jet fire

Qian WenKey Lab of Education Ministry for Power

Machinery and Engineering,

School of Mechanical Engineering,

Shanghai Jiao Tong University,

800 Dongchuan Road,

Shanghai 200240, China

Hyun Dong KimSchool of Mechanical Engineering,

Pusan National University,

Busan 609-735, South Korea

Ying Zheng LiuKey Lab of Education Ministry for

Power Machinery and Engineering,


Shanghai Jiao Tong University,

800 Dongchuan Road,

Shanghai 200240, China

Kyung Chun Kim1


Pusan National University,

Busan 609-735, South Korea

e-mail: [email protected]

Structure Analysis of a LowReynolds Number TurbulentSubmerged Jet InteractingWith a Free SurfaceIn this study, the spatial structures of a submerged turbulent jet interacting with a freesurface were investigated experimentally. The jet axis was located at three differentdepths (H/D¼ 2, H/D¼ 4 and H/D¼ 6) beneath the free surface and the Reynolds num-ber was fixed as 3480. Laser-induced fluorescence technique was used for qualitative vis-ualization and the time-resolved particle image velocimetry technique was used for thequantitative measurements. The dynamics of the flow structures were examined furtherusing the proper orthogonal decomposition analysis technique. The results revealed thatthe dynamic characteristics of large-scale turbulent motions were significantly differentwith the submerged depths. In case of H/D¼ 2, the dominant spatial structures displayeda surface vibration induced reverse flow along the boundary, and its subsequent deflec-tion changed the flow structures in the horizontal center plane. The violent free surfacevibration caused an unsteady up-and-down motion of the flow structures and had a“squeeze effect” on the flow structures. In case of H/D¼ 4, the upwelling motion of somevortices in the jet and their subsequently downward entrainment motion significantlychanged the dominant spatial structures both in the vertical and horizontal centralplanes. When the jet was fully attached to the free surface, the vortical structures under-went a merging and restructuring process due to the vertical confinement of the free sur-face. In case of H/D¼ 6, the dominant spatial structures both in the vertical andhorizontal central planes showed an approximately symmetric pattern, indicating that thedominant structures were not changed by the free surface. After attached to the free sur-face, the jet did not undergo a merging and restructuring process as shown in case ofH/D¼ 4. [DOI: 10.1115/1.4027620]

Keywords: submerged turbulent jet, free surface, time-resolved PIV, POD, dynamicstructures

1 Introduction

A submerged jet interacting with a free surface occurs in manyindustrial areas such as discharging wastewater into a shallowbody of water or a jetlike stream coming into a water reservoir,where an understanding of the turbulent structure is essential foroptimizing the discharge characteristics. In addition, the recentadvances in remote sensing technology are expected to allowworldwide monitoring of maritime traffic in the future. Techni-ques such as the synthetic aperture radar are capable of detectingthe free surface disturbances created by a ship’s turbulent wake[1,2]. Therefore, the understanding of the behavior of turbulent jetadjacent to a free surface is of considerable interest to the remotedetection of the ship’s wake since this flow configuration incorpo-rates many of the vortical interactions encountered in the turbulentship wake problem. On the other hand, due to the great complex-ity and variety of the phenomena observed, there is a lack ofunderstanding of the nature of the interaction of turbulent jet flowwith a free surface. Thus far, an experimental study on a sub-merged jet interacting with a free surface is needed to obtain acomprehensive understanding of this problem.

An early experimental investigation of the interaction of a sub-merged jet with the free surface was conducted by Evans [3]. Herevealed the calming effect on surface waves caused by the sur-face currents produced by the jet. Although Evans did not exam-ine the turbulent flow structures in detail, he showed that when the

waves and surface currents move in the same direction, the waveamplitude is decreased but the wavelength is increased. Rajarat-nam and Humphries [4] examined the scaling behavior of themean flow field of turbulent, nonbuoyant surface jets, and Rajarat-nam and Subramanyan [5] investigated the behavior of planarbuoyant surface jets. Swean et al. [6] reported the measurementsof the mean velocities and turbulent fluctuations in a two-dimensional turbulent jet at a free surface. They found that thegrowth rates of the length and velocity scales resemble moreclosely those observed in wall jets than those in free jets. Thework by Bernal and Kwon [7] on the vortex-ring problem pro-vided the first convincing evidence that a vortex tube will discon-nect in the vicinity of the surface and reconnect to the surface, andsubsequent important studies of Gharib and Weigand [8] on theinteraction of a vortex ring with a free surface presented a clearpicture of the stages that were involved in the early disconnectionand subsequent connection process.

