2.1 Experimental set-up

Experiments were carried out in a round air jet rig. Following Hussein, Capp & George (Reference Hussein, Capp and George1994), the rig was deployed in a spacious air-conditioned laboratory, centrally placed in an area of approximately 4.5 m in width and 4.0 m in height with the nozzle exit pointing at a wall 7.0 m away, to minimize the effects of the wall on the jet for example by pressure wave reflection. In view of the high sensitivity of the jet shear layer to background noise (Hussain Reference Hussain1986), there was no traffic, i.e. no object/person moving, at all during experiments. The rig consists largely of the main jet and minijet assemblies. The main jet and minijets came from a compressed air source with a constant 5 bar gauge pressure.

Figure 1(a) shows schematically the main jet assembly. On entering a large chamber, compressed air is mixed with seeding particles in the case of PIV or flow visualization measurements before passing through a tube, a plenum chamber, a 300 mm long diffuser of $15^{\circ }$ half-angle, two fine screens (7 mesh cm $^{-1}$ ) and a cylindrical settling chamber of 400 mm in length and 114 mm in inner diameter. The nozzle contraction contour is the same as used by Zhou et al. (Reference Zhou, Du, Mi and Wang2012) and Yang et al. (Reference Yang, Zhou, So and Liu2016), with a contraction ratio of 32.5 and an exit diameter $D$ of 20  mm. The nozzle is extended by a 47 mm long smooth tube of the same $D$ . The exit Reynolds number $Re_{D}=U_{e}D/\unicode[STIX]{x1D708}$ of the main jet is fixed at 8000, where $U_{e}=6~\text{m}~\text{s}^{-1}$ is the centreline velocity measured at the exit of the nozzle extension and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of air.

Figure 1. Schematic of experimental set-up: (a) main jet assembly; (b) minijet assembly.

The minijet assembly (figure 1 b) includes a stationary and a rotating disk (nozzle extension). A novel unsteady minijet actuator is developed. The stationary disk is made with two orifices of 0.9 mm diameter, separated azimuthally by $180^{\circ }$ . The two orifices are connected via short and equal length tubes to a constant-pressure chamber. The rotating disk is rather unique and is actually the rotor of a servo motor (Kollmorgen RBE-03010) with a maximum speed of $N=2950$  rpm. The rotating disk is drilled with 12 orifices of 1 mm in diameter, azimuthally equally spaced and located at 17 mm upstream of the extension exit, and its interior diameter is identical to the contraction nozzle exit diameter. Once the orifices on the stationary and rotating disks are aligned during rotation, a pulsed minijet is emitted radially towards the main jet axis, as shown in figure 1(b). The two opposing injections are in phase. The minijet pulsation or excitation frequency $f_{e}$ is then $12N/60$  Hz, with a maximum of 590 Hz, which exceeds $4f_{0}$ . The flow rates of both main jet and minijets are adjustable independently via two separate flow meters with a measurement uncertainty of ${<}$ 1 %.

The coordinate system is defined such that its origin is at the centre of the nozzle extension exit, with the $x$ axis along the streamwise direction, the $z$ axis along the radial minijet and the $y$ axis along the direction normal to both $x$ and $y$ , following the right-hand system. The ( $x,z$ ) and ( $x,y$ ) planes are referred to as the injection and non-injection planes, respectively (figure 1 b).

2.2 Measurements

A single tungsten wire of $5~\unicode[STIX]{x03BC}\text{m}$ in diameter, operated on a constant temperature circuit (Dantec Streamline) at an overheat ratio of 1.8, is used to measure the streamwise fluctuating velocity $u$ at $x^{\ast }\leqslant 20$ . In this paper, asterisk denotes normalization by the jet exit mean velocity $\overline{U}_{e}$ and/or nozzle diameter $D$ . The signal from the wire is offset, filtered at a cutoff frequency of 2.8 kHz, amplified and then digitized using a 12-bit analog/digital board at a sampling frequency of 6 kHz. The duration for each record is 80 s. This hot-wire probe is mounted on a computer-controlled two-dimensional traversing mechanism, whose streamwise and transverse resolutions are both 0.01 mm.

A planar PIV system (Dantec standard PIV2100) is deployed to measure velocities in the injection and non-injection planes as well as in a number of cross-sectional planes. A TSI oil droplet generator (TSI 9307-6) is used to generate fog for seeding flow. The seeding particles have a diameter of approximately $1~\unicode[STIX]{x03BC}\text{m}$ , which is adequate for tracking turbulent or high-speed gas flows (Melling Reference Melling1997). The particles are introduced into the upstream mixing chamber (figure 1 a), and thus homogenously distributed throughout the main jet. Meanwhile, ambient air is also seeded by filling the whole laboratory with the fog. Note that the concentration of the fog is not high enough to contaminate the camera lens of the PIV system. Flow illumination is provided by a light sheet, through the jet centreline, of approximately 1 mm in thickness, which is generated by two NewWave standard pulsed laser sources with 532 nm wavelength and a maximum energy output of 120 mJ per pulse. Particle images are captured at a sampling rate of 4 Hz using one HiSense MkII CCD camera (double frames, 2048 $\times$ 2048 pixels). Synchronization between flow illumination and image capturing is provided by a Dantec Flow Map Processor (PIV 2001 type).

