The present study investigates the vortex dynamics of the rectangular shaped synthetic jet and reports the occurrence of vortex ring bifurcation along with other reported modes such as axial switching and the vortex suction. The novel finding of vortex ring bifurcation of rectangular synthetic jets has been observed without any other mode of excitation except the periodic axial actuation. The experiments on synthetic jets have been conducted at different a ctuation frequencies and both qualitative and quantitative characterization of the flow structures has been carried out using Laser Induced Fluorescence (LIF) and Laser Doppler Velocimetry, respectively. LIF flow visualization provides insights into the size of the vortex and the vortex evolution with respect to time, enabling us to propose the flow physics behind the axial switching and the vortex bifurcation p rocesses for rectangular synthetic jets. The proposed flow physics is then quantitatively evidenced by the time -averaged velocity measurements. Vortex splitting or bifurcation is found to occur in the minor axis plane of orifice and the divergence angle depends on the actuation frequency and average velocity of fluid expelled through the orifice in the forward stroke of diaphragm. In the case of occurrence of axial switching, a maximum of three axial switching events are observed before vortex breakup. Fina lly, by systematically carrying out experiments across a wide range of operational parameters, a narrow region corresponding to the vortex bifurcation has been identified on a Reynolds Number -Strouhal Number map, along with other modes such as axial switch ing regime and the vortex suction regime. Based on our measurements, a mechanism of vortex bifurcation vis -à-vis axial switching has also been suggested. Keywords: Vortex bifurcation; axial switching; synthetic jet; Laser Induced Fluorescence ; Laser Doppl er Velocimetry European Journal of Mechanics B Fluids 2 1. Introduction The formation, propagation and interaction of vortex rings have been an active area of research due to its wide applications in nature and day -to-day life. Synthetic jets producing a train of large -scale coherent structures (vortex ring s) with zero net mass flow rate have several practical applications , where the net momentum gain is used for controlling the flow or to achieve thrust. The power supplied to the actuator is transferred to the fluid through oscillatory motion of a diaphragm resulting in vortex formation at the orifice exit. The vortex ring moves away from the exit plane under the influence of self-induced velocity and thus produces a jet called as synthetic jet. The net mass transfer through the opening in one cy cle is zero but there is a net transport of momentum to the ambient . Therefore, the synthetic jet , also known as Zero Net Mass Flux (ZNMF) system finds its application in mixing (Freund and Moin 2000; Wang and Menon, 2012 ), boundary layer control (Amitay, et al. 2001; Rathnasingham and Breuer 2003) , propulsion (Kruger and Gharib 2003, Krieg and Mohseni 2010 , Gu et al. 2017) , jet vecto ring (Wu and Ahmed 2014; Kobayashi, et al. 2018) , cooling (Anna. and Amitay 2006; Huang 2014 ; Shaikh K.A. 2016 ; Glowienko et al. 2018) and acoustic s (Mangate and Chaudhari 2015; Kanase et al. 2018) . The vortex ring of the synthetic jet is affected by the flow field developed nearer to the jet exit . The near-field of the jet exit is characterized largely by a non -dimensional parameter formation number, which is the ratio of slug length and the hydraulic diameter of the orifice, as given by (Gharib et al. 1998) . For a particular geometry of orifice , a threshold Formation number exists, beyond which any extra circulation generated by the ejecting shear layer ceases to flow inside the core region of the vortex ring. In such a case , the extra ejecting fluid gets pinch ed-off from the leading vortex ring a nd forms a trailing jet. For the similar phenomenon, another criterion was proposed by (Utturkar et al. 2003) using the order of magnitude analysis, where it was shown that for the successful formation of a vortex ring, the ratio of Reynolds number (Re) and the square of Stokes number (S), i.e. 𝑅𝑒 𝑆2⁄ must be greater than a particular constant value that depends upon the orifice geometry. Among the two widely used orifice shapes having circular and non -circular geometries , the vortex ring ejected out of the non -circular orifice shows a differential induced velocity and thus possesses greater instability as it travel s downstream due to the existence of three -dimensional vortex dynamics such as the azimuthal distortions caused by the inducti on of the asymmetric coherent structure s on its own , thus, increasing the fluid entrainment. Moreover, even among non-circular orifice s, rectangular shape is of special significance since it offer s passively improved mixing at the both the ends of the spectrum i.e. intensified large -scale entrainment due to axial -switching as well as enhanced small -scale mixing near corners and further downstream due to swift breakdown of vortex ring coherence. 