Anthony and Willmarth [9] examined the mean velocity fieldand Reynolds stress tensor of a turbulent jet issuing from a circu-lar nozzle beneath and parallel to the free surface using a three-component laser Doppler velocimetry (LDV). They reported thatthe turbulent fluctuations normal to the free surface were dimin-ished, whereas those parallel to the surface were enhanced. Theyalso reported the existence of a flow outward, away from the jetaxis in a thin layer near the surface. Based on the flow visualiza-tion results, they showed that this outward flow or “surfacecurrent” consisted mainly of vortical structures ejected from thejet. Within the surface current, turbulent mixing was reducedgreatly. Madnia and Bernal [10] examined the same flow over awide range of Reynolds and Froude numbers using flow

1Corresponding author.Contributed by the Fluids Engineering Division of ASME for publication in the

JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 15, 2013; final manuscriptreceived May 4, 2014; published online July 24, 2014. Assoc. Editor: Peter Vorobieff.

Journal of Fluids Engineering OCTOBER 2014, Vol. 136 / 101104-1Copyright VC 2014 by ASME

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visualization and single-component hot-film measurements. Usingthe shadowgraph method, they reported that significant surfacedisturbances occurred, where the large-scale structures in the jetfirst interact with the free surface. These surface disturbances formapproximately planar waves with a symmetrical pattern. They alsonoted the appearance of dark circular features in the shadowgraphimages, which they attributed to vortex line reconnection processes.Walker et al. [11] examined the Reynolds number and Froude num-ber effects on the lateral surface currents, jet spreading rates, turbu-lence kinetic energy redistribution and other phenomena in detail,and Walker [12] subsequently determined the origin of the “surfacecurrent.” Tsai and Yue [13] and Sarpkaya [14] concentrated on thedamping and modification of turbulence by surfactants.

More recently, Judd et al. [15] examined the thermal signatureof a low Reynolds number surface jet using high resolution infra-red methods. In their experiments, the temperature of the fluidissuing from the jet was higher than the fluid in the water tank.Shinneeb et al. [16] examined the coherent structures in shallowwater jets using the particle image velocimetry (PIV). Tian et al.[17] compared the characteristics of a round turbulent jet in the vi-cinity of a free surface with a free jet. They compared the meanvelocity, turbulent intensity, Reynolds shear stress and other sta-tistical variables of the surface jet and free jet.

Previous studies were limited to the mean characteristics of theinteraction of a jet with a free surface and few works were con-ducted with appropriate time and space resolution. The work byBernal and Kwon [7] and later by Gharib and Weigand [8] pre-sented the dynamic interaction process of the simple vortex ringwith a free surface. Kim et al. [18] demonstrated that the free sur-face sloshing motion interacted with bubble driven liquid flowincreased turbulent kinetic energy and turbulent mixing substan-tially in their time-resolved PIV measurement and proper orthogo-nal decomposition (POD) analysis. But until now, the dynamicinteraction process of a submerged turbulent jet with a free sur-face did not reported as the authors aware of and detailed experi-mental data with appropriate time and space resolution is highlyneeded. Toward this end, the present study examined the charac-teristics of the interactions of jet flow with a free surface, and ana-lyzed the large-scale dynamic structures using time-resolved PIVand POD techniques. Laser-induced fluorescence visualizationswere also used to obtain a first-hand look at the most interestingand intuitive flow changes associated with the interaction of thesubmerged jet with the free surface. In the present investigation,we examined the interaction of the submerged jet with the freesurface for three different depths of the jet below the surface toobtain a comprehensive understanding of this problem.

Fig. 1 Schematic diagram of the experimental setup and measurement section.(a) Experimental setup and coordinate system and (b) measurement section of thetime-resolved PIV.

101104-2 / Vol. 136, OCTOBER 2014 Transactions of the ASME


2 Experimental Setup

2.1 Experimental Apparatus. The experiments were carriedout in a recirculating system. Figure 1(a) shows a schematic dia-gram of the facility. The facility consisted of a free-surface tank,an overhead reservoir tank, a pump and associated piping and con-trol valves. The free-surface tank, 600 mm long, 600 mm wide and400 mm deep, was constructed from acrylic and raised 800 mmabove the laboratory floor to provide optical access through thebottom of the tank. A sluice gate was placed at one end of the fa-cility to maintain a constant water depth in the tank. A stainlesssteel circular pipe was machined and mounted on the side of thetank opposite the sluice gate, and used as a jet nozzle in this study.The pipe has an inner diameter of 4 mm (external diameter of5 mm) and a length of 280 mm (70 D). The flow at the exit wasfully developed at this length-diameter ratio. An acrylic attach-ment on the left side of the tank was used to avoid the cantilevereffect of the pipe. In this study, the axis of the jet was placed at aconstant depth but the height of the sluice gate was variable. Inthis condition, we can change the submerged depths of the jet.The jet was supplied from an overhead reservoir tank under theaction of gravity, and the reservoir was maintained at constanthead using a pump and two sluice gates. Three different depths(H¼ 2 D, 4 D, and 6 D) of the jet below the surface were exam-ined to obtain a comprehensive understanding of the depth effect.The Reynolds number based on the jet diameter and the nozzleexit velocity was kept 3480 in all experiments. Therefore, the sub-merged jet studied in this work was a low Reynolds number turbu-lent flow. In Fig. 1(a), the origin of the coordinate system was atthe center of the nozzle exit and x was the axial direction alongthe flow direction. The surface-normal direction was denoted asthe z axis, positive upward. The transverse, or horizontal, coordi-nate was y and the positive direction was defined using the righthand rule.