For PIV measurements in the ( $x$ , $y$ ) and ( $x$ , $z$ ) planes, the size of each image is 217 mm $\times$ 217 mm, covering the area of $x^{\ast }=0\sim 10$ and $y^{\ast }$ or $z^{\ast }=-5\sim +5$ . Both longitudinal and lateral image magnifications are 0.09 mm/pixel. The time interval is $75~\unicode[STIX]{x03BC}\text{s}$ between two consecutive laser pulses and a particle could travel only 0.45 mm (5 pixels or 0.02 $D$ ) at $U_{e}=6~\text{m}~\text{s}^{-1}$ . In image processing, a built-in adaptive correlation function of the Flow Map Processor (PIV 2001 type) is used. The initial interrogation window size was 256 $\times$ 256 pixels and the number of passes was set to 2. An interrogation window of 32 $\times$ 32 pixels with a 75 % overlap in both directions is chosen, producing 253 $\times$ 253 velocity vectors. This choice is based on an investigation on the effect of the interrogation widow size (32 $\times$ 32 and 16 $\times$ 16 pixels) and overlap (50 %–75 %) on the mean velocity, which indicates that the present choice leads to reliable measurements for the mean velocity field. Flow images captured are 1400 pairs for each set of PIV data. A convergence test has been conducted for the PIV-measured centreline mean velocity $\overline{U}_{c}^{\ast }$ , and it is found that the distributions of $\overline{U}_{c}^{\ast }$ obtained from the image pairs of 1000, 1400, 1800 and 2150 all collapse very well, and further agree well, with a maximum departure of approximately 1 % for $x^{\ast }\leqslant 5$ , with that from the hot-wire measurements (not shown).

Measurements are performed in nine cross-sectional or ( $y$ , $z$ ) planes over $x^{\ast }=0.1\sim 5.0$ . The light sheet is set at approximately 3 mm in thickness. The camera is placed approximately $50D$ downstream from the light sheet so that the feedback effect of flow impinging on the camera lens is negligibly small. The image magnification is tailor made and chosen for each plane in order not only to cover the entire cross-section of the jet but also to maximize the image resolution. As the out-of-plane velocity component is large compared with two in-plane velocity components, the seeding particles could go through the light sheet if the time interval between two consecutive images is large, thus causing poor correlation (Pattenden, Turnock & Zhang Reference Pattenden, Turnock and Zhang2005; Huang, Zhou & Zhou Reference Huang, Zhou and Zhou2006). The time interval is presently chosen to be $25~\unicode[STIX]{x03BC}\text{s}$ , which is found to yield satisfactory results. The number of velocity vectors is the same as that in the ( $x$ , $y$ ) and ( $x$ , $z$ ) planes. A total of 1800 pairs of flow images are captured for each set of PIV data.

The same PIV is used for flow visualization in the three orthogonal planes. So are the seeding and arrangement to provide a marker for flow issuing from the nozzle exit, although the ambient air is not seeded. The captured images cover an area of $x^{\ast }=0\sim 10$ and $y^{\ast }$ or $z^{\ast }=-5\sim +5$ in the ( $x$ , $y$ ) and ( $x$ , $z$ ) planes and an area of $y^{\ast }=-4\sim +4$ and $z^{\ast }=-4\sim +4$ in the ( $y$ , $z$ ) planes at $x^{\ast }=0.7$ , 1.0, 1.3, 1.6, 2.0, 2.4, 2.7, 3.0, 4.0, 5.0.

The decay rate $K$ of the centreline mean velocity is used to evaluate the jet entrainment and spread, given by $K=(\overline{U}_{e}-\overline{U}_{5D})/\overline{U}_{e}$ , where $U_{e}$ and $U_{5D}$ are the centreline velocities at $x^{\ast }=0$ and 5, respectively, and overbar denotes time-averaged quantity. Note that the manipulated jet may vary in its width in different planes through the $x$ -axis. Following Hussain & Husain (Reference Hussain and Husain1989) and Mi et al. (Reference Mi, Kalt, Nathan and Wong2007), Zhou et al. (Reference Zhou, Du, Mi and Wang2012) defined in their investigation of jet manipulation using two steady minijets an equivalent jet width $R_{eq}\equiv [R_{H}R_{V}]^{1/2}$ , where $R_{H}$ and $R_{V}$ are the half-widths of the mean-velocity distributions in the ( $x,z$ )- and ( $x,y$ )-planes, respectively. $R_{eq}$ was found to be correlated approximately linearly with $K$ , that is, $K$ is directly linked to the jet entrainment rate.

Figure 2. Power spectral density function of streamwise fluctuating velocity $u$ measured on the centreline: (a) the natural jet ( $f_{e}/f_{0}=0$ , $C_{m}=0$ ), (b) with the disk rotating at $f_{e}/f_{0}=0.895$ and $C_{m}=0$ .

6.1 Entrainment and momentum transport

Entrainment and momentum transport are crucial for the understanding of vortex dynamics. These aspects show the most marked change in the manipulated jet of Category I among the three categories, relative to the natural jet. We therefore focus on the flow of Category I ( $C_{m}=1.5\,\%$ ). The information on spread and entrainment may be obtained via examining the PIV-measured $\overline{W}^{\ast }$ and $\overline{V}^{\ast }$ contours (figure 11 a,c,e). $\overline{W}^{\ast }$ is negligibly small in the absence of excitation (figure 11 a) but becomes pronouncedly negative, its maximum magnitude jumping by 300 %, in the central region of the injection plane under excitation (figure 11 c), suggesting a strong entrainment of ambient fluid into the jet. On the other hand, $\overline{V}^{\ast }$ is positive almost over the entire region of $x^{\ast }>2.0$ in the non-injection plane (figure 11 e), its maximum reaching 0.14 or 800 % of that in the natural jet, indicating a very strong outward spread of fluid from the jet.

Figure 11. Contours of time-averaged lateral velocity (a,c,e) and Reynolds shear stress (b,d,f), the contour increments being 0.01 and 0.001, respectively.