3 The rectangular vortex ring shows broadly two types of vortex deformations: one that leads to axial switchin g of vortex ring and the other that causes bifurcation or splitting of vortex ring. The axial switching is common in rectangular vortex rings , as report ed by many researcher s in the past (Heertch 1976 ; Krothapalli et al. 1981 ; Zaman 1996 ; Watson et al. 2003 ; Kumar, et al. 2019) . It has been reported as the primary mechanism underlying the enhanced entrainment properties of non -circular jets relative to those of comparable circular jets. Bifurcatin g jets, due to their augmented spreading angle as well as mixing properties, are of particular interest for many practical applications (Danaila and Boersma 2000) . However , it occurs only within a limited range of Strouhal number and Reynolds number (Parek h et al. 1988 ; Reynolds, et al. 2003 ). Gohil et al. (2010) reported that a round continuous jet could be bifurcated by simultaneously imposing helical and axial modes of forcing. On the other hand, other researchers (Oshima et al. 1988 ; IiO et al. 2006 ) obtain ed the bifurcation in continuous jet or for a single vortex by combined effect of orifice shape and velocity of ejection. In this mode, the prime source of vortex splitting is variation in the self -induced velocity of vortex ring due to variation in curvature of nozzle or orifice. Oshima, Izutsu and Oshima (1988) observed a partial bifurcation for a single vortex ring since the vortex ring collapsed just after the splitting and no isolated path for split vortex rings was observed. However, in the ca se of single vortex rings, no perturbation exists in the environment before the formation of vortex rings and hence there is no influence of environment on the behavior of vortex rings. Further, in the case of a synthetic jet, the actuation frequency is an additional control para meter. Since in a synthetic jet, both the forward and the suction follow each other in a cyclic manner, the built up flow field of vortex ring continuously changes and influences the behavior of newly formed vortex ring. Therefore, the factors controlling the bifurcation process may behave differently in case of a synthetic jet. In an ea rlier work, we had investigated the flow physics and vortex behavior of rectangular orifice synthetic jets through LIF and Hot wire measurements and reported the occurrence of vortex bifurcation (Kumar et al. 2019), although no clear understanding was gaie nd as to what causes such bifurcation of rectangular orifice synthetic jets. Since the detailed mechanism of vortex bifurcation was not understood or discussed , a new series of experiments investigating the mechanism of vortex bifurcation was left as a fut ure work. Hence, in the current study, we have explored the detailed mechanism of vortex bifurcation vis-à-vis axial switching by a systematic variation of Reynolds number ( Re) and Strouhal number (St) and by measuring the time -averaged velocity through La ser Doppler Velocimetry measurements, as well as detailed flow -visualization in two orthogonal planes. Further, by systematically plotting the results of mutliple sets of experiments on an Re-St map, we have located a narrow region where the process of vor tex bifurcation occurs. European Journal of Mechanics B Fluids 4 The current paper is organized in the following manner : Section 2 describes the experimental setup and methodology for both qualitative and quantitative measurements. In Section 3, experimental observations on dynamics of vortex bifurcation have been extensively dealt with in five subsectio ns covering flow visualization, measurements on vortex size and evolution and the time -averaged velocity measurements. These measurements lead further to the description of th e flow physics underlying axial switching and vortex bifurcation and finally regions pertaining to vortex bifurcation have been identified on a Re-St flow map. Subsequently, in Section 4, conclusions of the current study are enlisted. 