2.2 Flow Visualization and Time-Resolved PIV. For flowvisualizations, LIF technique using Rhodamine B was used toobtain a qualitative understanding of the subsurface interaction.The maximum excitation wavelength of the Rhodamine B wasapproximately 555 nm, and its emission wavelength was approxi-mately 580 nm. A laser beam, 5 mm in diameter, originating froma 532-nm 3 -W CW laser, was passed through a spherical lens anda cylindrical lens, and turned into a thin laser sheet (�1 mm inthickness). The laser plane was oriented in the vertical centralplane of the jet. A 12 bit high-speed complementary metal oxidesemiconductor (CMOS) camera (Full resolution: 1024� 1024pixels, Photron, Fastcam SA1.1) was used with a 545 nm long-pass optical filter mounted on its lens.

The velocity fields were measured using a typical two-dimensional time-resolved PIV system. The PIV measurementswere carried out along the centerline of the jet in the vertical plane(x-z) as well as in the horizontal plane (x-y). Figure 1(b) showsthe field-of-view of the time-resolved PIV measurement regions.In case of H/D¼ 2, two overlapping fields-of-view (FOV1 andFOV2), each measuring a length of approximately 12D, were cho-sen to obtain the time-resolved PIV measurements in the verticalcenter plane. In cases of H/D¼ 4 and H/D¼ 6, three overlappingfields-of-view (FOV1, FOV2, and FOV3) were chosen in the ver-tical center plane since the interaction of the jet with the free sur-face occurred in the far field as the depths increased. On the otherhand, the field-of-view was same in the horizontal central planefor each depth. This study was interested in those dynamic struc-tures in the regions where significant interactions occur. For thisreason, the measurement sections included the significant interac-tion region as well as a certain distance before the interactionoccurred, instead of starting from the nozzle exit. The measure-ment section in the vertical central plane began from X/D¼ 6downstream of the jet exit. On the other hand, the measurementsection in the horizontal plane began from X/D¼ 16 and covereda region of 13 D. In the present time-resolved PIV experiments,

the high-speed camera and the laser system were the same as thatused in LIF. The tap water in the facility was seeded with 10 lmhollow glass spheres with a density of 1.04 kg/m3. The camerawas operated at 1024� 752 pixels, 1024� 896 pixels and1024� 1024 pixels in the vertical central plane for the case of H/D¼ 2, H/D¼ 4 and H/D¼ 6, respectively. The region we chose inthe surface-normal (z) direction was wide enough to contain thejet boundary for each case. The framing rate was 4000 Hz for eachcase in the vertical plane. At each field-of-view in the verticalplane of the case H/D¼ 2, 14,000 image frames were acquiredand stored in the camera’s internal memory (16 GB) successively.The ensemble size of each field-of-view in the vertical plane ofthe case H/D¼ 4 was 12,000 and a corresponding size of 10,800for the case of H/D¼ 6. On the other hand, the camera was oper-ated at 1024� 1024 pixels with the same framing rate in the hori-zontal central plane for all the experiments and 10,000 imageframes were acquired successively for each field-of-view. Theinterrogation window size was 24� 24 pixels with 50% overlap,which yielded a measurement grid of velocity vectors with a spac-ing of 0.57 mm� 0.57 mm in the vertical central plane for all thecases and a spacing of 0.61 mm� 0.61 mm in the horizontal cen-tral plane for all the cases. The standard cross correlation algo-rithm, in combination with window offset [19], sub-pixel

Fig. 2 LIF images. (a) A region covered X/D 5 13–29 for H/D 5 2,(b) A region covered X/D 5 21–37 for H/D 5 4, and (c) a regioncovered X/D 5 21–37 for H/D 5 6.

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recognition by Gaussian fitting [20] and sub-region distortion, wasused to improve the signal-to-noise ratio.