The Reynolds shear stresses provide a measure for the momentum transport. The $\overline{uw}^{\ast }$ and $\overline{uv}^{\ast }$ contours (figure 11 b,d,f) exhibit a great change compared to the natural jet. Without excitation, the maximum $\overline{uw}^{\ast }$ (0.014) occurs at $x^{\ast }=3.1\sim 3.2$ . Once excitation is introduced, $\overline{uw}^{\ast }$ in the injection plane shows another concentration of larger magnitude (0.016) at $x^{\ast }=1.7$ , much nearer to the nozzle exit. Similarly, $\overline{uv}^{\ast }$ in the non-injection plane also exhibits two pronounced concentrations of the positive sign, one at $x^{\ast }=3.6$ with its maximum reaching 0.017 and the other at $x^{\ast }=1.85$ . Note the occurrence of a negative-signed concentration in the central region near the nozzle exit, albeit with a relatively small maximum magnitude (0.007) at $x^{\ast }=2.1$ . The vorticity contours to be shown later indicate that the region of negative $\overline{uv}^{\ast }$ is associated with the events of vortex pairing, during which vortices are tilted. Please refer to figures 20 and 21 in Browand & Ho (Reference Browand and Ho1983) for details.

6.2 Downstream evolution

The downstream evolution of the $u$ -signals, measured in both injection and non-injection planes, are presented in figure 12. The same vertical and horizontal scales are used for all the $u$ -signals. The signal starts to show a quasi-periodicity at $x^{\ast }=2.0$ without excitation, but behaves rather differently from one category to another under excitation. A marked periodicity is seen at $x^{\ast }=0.0$ in the injection plane and at $x^{\ast }=1.0$ in the non-injection plane of Category I. The flow remains to be laminar until at $x^{\ast }=2.0$ in both planes. In contrast, the signals exhibit random fluctuations even at $x^{\ast }=0.0$ in both planes for Category III, implying a turbulent state right at the exit of nozzle (figure 12 d). Category II is a transition between I and III. The flow displays intermittent periodicity and small-scale random fluctuation from time to time.

Figure 12. Typical signals of streamwise velocity $u$ . Hot-wire was placed at $y^{\ast }$ or $z^{\ast }=0.3$ .

$E_{u}$ (figure 13 a) measured along the centreline of the manipulated jet displays very pronounced peaks at $f_{e}^{\ast }$ ( $=f_{e}D/U_{e}$ ) and even its second and higher harmonics up to $x^{\ast }=4$ for Category I, reflecting the presence of quasi-periodic large-scale structures and echoing the characteristics of the minijet-produced flow (figure 5 b). The peaks completely disappear at $x^{\ast }\geqslant 6$ , indicating that the manipulated jet becomes fully developed and turbulent at $x^{\ast }\geqslant 6$ . However, the peaks are much less pronounced for Category III (figure 13 b) and disappear essentially for $x^{\ast }\geqslant 5$ . Apparently, the jet is fully developed and turbulent at $x^{\ast }\geqslant 4$ , earlier than Category I.

Figure 13. Power spectral density function of $u$ measured on the centreline of the manipulated jets: (a) Category I ( $C_{m}=1.5\,\%$ for $f_{e}/f_{0}^{\prime }=1.0$ ); (b) III (10.6 %, 1.12).

6.3 The flow structure

Flow visualization was conducted in both injection and non-injection planes for all three categories of the manipulated jet, along with the natural jet, in order to gain further understanding of the flow physics. Figure 14 presents typical photographs from flow visualization. There is a profound change in the flow structure with and without excitation and even between different categories under excitation. For Category I, the shear layer rolls up early to form vortices stronger in both planes than those in the natural jet (figure 14 a,b,e). There is a distinct difference in the flow structure between the two orthogonal planes. A large amount of ambient fluid (dark coloured) in the injection plane appears engulfed vigorously into the jet, even penetrating the jet axis via vortical motions. Meanwhile, smoke-marked fluid (white coloured) is massively ejected from the braid region between two successive vortices in the non-injection plane, generating a much more extensive spread than the natural jet. Vigorous entrainment and spread contribute to the concentrations of the $\bar{W}^{\ast }$ and $\bar{V}^{\ast }$ contours in figure 11(c,e). For Category II, the initial turbulent state (figure 8 c,d) incurs a rapid diffusion of vortices shortly after their formation in both planes (figure 14 c,f) due to the increased $C_{m}$ , as noted by Fiedler & Mensing (Reference Fiedler and Mensing1985) in an initially turbulent plane mixing layer under periodic and strong excitation. In Category III, the flow becomes more turbulent in both planes even at $x^{\ast }=0$ . The observations are fully consistent with the findings from $u_{r.m.s.}$ measured at the nozzle exit (figure 8 c,d).

Figure 14. Photographs of typical flow structures from flow visualization. Flow is from the bottom up.

Figure 15. Typical instantaneous velocity vectors and corresponding $\unicode[STIX]{x1D714}_{y}^{\ast }$ contours: (a) natural jet and (b–d) the injection plane of the manipulated jet (Category I: $C_{m}=1.5\,\%$ , $f_{e}/f_{0}^{\prime }=1.0$ ). Contour interval $=$ 1.

On another note, with a large $C_{m}$ in Category III, the two minijets penetrate deeply into the potential core in the injection plane, and collide with each other around the centreline (Zhou et al. Reference Zhou, Du, Mi and Wang2012). Such a strong perturbation is naturally transferred to the non-injection plane, resulting in the transition from laminar to turbulent vortices in both planes. The turbulent vortices entrain more effectively ambient fluid into the jet and thereby contribute to a large $K$ . With increasing $C_{m}$ , the jet gradually gains a fully turbulent state and $K$ approaches an asymptotic value.

In summary, the significantly increased $K$ in Category I results from the enhanced strength of large-scale coherent structures. A large $K$ is also achievable in Category III, which is ascribed to enhanced turbulence with increasing $C_{m}$ . Category II is a transition between I and III and is characterized by relatively small $K$ . The excitation of Category I is apparently most efficient and will be further explored in following sections.