2. Experimental Setup and Methodology Figure 1 shows a schematic of the experimental setup used in the current study, which includes a transparent water tank, a synthetic jet cavity with a diaphragm, an electromagnetic actuator, and a frequency controller. Figure 1a shows a typical synthetic jet actuation system : It comprises of a mechanism to alter the volume of the chamber either through a flexible diaphragm or a piston . In our experiments, the actuation system consists of a cylindrical acrylic cavity, which has a convolute neoprene diaphragm at one end, and orifice at the other . Figure 1b shows the dimensions of the cavity and the diaphragm. It should be noted that the dimensions of the cavity, diaphragm, the water tank and the positioning of the orifice has been kept ident ical to the previously reported study (Kumar et al. 2019). The actuator lies at a distance of 250 mm from the bottom of the tank as well as from the free surface, and the orifice of hydraulic diamter 12 mm (hydraulic diameter) yields a low blockage ratio of 2.4 %. The dimensions of the rectangular orifice are 7 x 14 mm2 with an orifice thickness of 3 mm. The orifice cross -section, the axis notation and the separation distances between the two counter -rotating vortices coming out of the orifi ce in XZ plane ( HW) and in XY -plane ( HB) are shown in figure 1 c. Laser -Induced Fluorescence (LIF) has been used for flow visualization , along with an articulated arm and the sheet optics to direct the laser sheet within the water tank, as presented in figure 1 d. A 4W continuous wave Ar -Ion Laser is used as the light source and t he flow images are captured at 30 fps at a resolution of 600×1280 pixels . The LIF images are acquired at different instants of time in major and minor axis planes for a qualitati ve study. A concentrated solution of Fluorescein sodium is used as the dye for visulaization purposes . The actuation process is begun after the dye is injected slowly and carefully and the initial few cycles are captured. The vortex core location obtained from LIF images has an uncertainty of 6.2%. 5 (b) (c) (d) European Journal of Mechanics B Fluids 6 Figure 1 (a) Schematic of the synthetic jet actuator, (b) Cross -sectional view of the orifice, orifice cavity and diaphragm, (c) the nomenclature of orifice orientation, axis notations and separation distance between the core of counter rotating vortices (d) Schematic of the expe rimental set -up for LIF imaging, and (e) Schematic of the experimental set -up for five -beam Laser Doppler Velocimetry (LDV) measurements. The velocity measurements in the streamwise and cross -streamwise direction are carried out using a five -beam Laser Doppler Velocimetry ( LDV ) probe as presented in figure 1 e. Two colors of beams green (514.5 nm) and blue (488 nm) are used for measuring the two components of velocity. The waist diameter and length of the measuring volume are equal to 145 µm and 4.2 mm for 514.5 nm laser beam and 137 µm and 2 mm for wavelength 488 nm laser beam. The fringe spaci ng and number of fringes are 7.47 µm and 19 , respectively for a wavelength 514.5 nm . Similarly, for a wavelength of 488 nm , these are equal to 3.54 µm and 39, respectively. Since there are three different optical medi a such as air, Perspex, and water in th e current experiments, the necessary correction in traverse movement is given. Hollow glass spheres coated with silve r in the diameter range of 8 µm - 12µm are used as external flow seeding particles. At each point, the velocity data is sampled over a mini mum 60 operational cycles, and an arithmetic mean is obtained. A maximum fluctuation of ± 3.7 % around the mean is observed in the measured velocity components considering uneven sampling. 7 In general, the physics of the synthetic jet is characterized by the physical parameters such as hydraulic diameter of the orifice ( 𝐷ℎ), the synthetic jet exit velocity during the forward stroke ( 𝑈𝑜) , actuation frequency of synthetic jet ( f), suction stroke time ( 𝑇𝑠), ejection stroke time ( 𝑇𝑒), slug length (L), the orifice cross - sectional area ( A0) and volume of fluid expelled from orifice (VD) which is identically expressed as volume displaced by forward stroke of diaphragm ( VD). The total cycle time ( T) is given as the sum of suction and ejection stroke time as 𝑇= 𝑇𝑠+ 𝑇𝑒≈2𝑇𝑒, and thus the actuation frequency is given by 𝑓= 12𝑇𝑒⁄ . These parameters are commonly expressed using the three dimensionless groups: Reynolds number, 𝑅𝑒=𝑈𝑜𝐷ℎ𝑣⁄ ; Strouhal number , 𝑆𝑡=𝑓𝐷ℎ𝑈𝑜⁄ and the formation number, 𝐹𝑛=𝐿𝐷ℎ⁄ which is a normalized stroke length . The slug length L is given as 𝐿=𝑉𝐷 𝐴𝑜⁄ and the synthetic jet exit velocity is determined by 𝑈𝑜=𝑉𝐷 𝐴𝑜⁄ 𝑇𝑒, or 𝑈𝑜= 2𝑓L. Further, for the determination of slug length, VD is estimated using cavity inner diameter ( Dca), disk diameter ( Dcy) and amplitude of oscillation (∆) as given by (Mohseni 2006) : 𝑉D= 𝜋∆(𝐷𝑐𝑎2+ 𝐷𝑐𝑦2)/8, where ∆ is measured by an accelerometer in our experiments. The uncertainty in fluid volume ejection , formation number ( L/D h) and Reynolds number equals 3.6 %, 3.6% and 3.7%, respectively. 