3 Results and Discussions

3.1 Flow Visualization. Prior to the detailed structure analy-sis of the jet interacting with the free surface, a first-hand look atthe most interesting and intuitive flow changes were gained fromthe laser-induced fluorescence visualizations. Figure 2 shows theLIF results. In each figure, the flow moved from left to right, andthe red line represented the free surface. The resolution of thesethree images is same but the area shown in the image is differentbecause the jet attachment occurred in the far field in the case ofH/D¼ 4 and H/D¼ 6. In case of H/D¼ 2, shown in Fig. 2(a), the

jet approached the free surface in the near-field and subsequentlythe significant interaction happened, resulting in large-amplitudefree surface vibration. The large-amplitude downward motion hada “squeeze effect” on the subsurface jet flow and pushed the fluidaway. Due to the great complexity of the interaction process andthe propagation of the surface waves, the free surface does notoscillate in a harmonic manner. The free surface oscillated with alarge-amplitude in the region where initial interaction happenedand the surface deformation decreased as the downstream distanceincreased. Figure 2(b) shows the LIF results of H/D¼ 4. Thevibration amplitude reduced obviously in this case compared tothe case H/D¼ 2. In this case, the free surface oscillated with asmall-amplitude. From Fig. 2(b), one can recognize some vorticalstructures were stretched as the jet boundary interacting with thefree-surface. Due to the confinement in the vertical direction, dif-ferent vortical structures began to merge with each other to formlarger structures in the far field. The turbulence in the far fieldcould be restructured and quasi-two-dimensionalized by the freesurface (faster damping of the vertical component of turbulence).Moreover, the merging of vortices shifts the size distributiontowards larger structures and may give rise to a reverse energycascade [14]. Figure 2(c) shows a nearly symmetric pattern, butthe shear vortices in the jet boundary will be rebounded by themirrorlike free surface in the very far-field and its subsequentlyentrainment motion may have some effect on the main flow. Inthis case, the free surface behaves as an imperfect mirror withsome unsteady oscillation caused by the weak impingement of theshear vortices in the jet boundary and some small shed turbulentpatches.

3.2 Time-Resolved PIV Measurements. A preliminaryimpression of the interaction characteristics of a submerged jetwith a free surface was gained by examining the time-averagedflow pattern. Figure 3 shows the normalized mean streamwise ve-locity contour and vector profiles in the vertical central plane,where Uc is the centerline velocity at the respective X/D location

Fig. 4 Vertical profiles (on the vertical central plane) of thestreamwise mean velocity at X/D 5 28. The vertical dashed lineindicates the position of the jet centerline.

Fig. 3 Normalized mean streamwise velocity contour and vector profiles, Uc is thecenterline velocity at the respective X/D location. (a) H/D 5 2, (b) H/D 5 4, and (c) H/D 5 6.



Fig. 5 First four eigenmodes of H/D 5 2 on the vertical central plane. (a) 1st mode,(b) 2nd mode, (c) 3rd mode, and (d) 4th mode.

Fig. 6 A dynamic plot of the instantaneous flow field reconstructed by the firstfour eigenmodes (H/D 5 2 vertical central plane)

Table 1 POD information

Vertical central plane Horizontal central plane

POD domain Acquisition time POD domain Acquisition time

H/D¼ 2 X/D � 16–26 2.7 s X/D � 16–26 2.5 sH/D¼ 4 Part I X/D � 16–26 Part II X/D � 26.5–36.5 Part I 2.7 s Part II 2.7 s X/D � 16–26 2.5 sH/D¼ 6 Part I X/D � 16–26 Part II X/D � 26.5–36.5 Part I 2.7 s Part II 2.7 s X/D � 16–26 2.5 s



and the field-of-views were merged to obtain a continuous flowfield visually. The axial length of the laminar or transitionalregion before the turbulent flow in the case of H/D¼ 2 was shorterthan the results in other two cases, as shown in Fig. 3. The violent

free surface vibration in the initial strong interaction region andits subsequently upstream and downstream propagation increasedthe instability of the jet flow in the near field, which can be usedto explain the earlier spreading in the case of H/D¼ 2. The salient

Fig. 7 First four eigenmodes of H/D 5 2 on the horizontal central plane. (a) 1stmode, (b) 2nd mode, (c) 3rd mode, and (d) 4th mode.

Fig. 8 A dynamic plot of the instantaneous flow field reconstructed by the firstfour eigenmodes (H/D 5 2 horizontal central plane)



Fig. 9 First four eigenmodes of H/D 5 4 (Part I) on the vertical central plane. (a) 1st mode, (b)2nd mode, (c) 3rd mode, and (d) 4th mode.