7.1 Vortex formation, interaction and entrainment

The flow structure evolution is completely different between the injection and non-injection planes. Figure 15 presents typical instantaneous velocity vectors and corresponding $\unicode[STIX]{x1D714}_{y}^{\ast }$ contours in the injection plane (Category I). We have examined carefully the 1800 PIV images and 300 photographs of flow visualization and have found that the vortex pairing is a frequent event. The marked periodicity of the flow structure, especially at $x^{\ast }<3.0$ (figure 12 b), allows us to capture and identify the typical phases or stages, I through VI, of the vortex evolution during pairing. We wish to emphasize that the four panels are representative of typical structures, and the six phases or stages of the pairing process inferred from the four panels are also consistent with previous investigations on vortex pairing (e.g. Hussain & Zaman Reference Hussain and Zaman1980; Husain & Hussain Reference Husain and Hussain1991). Once perturbation is introduced, the vortices seen in the injection plane are changed substantially, compared with the natural jet (figure 15 a). A relatively small vortex, marked by ‘B’ in figure 15(b), catches up a large leading vortex ‘A’, running towards the inner side of the latter, meanwhile pushing the latter outward (figure 15 c), due to the mutual induction between them. The violent interaction between ‘A’ and ‘B’ subsequently leads to the breakdown of ‘B’ (figure 15 d). The $\unicode[STIX]{x1D714}_{y}^{\ast }$ contours suggest that the identities of the two vortices persist, up to phase V. Meanwhile, a large amount of ambient fluid is engulfed downstream of interacting ‘A’ and ‘B’ in phases III and IV, as evident from the transverse component of velocity vectors. On the other hand, a remarkable outward lateral motion occurs in the non-injection plane, as is evident from the typical instantaneous velocity vectors (figure 16). The fragmented concentrations of vorticity are sequentially ‘tossed’ out to ambient fluid from the vortical structure ‘A’. The vortex pairing is discernible, resulting from the mutual induction of two vortices, marked by ‘ $+$ ’ and ‘ $\times$ ’. The observation prompts us to examine further the three-dimensional aspects of the flow structure.

Figure 16. Typical instantaneous velocity vectors and corresponding $\unicode[STIX]{x1D714}_{z}^{\ast }$ contours in the non-injection plane (Category I: $C_{m}=1.5\,\%$ , $f_{e}/f_{0}^{\prime }=1.0$ ). Contour interval $=$ 1.

7.2 Development of streamwise structures

7.2.1 Two pairs of counter-rotating streamwise vortices

The streamwise structures may be investigated by examining the jet in a series of cross-sectional planes at $x^{\ast }=0.7$ , 1.0 and 1.3 via typical photographs from flow visualization (figure 17). As a reference, the natural jet images look like a full moon up to $x^{\ast }=1.3$ , as illustrated by the image at $x^{\ast }=0.7$ (figure 17 a), suggesting no roll-up motion. Once excited, the shear layer displays the roll-up motion about the injection and the non-injection planes. At $x^{\ast }=0.7$ , the shear layer rolls up about the injection plane, forming two vortical structures (figure 17 b,e). This is caused by a higher level of initial velocity fluctuation about the injection plane than about the non-injection plane, as evidenced by the $u$ -signals at the nozzle exit in figure 12(b). This higher initial velocity fluctuation hastens the shear-layer evolution (Hussain & Zedan Reference Hussain and Zedan1978). Note that the two vortical structures are symmetrical about a plane through the jet axis, at an angle of approximately $15^{\circ }$ with respect to the non-injection plane (please refer to the sketch in figure 17). Such an angle results from the effect of the rotating nozzle extension. Note that the rotation of approximately $15^{\circ }$ shown in figure 17 is from one instant of the instantaneous flow field. The time-averaged flow field indicates a smaller rotation (to be presented in § 7.2.3). Further downstream at $x^{\ast }=1.0$ , the shear layer roll-up is also evident about the non-injection plane, forming a ring vortex (figure 17 c). A close examination of two sequential phases (figure 17 c,f), separated by $450~\unicode[STIX]{x03BC}\text{s}$ out of one typical period of 7.8125 ms ( $f_{e}=128$  Hz, figure 13 a), of the ring vortex unveils that the segment of the ring vortex near the non-injection plane is advected ahead of that near the injection plane, as indicated by the incomplete segments (broken line square) of the ring vortex about the non-injection plane.

Figure 17. Photographs of flow visualization in the cross-sectional planes of $x^{\ast }=0.7$ , 1.0, 1.3. Flow is outward.

Two pairs of counter-rotating streamwise vortices are generated, following the shear layer roll-up about the injection plane. At $x^{\ast }=0.7$ , the cross-section in the braid (figure 17 h) displays two indentations under the influence of earlier roll-up about the injection plane (figure 17 b,e). With increasing $x^{\ast }$ , two pairs of counter-rotating streamwise vortices occur simultaneously in the braid region and on the outer side of the ring vortex, as marked by circles in figure 17(c,f,i). Interestingly, their spatial locations all coincide, be that in the cross-section of the ring vortex or that of the braid, suggesting that these streamwise vortices run longitudinally through the regions of both ring vortex and braid. The counter-rotating vortex pair has an ‘outflow’ sense of rotation about the non-injection plane, that is, fluid is ejected from the jet core region to ambient air as a result of the interaction between the streamwise vortices of each pair. The vortex pairs exhibit an appreciable growth in the cross-sectional size with increasing $x^{\ast }$ . This is evident by comparing the images at $x^{\ast }=1.3$ (figure 17 d,g,j) with those at $x^{\ast }=1.0$ (figure 17 c,f,i). The formation, including initial evolution, of the streamwise vortex pairs occurs at azimuthally fixed locations, as observed by Husain & Hussain (Reference Husain and Hussain1993) in an acoustically excited elliptic jet. The rotational senses of their streamwise vortices are also the same as presently observed, even though the two excitation techniques are very different. On the other hand, for the cases of steady control jets (e.g. New & Tay Reference New and Tay2006; Alkislar et al. Reference Alkislar, Krothapalli and Butler2007; Alvi et al. Reference Alvi, Lou, Shih and Kumar2008) and tabs (Reeder & Samimy Reference Reeder and Samimy1996; Zaman Reference Zaman1996, Reference Zaman1999), the streamwise vortex pairs are all produced with an initial ‘inflow’ sense, that is, ambient fluid is brought into the jet core region under the interaction between the streamwise vortices of each pair.