3. Results and Discussion Experiments are conducted on a rectangular orifice of aspect ratio two at a range of actuation frequencies in the range of 1 – 3 Hz, and the resulting flow physics is recorded using both qualitative (LIF) and quantitative (LDV) measurements as the LIF images are not free from attenuation and stagn ant dye illumination , and thus the captured images being considered belong to the initial few cycles. The resulting measurements provide an insight into the flow physics involved in axial switching and vortex bifurcation. An orifice of aspect ratio two is chosen for these experiments based on the information acquired from prior reports in the literature. Table 1 below presents the details of all the experiments conducted at which bifurcation or axial switching phenomenon has been observed. Table 1 . Details of the experimental conditions European Journal of Mechanics B Fluids 8 3.1. Flow Visualizatio n Side view ( XZ-plane) Top view ( XY-plane) (a) Case I (b) Case II (c) Case III Figure 2. Flow visualization images of synthetic jet in XZ - plane (side view) and in XY- plane (top view) for bifurcation cases: (a) Case 1, (b) Case II and (c) Case III. It may be noted that the images are not exactly at the same instant of time with reference to the actuation cycle. Figure 2 shows the LIF images of vortex ring bifurcation at actuation frequency of 1, 2 and 3 Hz. The LIF images of vortex ring are captured from both the XZ - plane (or minor axis plane ) and the XY-plane (i.e. the major axis plane ). It may Crosslinking or reconnection of vortex tube Direction of bifurcated vortex ring Oscillating envelope 9 be pointed out that although the reported images are exactly not at the same instant of time for both the views, care has been taken to ensure that the number of cycles elapsed since th e initiation of the synthetic jet is kept same for different cases of actuation frequency. Side view ( XZ-plane) Top view ( XY-plane) (a) Case IV (b) Case V European Journal of Mechanics B Fluids 10 (c) Case VI Figure 3. LIF visualization of the synthetic jet in the side view ( XZ – plane ) and in the top view ( XY- plane ) for no -bifurcation cases: (a) Case IV, (b) Case V and (c) Case VI. It may be noted that the images are not exactly at the same instant of time with the reference to the actuation c ycle. Figure 2 a shows the splitting of vortex ring for Case I, where the vortex ring bifurcates in the XZ-plane and moves approxiamtely at an angle of 620 with each other in the downstream direction. Figure 2b shows the vortex splitting with splitting angle equal to 460 for Case II with some portion of vortex ring left at the center during the splitting, forming a Ψ - shape of flow structure. In top view, the converging angles of counter rotating vortices from orifice exit to the point of merging are app roximately 560 and 400 for Case I and Case II , respectively. Further, as illustrated in figure 2c for Case III , the split vortex rings show a smaller splitting angle equal to 340 with no clear or distinct splitting being observed in the side view images. H ere, the process of bifurcation initiate s but before the completion of bifurcation or splitting, the vortex ring breaks into smaller vortices and moves all around randomly. Oshima et al. (1988) reported that at the point of vortex reconnection (see figure 2a), counter rotating vortices comes closer by cancelling the outer part of adjacent vortex filament. At the same time, a breakdown is initiated at the crosslinking region, generating abrupt turbulence in the vortex filament. These turbulence structures pr opagate around the remaining vortex tube from and tear apart the vortex ring into further tiny vorti cal structures , and thus the bifurcation phenomenon is not observed . In all the three cases of bifurcation - Case I, II and III, the vortex rings either split or show a tendency to split just after the first axial switching in the minor axis plane of the orifice. Such splitting of vortex rings has been reported by Kiya, et al. (1992) with the help of numerical simulation s and experimental data. They showed th e bifurcation of single pseudo -elliptical vortex ring in both planes (minor and major axis plane) for aspect ratio s in the range of 2 to 20. They observed four different patterns as, pseudo -periodic a xial switching for 2 < AR < 4, axial switching followed by vortex splitting in the minor axis plane for 5 < AR < 8, vortex ring splitting without axial switching in the major axis plane for 8.9 < AR < 11 and, vortex ring splitting into three distorted vortex ring s without experiencing any axial switching for large aspect ratios in the range of 11< AR < 20. Vortex splitting in the major axis plane has also been reported b y Auerbach and Grimm (1994) , based on the divergence or convergence of the counter rotating vortices in the captured images. Although the prior studies have indicate d that ifurcation can occur in both the minor or major plane s, in the present study, bifurcation was found to occur only