Fig. 10 First four eigenmodes of H/D 5 4 (Part II) on the vertical central plane. (a) 1st mode, (b)2nd mode, (c) 3rd mode, and (d) 4th mode.



Fig. 11 A dynamic plot of the instantaneous flow field reconstructed by the first foureigenmodes (H/D 5 4 vertical central plane, Part I)

Fig. 12 A dynamic plot of the instantaneous flow field reconstructed by the first foureigenmodes (H/D 5 4 vertical central plane, Part II)



Fig. 13 First four eigenmodes of H/D 5 4 on the horizontal central plane. (a) 1st mode, (b) 2ndmode, (c) 3rd mode, and (d) 4th mode.




feature of the time-averaged field was the vector profiles began toshift to the free surface and the maximum velocity was no longerlocated at y/d¼ 0, but moved toward the free surface rapidly asthe depths decreased. This behavior of the surface jet was consist-ent with the results reported by Anthony and Willmarth [9]. Inorder to better illustrate this point, the profile of the streamwisemean velocity in the vertical central plane at X/D¼ 28 is shownin Fig. 4. In the case of H/D¼ 2, the jet flow already attached tothe free surface and was developed at X/D¼ 28, so the velocityprofile showed an obvious shift to the free surface and the maxi-mum velocity was located towards the free surface. In the case ofH/D¼ 4, the jet flow attached to the free surface and was develop-ing at X/D¼ 28. Though the maximum mean streamwise velocityacross the profile was almost located at the jet centerline, the mag-nitude of the velocity profile in the portion close to the free sur-face was higher than that of the lower portion of the jet. In thedeepest case, the jet flow was about to attach to the surface at thislocation, the velocity profile showed a similar trend as shown inthe profile of H/D¼ 4, but the velocity profile in this case spread alittle faster.

3.3 POD Analysis. Dynamic information of the flow fieldcan be explained effectively by the POD, from which the relativeenergy distribution is acquired. Using the POD technique pro-posed by Lumley et al. [21], the flow field can be decomposedinto the optimal orthogonal spatial modes and optimal orthogonaltemporal modes. Before showing the POD results, the PODmethod used in the present study is briefly introduced. The generalgoal of POD is to find the optimal representation of the field

realizations, which leads to a Fredholm integral equation of theso-called classical POD,

ðR x; x0ð Þ/ x0ð Þdx0 ¼ k/ xð Þ (1)

Here, R(x, x0) is the two-point correlation matrix of realizations ofthe random field,

R x; x0ð Þ ¼< u xð Þu � x0ð Þ > (2)

The operator <…> and * denotes ensemble average and complexconjugate, respectively. The eigenvalue kn of Eq. (1) has a finiteset of eigenfunctions /n xð Þ (n¼ 1,…N) (N is the number of gridpoints of each flow realization), which are then used to reconstructthe original flow field. To reduce the computational effortinvolved in solving the above-mentioned eigenvalue problem, thesnapshot POD method [22] was adopted in present study to pro-cess the PIV data.

Table 1 gives the detailed information of the present POD anal-ysis. The time interval between two snapshots was 1/2000 s foreach case. An acquisition time of 2.7 s was chosen, correspondingto a number of snapshots N1¼ 5400 in the vertical plane for allcases. On the other hand, an acquisition time of 2.5 s was chosen,corresponding to a number of snapshots N1¼ 5000 in the horizon-tal plane for all cases. The ensemble size of the POD analysis wastested to be sufficient for providing statistically converged results.Figure 5 shows the first four spatial modes in the vertical plane, atH/D¼ 2. They represent the dynamics of large-scale motion in thefree surface jet flow. The first spatial mode in Fig. 5(a) contains

Fig. 15 First four eigenmodes of H/D 5 6 (Part I) on the vertical central plane. (a) 1st mode, (b)2nd mode, (c) 3rd mode, and (d) 4th mode.



the largest turbulent kinetic energy and shows the spreading andentrainment trend, which is the intrinsic feature in a jet flow. Theupward spreading motion of the jet flow and the subsequentlyimpingement caused the violent free surface vibration in the near-field. In the far-field, the portion close to the free surface showeda weak reverse flow trend, indicating the surface ‘push awayeffect’ on the jet flow due to the free surface vibration in thisregion. When the reverse flow met the main spreading flow, itsflow direction was changed and began to move downward andeventually was merged into a stream with the main spreading flowin the lower portion of the jet. The second spatial mode inFig. 5(b) is highly correlated with the first spatial mode and showsthe same large-scale structures, except for a shift in phase. Themost important feature of the third mode in Fig. 5(c) is that a largeclockwise vortex appears at the left side free surface, which canbe attributed to the formation of the secondary vortex in the regionwhere the free surface was strongly distorted [8]. The fourth spa-tial mode shows the long-narrow elliptical structures near the sur-face, indicating a “squeeze effect” of the surface boundary on theflow structures.