It is of fundamental importance to understand how the contorted ring vortex interacts with the streamwise vortices. To this end, the PIV measurements were conducted at the cross-sectional ( $y$ , $z$ ) plane of $x^{\ast }=1.5$ , immediately after the vortices are formed. Figure 18 presents four typical instantaneous velocity vector maps overlapped with the corresponding $\unicode[STIX]{x1D714}_{x}^{\ast }$ contours, which represent four typical phases in the process of the interaction. The separation between the $\unicode[STIX]{x1D714}_{x}^{\ast }$ concentrations exhibits a large variation from one phase to another, in distinct contrast to quasi-steady streamwise vortex pairs produced by steady minijets and tabs. The velocity vectors suggest that the contorted ring vortex be highly three-dimensional. Note that two pairs of ‘inflow’-type streamwise vortices, closer to the jet axis than those of the ‘outflow’ type, entrain the ambient fluid into the jet core about the non-injection plane in figure 18(b). Also, the maximum magnitude of the ‘inflow’-type $\unicode[STIX]{x1D714}_{x}^{\ast }$ concentrations is comparable to that of adjacent ‘outflow’ type. As reported by Zaman (Reference Zaman1996) in a rectangular jet, these ‘inflow’ streamwise vortices may be produced by the re-orientation (or contortion) of the ring vortex.

Figure 18. (a–d) Typical instantaneous velocity vectors and corresponding $\unicode[STIX]{x1D714}_{x}^{\ast }$ contours in a cross-sectional plane of the manipulated jet (Category I: $C_{m}=1.5\,\%$ , $f_{e}/f_{0}^{\prime }=1.0$ ) at $x^{\ast }=1.5$ ; the ‘outflow’ sense of the vortex pair is defined as that the jet fluid between vortices (i.e. the fluid about the non-injection plane) is ejected outwards by their induction; (e) model of the contorted ring vortex and streamwise vortex pairs when they are passing through $x^{\ast }=1.5$ . The a to d in (e), corresponding to panels (a) to (d), respectively, represent four typical phases in the process of the interaction of the contorted ring vortices with streamwise vortex pairs.

It is of interest to examine how the separation varies between the $\unicode[STIX]{x1D714}_{x}^{\ast }$ concentrations associated with the vortex pairs. Use $S_{I}$ and $S_{N}$ to denote the separations between the vortices about the injection and non-injection planes, respectively, as marked in figure 18(a–d). $S_{N}$ changes significantly, while $S_{I}$ does little. Bernal & Roshko (Reference Bernal and Roshko1986), Lasheras, Cho & Maxworthy (Reference Lasheras, Cho and Maxworthy1986) and Lasheras & Choi (Reference Lasheras and Choi1988) observed in-plane mixing layers that streamwise structures first form in the braid region between successive spanwise vortices, and then propagate upstream and downstream between the high-speed side of a spanwise vortex and the low-speed side of the following one. Liepmann & Gharib (Reference Liepmann and Gharib1992) experimentally confirmed that similar streamwise structures also existed in round jets, and evolved in the braid region between consecutive vortex rings, similarly to those of the in-plane mixing layer. Inspired by these findings, we propose a model in figure 18(e) for the interrelationship between the contorted ring vortices and streamwise vortex pairs under the excitation. We wish to highlight two points. Firstly, figure 18(e) is a model extracted from figure 18(a–d), presenting the flow structure passing through a cross-sectional plane of $x^{\ast }=1.5$ , thus being sketched in the time domain. The flow is actually from left to right. Secondly, the ring vortex is approximately axisymmetric in the ( $y,z$ ) plane. The seemingly ‘U’ shape of the ring is just the side view of the circular structures. In this model, the upstream part of the streamwise vortex joins the outer side of the immediately upstream ring vortex, whereas the downstream part stretches towards the inner side of the ring vortex immediately downstream. Such a feature leads to a considerable variation in $S_{N}$ . The locations (a–d) of the cross-sectional plane, with respect to the contorted ring vortex, correspond well to the four typical phases illustrated in figure 18(a–d). If the PIV image captures the instant or phase of (b), the measurement plane lies midway between the four azimuthal segments of one contorted ring vortex. This is why velocity vectors in figure 18(b) show simultaneously the outward and inward radial motions about the injection and the non-injection planes, respectively. As shown in this model, the upstream part of the streamwise vortex joins, on the jet low-speed side, the streamwise segment of the contorted ring vortex.

7.2.2 Mushroom-like streamwise structures

The extraordinarily strong spreading in the non-injection plane (figure 11(e) and 14 e) is linked to the sequentially tossed out mushroom-like structures (figure 16). Mushroom-like streamwise structures are observed in the natural round jet due to the braid instability (e.g. Liepmann & Gharib Reference Liepmann and Gharib1992) but are distinct from those in figure 16. Naturally, we are tempted to find out how the mushroom-like structures under excitation are generated, how they evolve and how they differ from those in the natural jet. Figures 19 and 20 present the images with and without excitation captured in a series of cross-sectional planes at $x^{\ast }=2.0{-}5.0$ . Both the ring or distorted ring structure and the braid are presented for $x^{\ast }=2.0{-}3.0$ (figures 19 and 20), which are distinctly different between the natural and manipulated jets.

Figure 19. Photographs of flow visualization in the cross-sectional planes of the natural jet ( $C_{m}=0$ , $f_{e}/f_{0}^{\prime }=0$ ). (a,e)  $x^{\ast }=2.0$ , (b,f) 2.4, (c,g) 3.0, (d) 5.0. Flow is outward.