in the minor axis plane and no sign of bifurcation is observed in the major axis plane of the orifice for all the considered cases. However , the trend of the vortex ring splitting obtained in our experiments for a rectangular synthetic jet ejected out of an orifice of aspect ratio two is in good 11 agreement with the results of Kiya et al. (1992) for a single pseudo -elliptical vortex ring at an identical orifice aspect ratio . Since, subsequent to the first axial switching , the major axis of vortex ring becomes minor and vice -versa, the initially shorter side of the vortex rings switches in the minor axis plane ( XZ-plane) of the orifice. Therefore, the vortex reconnection and splitting events occur in the XZ-plane , perpendicular to the longer side of orifice. Another noteworthy observation is the location of the vortex crosslinking , highlighted by the dots in the top view of LIF images ( see figure 2a, 2b ). This location varies between X/B = 1.5 for Case I to X/B = 2.5 for Case II. It indicates that the point of the vortex splitting is not fixed and may vary depending on other experimental parameters. Further , the top view in the LIF images (see figure 2 ) also present an interesting aspect of the synthetic jet flow physics - the occurrence of partial vortex leap forging, whereby the newly formed counter rotating vortices penetrate inside the leading vor tex ring and moves ahead due to a velocity difference. In this process, the vortex rings are squeezed in the beginning and are finally consume d inside the envelope of previous rings. Careful examination of the video corresponding to the LIF images in the XY-plane suggests that the piercing action of the converging vortices pushes the envelope of fluid away from the synthetic jet centerline in the region between X/B = 0.5 to 1.5 during advection . As the counter rotating vortices move ahead, the envelope move s down to fill the gap. This cycle repeat s and the envelope oscillates in Y-direction for each passage of counter rotating vortices as shown clearly in figure 2a and 2b. Figure 3 presents the LIF images of the synthetic jet at identical actuation frequencies of 1, 2 and 3 Hz, but with an increased diaphragm displacement . As figure 3 shows, the synthetic jet experiences an axial switching instead of vortex ring bifurcation in these cases . The vortex rings are isolated and the tra iling jet is negligible for Case IV, but a small amount of trailing jet forms for Case V, which interacts with the following vortex rings. The increased actuation frequency from 1 to 2 Hz decreases the spacing between the vortex rings and increases the ir interaction , which can be seen from the early breakdown of the vortex ring. In Case VI, the images in both the planes show a significant amount of trailing jet . 3.2. Size of the vortex To explain the vortex growth and behavior of the vortex ring , the vortex size variation has been studied extensively . The trajectory of the counter rotating vortices is studied from the series of LIF images in XZ and XY- plane and is presented in figure 4 . The figure shows that t he formation of trailing jet s is also observed in some cases but the global flow pattern largely depends on the vortex dynamics of the leading vortex ring s. Hence, the separation distance between the cores of counter rotating vortices of leading vortex ring provides useful information about the formati on and evolution of the synthetic jet. To properly characterize the size of the vortex, the separation distances in the spanwise (i.e. European Journal of Mechanics B Fluids 12 the XY plane) and the vertical directions (i.e. the XZ plane) have been marked as HB and HW, respectively as shown in figure 4. Next , the measured values of separation distances are presented in both time and space domain for all the six cases . In the bifurcation cases, I, II and III shown in figure 4a , the separation distance between the oppositely rotating vortices in both the orthogonal planes follow the same trajectory in time domain before the first axial switchover. After the first axial switchover, the initially shorter side becomes longer and vice versa between t/T = 0.6 to 0.9 in the time domain corresponding to X/W = 1 in downstream direction. The trajectory of counter rotating vortices in the XZ-plane for bifurcation cases have three distinct regions represented by three straight lines as shown in figure 4a . The regions are: (i) duration in which shear layer rol ls into a vortex ring (line -A), (ii) duration after first axial switching when the longer side of vortex ring interconnects and then splits (line -B) and (iii) the split vortex rings moving at an angle (line -C). Smaller slope of line -B indicates that during the vortex reconnection and the splitting period, the size of vortex ring in bifurcation