To better reveal the evolution of dominant structures in the ver-tical plane, a dynamic plot of the instantaneous fluctuating flowfield reconstructed by the first four eigenmodes is shown in Fig. 6.The four reconstructed flow fields revealed a typical interactionprocess of the large-scale structures in the surface jet with the freesurface and contained different free surface boundary conditions.For better understand the interaction process, the original PIVboundary image was also shown together with the correspondingreconstructed field. In Fig. 6(a), the free surface has violent vibra-tion and a pair of valley and peak can be identified easily. The sa-lient feature of the reconstructed fluctuating flow fields is thestrong downward reverse flow just beneath the surface depressionregion in the near field. The strong free surface downward motionpushed the surrounding fluid away and gave rise to the downwardreverse flow trend, and subsequently it encountered with the mainjet flow and forced the main flow to change its direction. In addi-tion, a small vortex was induced due to the changing of main flowdirection. In Fig. 6(b), the valley and peak identified in Fig. 6(a)were transferred to downstream and a new peak appeared at theleft side due to the convection of the large-scale structures. The

Fig. 16 First four eigenmodes of H/D 5 6 (Part II) on the vertical central plane. (a) 1st mode, (b)2nd mode, (c) 3rd mode, and (d) 4th mode.



downward reverse flow was also transferred to downstream butthe strength was reduced due to the reduction of surface vibrationenergy. Consequently, the changing of the main flow directionwas not so obvious compared to the results in Fig. 6(a) and theinduced vortex became larger. As the convection proceeding, thevalley and peaks were transferred further downstream and the am-plitude of the surface vibration decreased obviously in Fig. 6(c).Due to the rapidly decreasing of surface vibration energy, the freesurface downward motion caused reverse flow became weakerand its flow direction was changed by the main jet flow and beganto move downward and eventually was merged into a stream withthe main spreading flow in the lower portion of the jet. InFig. 6(c), the jet flow in the near-field kept its flow direction andshowed a spreading trend, causing the surface elevation. The mainflow direction in Fig. 6(d) was approximate parallel to the stream-wise direction since the free surface behaved as a flat surface atthis moment and consequently the upward spreading was limitedcompared to the situation revealed in Fig. 6(c). The initial inducedvortex in Fig. 6(a) developed into a long-narrow vortex inFig. 6(d). The four reconstructed fluctuating flow fields possessvarying degree free surface deformations, demonstrating that thefree surface oscillates in an unpredictable nonharmonic pattern.

Figure 7 shows the first four dominant spatial modes in the hori-zontal central plane, at H/D¼ 2. The jet spreading and entrain-ment motion was not obvious in the first spatial mode, only couldbe identified in a short distance at the left side. From the precedingdiscussion it was clear that the large-scale surface-parallel struc-tures moved up-and-down randomly due to the violent free sur-face oscillation and consequently destroyed the normal jetspreading motion in the horizontal central plane. Moreover, thereverse flow which was revealed in the first spatial mode in the

vertical plane and its subsequently downward motion alsochanged the structures in the horizontal central plane. The secondspatial mode in Fig. 7(b) shows the similar large-scale structuresas is shown in Fig. 7(a) with a phase difference. Figures 7(c) and7(d) show the third and fourth eigenmodes, which reveal that thelarge-scale structures become smaller. Figure 8 shows a dynamicplot of the instantaneous fluctuating flow field reconstructed bythe first four eigenmodes in the horizontal planes. Unlike theresults in the vertical central plane, the convection of the large-scale structures showed the discontinuities compared to the resultsin the vertical plane. Because the surface-parallel structures in thevertical plane have random up-and-down motion and frequentlydestroy the structures in the horizontal central plane, the vorticalstructures will “disappear” from the horizontal central plane andshow the discontinuities during the convection.

Figure 9 shows the first four spatial modes in the vertical plane,at H/D¼ 4 (Part I). In Fig. 9(a), a large counterclockwise vortexwas found near the free surface and it had a weak push-downeffect on the jet flow in the near-field. The surface jet has anupwelling trend due to the effect of the free surface, so some shearvortex rise up, are rebounded by the free surface, entrain the sur-rounding fluid and eventually affect the main flow. The first spa-tial mode revealed a weak interaction process of the reboundingstructures with the main flow. On the other hand, when the risingstructures have a relatively high energy, they will entrain the sur-rounding structures rapidly and become very large rotating vortexand strongly affect the flow structures. The second spatial mode inFig. 9(b) represented a strong interaction process of large-scalestructures with the main flow. The most remarkable feature inFig. 9(b) was a very large vortex appears near the free surface andspan to the lower portion of the jet. Due to its existence, the

Fig. 17 A dynamic plot of the instantaneous flow field reconstructed by the firstfour eigenmodes (H/D 5 6 vertical central plane, Part I)



topology of the flow field was totally changed. The third spatialmode in Fig. 9(c) was correlated with the second mode with aphase difference. The large-scale structures became smaller in thefourth spatial mode and several small-scale vortices wereobserved in the far-field.