Figure 20. Photographs of flow visualization in the cross-sectional planes of the manipulated jet ( $C_{m}=1.5\,\%$ , $f_{e}/f_{0}^{\prime }=1.0$ ). (a,e)  $x^{\ast }=2.0$ , (b,f) 2.4, (c,g) 3.0, (d) 5.0. Flow is outward.

The coherent structure in the natural jet is characterized by a small size, showing little or rather regular azimuthal variation for $x^{\ast }<5.0$ . At $x^{\ast }=2.0$ the shear layer rolls up, forming a ring vortex (figure 19 a). The dark ring region, approximately a circle, is the entrained ambient fluid by the roll-up motion of the ring vortex and the solid inner circle is the potential core. In the braid region (figure 19 e), the image appears to be a full moon. The jet is basically axisymmetric, regardless of the ring vortex or the braid region. Moving downstream to $x^{\ast }=2.4$ , the ring vortex (figure 19 b) changes little, while a number of small lumps, azimuthally separated, occur in the braid region (figure 19 f), suggesting the occurrence of the azimuthal instability in the braid region, fully consistent with Liepmann & Gharib’s (Reference Liepmann and Gharib1992) experimental finding in a natural round jet at $Re_{D}=5500$ . At $x^{\ast }=3.0$ mushroom-like streamwise structures are evident in both the ring vortex and the braid region (figure 19 c,g). These mushroom-like structures are characterized by counter-rotating streamwise vortex pairs of the ‘outflow’ type, and by approximately equal azimuthal separation. Liepmann & Gharib (Reference Liepmann and Gharib1992) pointed out that, once formed, the mushroom-like structures first moved outward into the jet low-speed side due to self-induction and then went through the induced velocity field of the ring vortex. They were stretched in the braid region and re-entrained upstream into the adjacent ring vortex. This is why the streamwise structures generated are also observed in the ring vortex region. The jet has become fully turbulent at $x^{\ast }=5.0$ (figure 19 d) and it is difficult to distinguish between the ring vortex, the braid and the mushroom structures.

It is worth mentioning that only one single ‘generation’ of the mushroom-like streamwise structures is generated all the way to the end of the potential core in the natural jet. However, as shown in figure 16, a number of structures are sequentially ‘tossed’ out, one following another, along the radial direction in the non-injection plane of the manipulated jet. One may surmise that there could be several ‘generations’ of the mushroom-like streamwise structures produced under excitation. At $x^{\ast }=2.0$ , the mushroom-like structures grow initially only between the streamwise vortices of the ‘outflow’-type pair (figure 20 a,e) and are seen in both the distorted ring vortex and the braid region, in distinct contrast to the natural jet. The difference may be ascribed to the outward radial induction from the azimuthally fixed streamwise vortex pairs in the manipulated jet (figure 18 e). At $x^{\ast }=2.4$ , the ‘first generation’ of mushroom-like structures is fully developed and starts to move outward, away from the jet core. Meanwhile, another generation of new mushroom-like structures (figure 20 f) emerges. The mushroom-like structures undergo a much more rapid ‘production’ from $x^{\ast }=2.4$ to 3.0 than those from $x^{\ast }=2.0$ to 2.4. Many mushroom-like counter-rotating structures are sequentially ‘tossed’ out along the radial direction about the non-injection plane, often one pair after another (figure 20 c). Sometimes, one mushroom-like structure is alternately interwoven with another (figure 20 g). This is accompanied by a strong ejection of jet core fluid, resulting in greatly enhanced jet spreading. As the case of the natural jet, the manipulated jet is also fully turbulent at $x^{\ast }=5.0$ . Nevertheless, the image in figure 20(d) shows unequivocally a much larger spread, than that in figure 19(d), about the non-injection plane due to a number of generations of mushroom-like structures tossed out from the jet core region.

There is a marked difference in the radial outward motions of mushroom-like structures between the natural and manipulated jets. In the natural jet the mushroom-like structures formed occur near the ring vortex or braid region (Liepmann & Gharib Reference Liepmann and Gharib1992) since the outward self-induction of these structures is at least partially curtailed by the inward induction of passing ring vortices. In contrast, the mushroom-like structures in the manipulated jet can often move out for two or more nozzle diameters from the jet axis. The difference is attributed to the presence of the azimuthally fixed streamwise vortex pairs of the ‘outflow’ type in the manipulated jet. Their presence tips the balance between the inward and outward inductions in the natural jet, resulting in a predominance of the radial outward induction. As a consequence, the mushroom-like structures are tossed out from the jet core region. This mechanism is similar to the production mechanism for the side jets in a heated round jet or strongly excited cold jet (Monkewitz et al. Reference Monkewitz, Bechert, Barsikow and Lehmann1990; Monkewitz & Pfizenmaier Reference Monkewitz and Pfizenmaier1991; Brancher, Chomaz & Huerre Reference Brancher, Chomaz and Huerre1994). The side jet is produced by streamwise vortex pairs in the braid region and acts to eject vigorously fluid from the jet core region.

7.2.3 Time-averaged streamwise vorticity

The development of the streamwise vortices is reflected in the time-averaged streamwise vorticity ( $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }=\overline{\unicode[STIX]{x1D714}}_{x}D/U_{e}$ ). At $x^{\ast }=0.45$ , two pairs of oppositely signed $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations occur symmetrically about the centre, protruding into the potential core (figure 21 a). They are apparently generated by the two symmetrically placed and oppositely pointing minijets. Issuing from the radial orifices, as shown in figure 6(a), each of the two minijets may have produced a leading vortex ring followed by trailing fluid and, when viewed in the ( $y,z$ ) plane, the ring shows one pair of counter-rotating vortices (figure 6 b). The two pairs of vortices exhibit a rapid decay at $x^{\ast }=1.0$ (figure 21 b) and are barely discernible at $x^{\ast }=1.5$ (figure 21 c). Note the ring-like $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations at $x^{\ast }=0.45$ , which are attributed, at least partially, to the nozzle extension rotation (§ 3). It is cautioned that the streamwise measurements might not have fully captured the minijet structures at sufficiently far downstream, say approximately $x^{\ast }=3$ and beyond, since the contours of time-averaged streamwise vorticity point to the most likely rotation of $7^{\circ }$ at $x^{\ast }\leqslant 1.0$ (figure 21 a,b) and even larger rotation from $x^{\ast }=3.0$ (figure 21 f,g).