plane does not change. Once the splitting is completed, the split vortex rings moves at an angle to each other, as evident from a great er separation distance between the upper and the lower vortex rings. The vortex size variation for the bifurcation cases I, II and III follow the same trajectory in downstream direction in both the o rthogonal planes , as illustrated in figure 4b . The opposite spinning vortices in the XY-plane drift towards the center (see Fig. 2) and vanish at X/W = 3, whereas the vortices are present up to X/W = 5 in the XZ-plane. In general, the rectangular shape d vortex ring expands in the direction of minor axis and contract s in the direction of major axis due to differences in its self- induced velocities in the two directions . Shortly thereafter, minor and major axes switch, and once this first switchover is com pleted, a second switchover is between the axes is also observed after a while. However, this process of axial switching cannot continue indefinitely. The vortex size expansion, entrainment of the surrounding fluid, growth of core instability and subsequen t reduction in velocity restricts the number of total axial switching before the vortex breakdown. A maximum of three axial switching events have been reported for elliptical jets by Hussain and Husain (1989) . They also reported that the third axial switch ing is usually faint and may not be easily detectable. Similar findings were also reported by Ho and Gutmark (1987) , who observed maximum three axial switching in an elliptical nozzle of aspect ratio two for a free air -jet. A maximum of three axial switch ing is observed from the trend ( HB and HW switching their value relative to each other) of counter rotating vortices in figure 4c and 4d for Case IV, V and VI. The trajectory of counter rotating vortices shown in figure 4d , shows that the size of both the minor and major axis of vortex ring is equal at X/W ~ 1. However, the location of the first axial switch -over vary significantly for Case VI in comparison to Case IV and V which is likely to be linked with the strong trailing jet observed for the former case, as evident from figure 4c. 13 (a) Bifurcation cases (b) Bifurcation cases (c) No-bifurcation cases (d) No-bifurcation cases Figure 4. (a) Time evolution of separation distance between the cores of counter rotating vortices for bifurcation cases (b) location of cores in XZ and XY planes for bifurcation cases , (c) Time evolution of separation distance between the cores of counter rotating vortices for non-bifurcation cases, and (d) location of cores in C B A European Journal of Mechanics B Fluids 14 XZ and XY planes for non-bifurcation cases. (*The values of HB and HW are displaced along the Y axis by step size equal to two for clarity). 3.3. Vortex evolution The instantaneous images of vortex evolution and bifurcation process are shown in minor and major axis planes in figure 5 and figure 6, respectively. The cross - sectional view of vortex tube appeared in LIF images continuously changes its shape during its evolution near the orifice exit due to variation in self -induced velocity initiated by the orifice curvature. Figure 5 and Figure 6 presents the qualitative information on vortex evolution in both the XY and XZ planes at different times . At t/T = 0.4 in figure 5 , the fluid ejected from the orifice center is ahead than the fluid curling to form the vortex tube near the orifice wall. However, at the same instant of time in figure 6, the fluid ejected at the orifice center lags behind the fluid at the orifice wall. Another interesting observation is that the rolling of shear layer to form the vortex tube in XY-plane is we aker than that of the curling of shear layer in XZ-plane at the same time. The differences in curling radius of the vortex tube formation in XY and XZ-plane forms vortex ring of a varying tube radius and velocity. As a result, the axis of the vortex tube gets stretche d and tilted (indicated by small straight lines drawn just above the upper counter rotating vortices) in the XZ-plane and contracts in the XY-plane. As shown in Figure 4a, the region on line -A that overlaps with Line-B corresponds to this contraction and stretching phenomenon where the vortex rolls to form counter rotating vortices. At the end of the forward stroke, when the vortex ring detaches itself from the orifice and moves downstream and nearly at the same instant, the backward stroke of the diaphragm initiate s the suction stroke. Hence, the fluid moving towards the orifice cavity squeezes the newly formed vortices at its rear end and changes the shape and orientation of vortex tube as shown in figure 5 at t/T ~ 0.6. Due to changes in or ientation and shape, the counter rotating vortices moves away from the synthetic jet centerline in XZ-plane in figure 5 and