: Streakline in a perturbed shear flow. Phys. Fluids 5, 644 650 Long, T. A.; Petersen, R. A. 1990: Controlled interactions in a forced axisymmetric jet. Part 1 : The distortion of the mean flow. (submitted to J. Fluid Mech.) Merzkirch, W. 1987: Flow visualization, pp. 126-137. London: Academic Press Paschereit, C. O.; Wygnanski, I. J. 1990: On instabilities in the axisymmetric jet: subharmonic resonance. (submitted to AIAA) Petersen, R. E.; Long, T. A. 1990: Controlled interactions in a forced axisymmetric jet. Part 2: The modulation of broadband turbulence. (submitted to J. Fluid Mech.) Widnall, S. E.; Bliss, D. B.; Tsai, C. Y. 1974: The instability of short waves on a vortex ring. J. Fluid Mech. 66, 35-47 Received July 18, 1991