Figure 10 shows the first four spatial modes in the far-field inthe vertical plane, at H/D¼ 4 (Part II). The jet flow in this regionwas fully attached to the free surface. A large vortex across thewhole upper half of the jet was observed in Fig. 10(a), indicatingthat the first spatial mode was related to the merging and restruc-tured process of the vortical structures. The second spatial modeshowed the similar large-scale structures and was also related tothe merging process. We conjectured that turbulence field mightbe restructured and quasi-two-dimensionalized by the free surface(faster damping of the vertical component of turbulence). In addi-tion, the merging of like-sign vortices shifted the size distributiontowards larger structures and gave rise to a reverse energy cascade[14]. The vortical structures in the third and fourth modes inFigs. 10(c) and 10(d) became smaller compared to the first twomodes.

Figure 11 shows a dynamic plot of the flow field reconstructedby the first four eigenmodes in the vertical plane (Part I, H/D¼ 4).The four reconstructed instantaneous flow fields revealed theinteraction process of the rebounding structures with the mainflow. In Fig. 11(a), a weak vortex was forming since the risingvortex entrained the surrounding fluids and this developing vortexhad a weak effect on the main flow at this moment. In Fig. 11(b),the vortex became larger and began to entrain the fluids in themain flow due to the confinement in the vertical direction. As aresult, the main flow direction was significantly altered. As theconvection proceeding, this rebounding vortex became even largerand span across the whole upper portion of the jet, as is shown inFig. 11(c). The portion above the jet centerline was rolled up andthe lower portion of the jet was pushed down. As the large vortextransferred to the far-field, it began to stretch as is shown in Fig.11(d). The main flow continuously rolled up and pushed up thevortex, resulting in the stretching and deformation of the vortex atthe free surface. The procedures described above occur frequentlyin the surface jet and sometimes the initial upwelling vortex con-tains relatively high energy, which will totally change the

Fig. 18 A dynamic plot of the instantaneous flow field reconstructed by the first four eigenmo-des (H/D 5 6 vertical central plane, Part II)



topology of the flow field in a short time. Figure 12 shows the con-vection of large-scale structures in the far-field (Part II, H/D¼ 4).Figure 12(a) shows two large-scale vortices, making a counter-rotating vortex pair. In Fig. 12(b), the counter-rotating vortex pairwas transferred to downstream and a new counterclockwise vortexappeared at the left side. As the convection proceeding, a newclockwise vortex was developing at the left side. In Fig. 12(d), theformer counter-rotating vortex pair disappeared from the field ofview and a new vortex pair appeared at the same position. Twofeatures of the large-scale vortex must be mentioned here, the sizeand the orientation. The size of the vortex spans across the wholeupper half and the vortices are orientated almost in a line, indicat-ing that there is a merging and restructured process during theinteraction of the jet flow with the free surface.

As discussed above, the upwelling motion of the surface jet andthe subsequent large surface-parallel vortex revealed in Figs. 9and 11 totally changed the flow structures in the vertical plane(Part I). Therefore there must be a corresponding change of the to-pology of the flow field in the horizontal central plane. Figure 13shows the first four spatial modes in the horizontal central plane,at H/D¼ 4. In Fig. 13(a), the first spatial mode was separated intotwo parts. Two large vortices appeared at the right side, making acounter-rotating vortex pair. The left side showed the jet spread-ing motion. If we think of the surface-parallel vortex revealed inFigs. 9 and 11, then it is easy to understand that the spatial struc-tures in Fig. 13(a) is associated with the rotating motion of thelarge-scale surface-parallel vortex. The large rebounding vortex,shown in Fig. 11, passed through the horizontal central plane andseparated the flow structures. The second and third spatial modein Figs. 13(b) and 13(c) both show a very large vortex, which isassociated with the entrainment motion of the large-scale surface-parallel vortex. The size of vortical structure became smaller inthe fourth spatial mode.