Figure 21. Contours of time-averaged streamwise vorticity $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ in the cross-sectional planes of the manipulated jet (Category I: $C_{m}=1.5\,\%$ , $f_{e}/f_{0}^{\prime }=1.0$ ). (a) $x^{\ast }=0.45$ , (b) 1.0, (c) 1.5, (d) 2.0, (e) 2.5, (f) 3.0, (g) 4.0, (h) 5.0.

Three pairs of alternatively signed $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations are seen over $x^{\ast }=1.0{-}3.0$ about the non-injection plane (figure 21 b–f), referred to as the inner, intermediate and outer pairs, respectively, for the convenience of discussion. Both inner and outer pairs of the  $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations are of the ‘outflow’ sense of rotation, opposite to that of the intermediate pair. Based on the proposed model for the contorted ring and streamwise structures (figure 18 e), we may easily see that the intermediate pair of the  $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations corresponds to the reoriented or predominantly streamwise segments of the contorted ring vortex, and the inner and outer pairs are associated with the two pairs of ‘outflow’ streamwise vortices. Naturally, the inner and outer $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations result from the downstream and upstream portions of the two pairs of streamwise vortices, respectively.

The maximum level of the $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations occurs at $x^{\ast }=1.5$ for the outer and intermediate pairs but at $x^{\ast }=2.5$ for the inner pair. This indicates that the upstream part of one pair of streamwise vortices develops more rapidly than its downstream part, which is fully consistent with flow visualization in the ( $y,z$ ) plane (figure 20). This is because the shear in the braid region is more intense immediately downstream than upstream of the ring vortex (Martin & Meiburg Reference Martin and Meiburg1991). The intense shear accelerates the development of the upstream part. At $x^{\ast }=4$ (figure 21 g), the maximum levels of the inner and outer $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations decay slowly. On the other hand, the intermediate $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations already vanish. The result suggests that the streamwise structures persist farther than the ring vortex, in agreement with Liepmann & Gharib’s (Reference Liepmann and Gharib1992) report. The outer $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ concentrations at $x^{\ast }=4$ are extended significantly outward along the radial direction due to the sequential generation of mushroom-like structures and their outward motion. At $x^{\ast }=5.0$ (figure 21 h), $\overline{\unicode[STIX]{x1D714}}_{x}^{\ast }$ becomes very small in magnitude, suggesting grossly weakened streamwise structures.

8.1 Role of the unsteady minijets in vortex dynamics

Issuing from the radial orifice, each unsteady minijet may produce isolated structures with a leading vortex ring accompanied by trailing fluid (§ 4). Beyond $x^{\ast }\approx 1.0$ , the minijet-produced flow structures exhibit a rapid decay and are barely discernible at  $x^{\ast }=1.5$ (figure 21 b,c). These structures induce the early roll-up of the shear layer about the injection plane, compared with that about the non-injection plane, forming a contorted ring vortex, which is distinct from that in the natural jet (figures 14 and 17). The initial development of the shear layer can be predicted from linear stability theory (Michalke Reference Michalke1965a ,Reference Michalke b ; Freymuth Reference Freymuth1966). The initial instability wave undergoes an exponential growth before the shear layer rolls up to form vortices. The initial shear layer is slightly sinuous and the velocity disturbance is small in the natural jet. Under the minijet excitation, a highly periodical velocity perturbation appears about the injection plane even upstream of the main jet exit (figure 5) and persists in the shear layer issuing from the nozzle (figure 12 b). The highly periodical velocity disturbances may induce the shear layer about the injection plane, through the exponential growth to roll up into vortices in a short time or distance compared with that in the natural jet or the non-injection plane of the manipulated jet. This early roll-up, evident by comparing the velocity signals in figure 12(a,b), results in the contorted vortex ring. With the frequency of the unsteady waves coinciding with the unsteady minijet injection, the periodicity of the vortex formation is strengthened in the main jet. Two vortices are formed during each cycle of injection (figure 12 b). The observation is fully consistent with Ho & Huang’s (Reference Ho and Huang1982) report that, if forced at frequency $f_{e}=1/2f_{n}$ , where $f_{n}$ is the initial vortex formation frequency ( $f_{n}$ equals presently to $2f_{0}$ , as indicated by the predominant peak at $x^{\ast }=2$ in figure 2 a), the vortices in a mixing layer are formed at frequency $f=2f_{e}$ . Such subharmonic excitation may enhance the mutual motions of two adjacent vortices, e.g. vortex pairing or merging, in the perturbed shear layer (Ho & Huerre Reference Ho and Huerre1984). This also explains the vigorous vortex interactions in the present manipulated jet.

The unsteady minijet may produce another important effect. Two steady minijets yield two pairs of streamwise counter-rotating vortices in a laminar round jet (New & Tay Reference New and Tay2006, $Re_{D}=1000$ ). The mechanism is found to be similar to that for the steady transverse jet in cross-flow (Cortelezzi & Karagozian Reference Cortelezzi and Karagozian2001). Naturally, one may wonder whether the same mechanism may account for the occurrence of the two pairs of azimuthally fixed streamwise vortices in the present manipulated jet. As shown in figure 17, the streamwise vortices emerge right after the formation of the contorted ring vortex and braid, showing little connection with the minijet-produced structures. Moreover, due to a small diameter ratio $d_{r}/D$ ( $=$ 0.05) presently used, the minijet-produced vortical structures are relatively weak and undergo a rapid decay, barely discernible at $x^{\ast }=1.5$ (figure 21 b,c). It seems plausible that the two pairs of azimuthally fixed streamwise vortices are not directly linked to the minijet-produced vortical structures; rather, they result from the ring vortex and braid contortions, which originate from the highly periodical disturbance, produced by the pulsed minijets, in the shear layer issuing from the nozzle. This is fully consistent with Tamburello & Amitay’s (Reference Tamburello and Amitay2007) proposition that, when a synthetic excitation jet was placed upstream of the main axisymmetric jet exit, its dominant effect was the growth of the unstable modes.