comes closer in XY-plane at t/T ~ 0.8 and 1.0 in figure 6 . In the XY-plane, HB decreases continuously with time and the left over portion of the former vortex rings creates an envelope over the newly formed vortices and squeeze s it along the synthetic jet centerline. This physical phenomenon corresponds to the region on line -B that overlap s with line-C, where Hw does not changes significantly. The contraction of counter rotating vortices at t/T = 1.2 to 1.6 in figure 6 leads to vortex tube reconnection in XY-plane and bifurcation in XZ-plane as seen in figure 5 (line-C in figure 4a ). The sequence of images reveals that the thickness of envelope increases initially , but remains unchanged with the progression of time. 15 Figure 5. Sequence of LIF images showing vortex evolution and bifurcation process at different instants of time in the XZ-plane for Case I. Colors are introduced to enhance visibility of LIF images. Low velocity region Envelope of former vortex ring High er Velocity region Diameter and orientation of vortex tube European Journal of Mechanics B Fluids 16 Figure 6. Sequence of LIF images showing vortex evolution and bifurcation process at different instants of time in the XY-plane for Case I. Colors are introduced to enhance visibility of LIF images. Based on the above experimental observations, the schematic of axial switching and bifurcation of rectangular shape vortex ring has been shown in figure 7. At the orifice exit, the shorter sides of vortex tube are labeled as S1 and S2 and longer sides are labeled as l1 and l2. The vortex ring experiences axial switching or splitting depending on the flow conditions imposed on it. As soon as the vortex ring detaches itself from the orifice, the shorter side ( S1, S2) moves swifter than the longer side ( l1, l2). The differences in the velocities along two orthogonal directions produce strain within the vortex ring. However, a greater strain rate results in the shorter side of vortex ring that makes it move towards the vortex center and pushes the longer side a way from the center. If the vortex ring has enough energy and a comparatively lower velocity difference between the shorter and the longer side, the two edges exchange roles, i.e. the initially shorter edge becomes elongated, whereas the initially longer e dge contracts and becomes short. This transition is depicted in figure 7a, where the shorter side moves ahead towards the vortex center pushing the longer side away from the orifice (shown by arrowheads) such that the shorter side S1, S2 becomes longer, an d longer side l1, l2 becomes shorter. This process continues until the vortex breakdown, as also evident from the oscillating variation of Hw and HB, as shown in figures 4c and 4d. A slightly different physical mechanism is observed in the event of vortex bifurcation, as shown in figure 7b. The shorter sides of vortex ring ( S1, S2) approach each other very closely as compared to the axial switching cases, leading to the vortex interconnection (see separation distance HB of counter rotating vortices in figu re 4b and corresponding images in figure 5). The envelope formed from previously ejected vortex rings (figure 6) also supports the interconnection of vortex tube, which is also called as crosslinking or connect -and-cut process . The crosslinking of vorticit y is a cut and connect process in which the core deformation and stretching is followed by annihilation and bridging, which is completed by threading and splitting (Melande and Hussain 1989) . Similar observations have been made in the work of Yao and Xunga ng (1997) , which report that the opposite -signed vorticity (here counter rotating vortices of vortex ring) inside the contact zone gets cancelled out by viscous cross -diffusion. These cancelled vortex lines of vortex tube gets connected with their counterp art and forms isolated vortex rings. Thus, the process of vortex splitting is the result of crosslinking of vortex tube. 17 Figure 7. A schematic comparing the process of (a) axial switching and (b) bifurcation for a rectangular synthetic jet. 3.4. Time -averaged velocity measurements The velocity components measured using Laser Doppler Velocimetry along the synthetic jet centerline is shown in figure 8 . The filled and gray symbols represent the cases of axial switching (no -bifurcation) and bifurcation of vortex rings , respectively . Figure 8a presents the streamwise ( Uavg) velocity along the synthetic jet centerline for the bifurcation and no -bifurcation cases. The streamwise velocity component decreases rapidly from the orifice exit to X/W = 4 for all the bifurcation cases. This rapid reduction in the streamwise velocity component is linked to the vortex reconnection process, where the counter rotating vortices cancel each other’s vorticity leading to a