8.2 Role of vortex pairing in the generation of mushroom-like structures

The mushroom-like streamwise structures undergo a much more rapid generation over $x^{\ast }=2.4{-}3.0$ than over $x^{\ast }=2.0{-}2.4$ (figure 20). The observation may be connected to vortex pairing observed in the non-injection plane. The reason is twofold. Firstly, the streamwise extent where vortex pairing occurs (figure 15) coincides well with that where the mushroom-like structures are rapidly generated. Secondly, there is a general consensus that vortex pairing may produce the three-dimensional perturbation via expansion and contraction of the vortices in pairing (e.g. Yule Reference Yule1978; Hussain & Zaman Reference Hussain and Zaman1980; Zaman & Hussain Reference Zaman and Hussain1980; Hussain Reference Hussain1986; Liepmann & Gharib Reference Liepmann and Gharib1992). As discussed earlier, the production of the mushroom-like structure is associated with the instability of the braid region. The braid region associated with large lateral shear and positive strain rate may respond nonlinearly to any small perturbation. The three-dimensional perturbation due to vortex pairing may cause the azimuthal vorticity line in the braid to deform. Under the influence of large lateral shear, the deformed azimuthal vorticity line may be re-oriented to yield the streamwise vorticity line, and the positive strain rate in the braid stretches the streamwise vorticity line to form a mushroom-like structure.

8.3 Physical model of the flow structure under excitation

Experimental data have unveiled that the flow structure under the excitation of Category I is characterized by the contorted ring vortices, two pairs of counter-rotating streamwise vortices and sequentially ‘tossed out’ mushroom-like structures. Two aspects of this flow are distinct from those manipulated by tabs, steady secondary jets and other techniques. The unsteady minijet excitation creates the contorted vortex rings and thus the deformed braid region, producing two pairs of counter-rotating streamwise vortices of the ‘outflow’ type, not the quasi-steady ‘inflow’ vortex pairs when the tabs (e.g. Zaman et al. Reference Zaman, Reeder and Samimy1994; Reeder & Samimy Reference Reeder and Samimy1996; Zaman Reference Zaman1999) and steady secondary jets (e.g. New & Tay Reference New and Tay2006; Alkislar et al. Reference Alkislar, Krothapalli and Butler2007; Alvi et al. Reference Alvi, Lou, Shih and Kumar2008) are deployed. Furthermore, the mushroom-like structures are sequentially ejected, which is reported for the first time.

The presently manipulated jet exhibits some similarity to a heated round jet, which also displays a large spread when the density ratio of jet at exit to ambient fluid is below 0.72 (Monkewitz & Bechert Reference Monkewitz and Bechert1988). The large spread is linked to the formation of a so-called ‘side jet’, which is directed radially away from the main jet axis. The heated jet is also characterized by strong ring structures and two to six pairs of streamwise vortices as well as a rapid spread (Monkewitz et al. Reference Monkewitz, Lehmann, Barsikow and Bechert1989). However, there is a marked difference, that is, the mushroom-like structures are absent from the heated jet. This might be due to the relatively small separation in the ( $y$ , $z$ ) plane between the adjacent pairs of counter-rotating streamwise vortices in the heated jet, as is evident in Monkewitz & Pfizenmaier’s (Reference Monkewitz and Pfizenmaier1991) and Brancher et al.’s (Reference Brancher, Chomaz and Huerre1994) models for side jet production (their figures 6 and 8, respectively). In order to produce the mushroom-like structures, this separation needs to be adequately large, as shown in figure 17(j) and 20(e).

Figure 22. Conceptual model of the flow structure under the perturbation of two unsteady minijets.

A conceptual model is proposed based on the present experimental data for the jet flow structure under the excitation of two radial unsteady minijets, as schematically shown in figure 22. Issuing from the radial orifices, each unsteady minijet produces periodically isolated structures (figure 6), resulting in strong velocity disturbances in the injection plane (figure 12 b). Such periodic perturbations excite the shear layer, causing the early roll-up about the injection plane than that about the non-injection plane (figure 17 b,e). The early roll-ups produce an inward induction on their upstream fluid, generating two indentations in the braid about the injection plane (figure 17 h). The braid deformation reorients azimuthal vorticity to produce four streamwise vorticity lines at the corners of the indentations (figure 17 i), which are further stretched into two pairs of azimuthally fixed counter-rotating streamwise vortices (figure 17 j, 18 e). Each pair has an ‘outflow’ sense of rotation about the non-injection plane (figure 18 d), thus ejecting the jet core fluid between each pair away from the jet axis. Under the effect of three-dimensional perturbation arising from vortex pairing, the braid instability is amplified to generate the mushroom-like counter-rotating streamwise structures (figure 20 e). These mushroom-like structures are sequentially ‘tossed out’ along two opposite directions of the non-injection plane, one pair after another (figure 20 c), due to the strong outward induction, along the non-injection plane, of the azimuthally fixed streamwise vortex pairs. Meanwhile, the ring vortex about the injection plane (vortex B in figure 15) moves inwards, catching up with the downstream contorted ring vortex (vortex A in figure 15). The two vortices undergo pairing, engulfing vigorously ambient fluid into the jet core region (figure 14 b, 15 b,d). This greatly amplified engulfment may also act to push out or accelerate the ejection of the mushroom-like structures from the non-injection plane.