decrease in time -averaged velocity in streamwise direction. After X/W = 4, the velocity is negligible as the vortex ring splits and moves away from the synthetic jet centerline (see figure 3 ). On the other hand, in the case of no occurrence of vortex bifurcation, an increase in velocity within the suction zone ( X/W < 3) is observed. The undulation of velocity in the region between X/W = 4 to 9 is related to the axial switching of vortex ring. During the process of axial switching, fluid along the synthetic jet centerline experiences periodic variation in its magnitude. Z Y X (b) (a) European Journal of Mechanics B Fluids 18 (a) (b) Figure 8. Time -averaged velocity measurements using LDV for (a) streamwise velocity (Uavg) and (b) cross -stream velocity ( Vavg) along the synthetic jet centerline for all the cases. The cross -stream velocity component ( Vavg) shown in figure 8b is negative (moving towards the synthetic jet centerline) for all the cases in the suction region. The cross -stream velocity increases initially upon moving away from the orifice exit and approaches to zero value near X/W = 3 for all bifurcation cases whe reas it is positive for all no n-bifurcation cases with a peak at X/W = 4. This indicates that the suction stroke strongly affects the vortex propagation in downstream direction for bifurcation cases in comparison to that of non -bifurcation cases. At X/W = 3.5, where the first axial switching is completed as observed from figure 4d, the cross -stream velocity is positive and maximum for non -bifurcation cases but negative or zero for bifurcation cases as seen in figure 8b . The positive value of cross -stream ve locity at X/W = 3.5 for no n-bifurcation cases shows that the fluid at the vortex center moves away and prevent the possible reconnection of vortex tube for no n-bifurcation cases. 3.5. Different regimes of vortex rings on an Re – St flow map The range of Reynolds number and Strouhal number for which the rectangular shaped synthetic jet leads to vortex bifurcation under the mentioned experimental conditions are shown in figure 9 for a range of actuation frequenc ies. First, a fixed value of actuation frequen cy is chosen, and Re is varied by changing the magnitude of diaphragm displacement . The resulting average velocity at a particular diaphragm displacement and the actuation frequency fixes the Strouhal number, St. Thus, experiments are conducted at all poss ible values of Re and St and the range in which vortex bifurcation occurs is recorded . In case of no bifurcation, care has been taken to record the vortex regime – axial switching or 19 vortex suction regime, respectively. It has been observed that the occurr ence of vortex bifurcation is crucially dependent upon both Re and St. The vortex bifurcation cases in the major axis ( XY) plane, when plotted on an Re-St flow map, falls within a distinctive cornet -like region. To the left of this region, where St is low, no distinct vortex splitting is observed and the formed vortex ring undergoes axial switching. And, to its right, exists the vortex suction regime in which there is no distinct formation of vortex ring. In the vortex suction regime , the fluid eject ed out from the orifice is sucked back partially or completely inside the cavity during following suction stroke. Figure 9. Different vortex regimes shown on an Re-St flow map. 4. Conclusions The bifurcation and axial switching of leading vortex have been studied quantitatively and qualitatively for a rectangular orifice of aspect ratio two. The axial switching and bifurcation of vortex ring are observed and the physical mechanisms behind their occurrence has been proposed using the LIF imaging and the time -averaged velocity measurements . Vortex splitting or bifurcation is observed on the plane coinciding with the minor axis of the orifice. The divergence angles as obtained from LIF images, obtained between the two trajectories of vortex rings are 124 (Re = 275, St = 0.33) at 1 Hz, 112 (Re = 1101, St = 0.13) at 2 Hz and 68 (Re = 1309, St = 0.17) at 3 Hz of actuation frequency. On the other hand, ax ial switching of vortex ring has been observed at 1, 2 and 3 Hz of actuation frequency for Re = 625, 1348 and 2038 and St = 0.15, 0.11 and European Journal of Mechanics B Fluids 20 0.11 respectively. The main source of bifurcation is believed to be the variation in vortex tube cross section that r esults in varying self -induced velocity along the length of the vortex tube. When plotted on an Re-St flow map, It is observed that the vortex bifurcation regime is a very narrow one between the other regimes such as axial switching and the vortex suction regime. Acknowledgment This research was supported by Naval Research Board (NRB) , DRDO, Government of India and we than kfully acknowledge their financial asistance.