To clarify how the surface-parallel vortex affects the flow fieldin the horizontal central plane, a dynamic plot of the reconstructedfield is given in Fig. 14. In Fig. 14(a), we conjectured that asurface-parallel vortex reached the horizontal central plane. Thearrival of the vortex pushed away the fluid in the near-field andcompelled the jet to change the direction of propagation. More-over, the entrainment motion of the surface-parallel vortexinduced two large vortices at the right side. In Fig. 14(b), thestrength of the surface-parallel vortex increased and the vortexpassed through the horizontal plane, resulting in a reverse flowalong the jet centerline in the near-field. As the convection pro-ceeding, the induced structures and the reverse flow were trans-ferred downstream, shown in Fig. 14(c). In Fig. 14(d), the surface-parallel vortex may begin to stretch and its effect on the horizontalcentral plane reduced. The preceding reverse flow merged into thespreading flow and the large vortex began to tilt at the right side.

Figure 15 depicts the first four spatial modes in the verticalplane, at H/D¼ 6 (Part I). The first spatial mode showed anapproximately symmetric spreading pattern since the free surfaceeffect in this region was weak at this depth. The second spatialmode was also related to the large-scale motion in the jet flow.The third and fourth spatial modes showed the well-organizedvortical structures, but the size of these structures became smallercompared to the first two modes. Figure 16 shows the first fourspatial modes in the far-field in the vertical plane, at H/D¼ 6 (PartII). Unlike the H/D¼ 4 case, the jet at this depth did not fullyattach to the free surface and, therefore, the eigenmodes showedthe different spatial structures. The first spatial mode in Fig. 16(a)showed a large vortex across the jet centerline. The second spatialmode displayed two large vortices, one was located near the cen-terline and the other one appeared in the upper half. Another sa-lient feature of the second spatial mode was the reverse flow at theright side. The notable feature in the third spatial mode was a

Fig. 19 First four eigenmodes of H/D 5 6 on the horizontal central plane. (a) 1st mode, (b) 2ndmode, (c) 3rd mode, and (d) 4th mode.



large counterclockwise vortex near the surface at the rightside, which is associated with the shear vortex entrainmentmotion. The relatively large shear vortex in the far-field wasrebounded by the mirrorlike free surface, then entrained the sur-rounding fluids and eventually merged into large structures. Thefourth spatial mode showed two large vortex as well as severalsmall vortices.

Figure 17 shows a dynamic plot of the reconstructed flow fieldin the vertical central plane (Part I, H/D¼ 6). Unlike the dynamicplot shown in Figs. 6 and 11, Fig. 17 did not show the evolutionof a certain interaction process with very short time interval. Thefour instantaneous flow fields chosen in Fig. 17 ensured that theflow field structures shown in Fig. 17(a) reappeared in Fig. 17(d).The free surface in this region did not show an obvious effect onthe jet flow. Figures 17(a), 17(c), and 17(d) show an approxi-mately symmetric pattern and Fig. 17(b) shows several organizedvortices. Figure 18 shows a dynamic plot of the reconstructedflow field in the vertical central plane in the far-field (Part II, H/D¼ 6). The four instantaneous flow fields depicted the convectionof the large-scale structures. Unlike the results in Fig. 12, wherethe merging and restructured process occurred in the upper halfdue to the relative strong interaction, the vortex were not orien-tated in a line in this case and were distributed obliquely.

Figure 19 displays the first four spatial modes in the horizontalplane, at H/D¼ 6. Unlike the spatial modes shown in Figs. 7 and13, the first spatial mode in Fig. 19(a) showed the symmetric pat-tern, indicating that the dominant flow structures in the horizontalcentral plane were not changed at this depth. The second spatialmode in Fig. 19(b) also showed the symmetric pattern which isrelated to the large-scale motion. Figures 19(c) and 19(d) showthe third and fourth spatial mode which revealed that the large-scale structure became smaller throughout the turbulent energy-cascading process. Figure 20 shows a dynamic plot of the recon-structed flow field in the horizontal central plane at H/D¼ 6. Thefour instantaneous reconstructed flow fields showed the approxi-mately symmetric flow pattern, demonstrating the flow structureswere not changed by the free surface in this region.

4 Conclusions

Dynamic structures in the free-surface jet flows were examinedusing the time-resolved PIV technique and Laser-induced fluores-cence technique at three different depths. The measured flow fieldwas later decomposed by the time-resolved POD technique, whichexposed the large-scale structures buried in the surface jet. Eventhough the time-averaged mean flow fields show similar flow pat-terns for all depths, the dynamic characteristics of large-scale tur-bulent motions are significantly different with respect to thedifferent depths. The major conclusions of the study are summar-ized below:

(i) In the case of H/D¼ 2, dynamic structures in the verticaland horizontal central planes were investigated in theregion of X/D � 16–26, where the surface jet was alreadyfully attached to the free surface and strongly deformedthe free surface. The large-scale turbulent motions arechanged in the vertical central plane as well as in the hori-zontal central plane. In the vertical central plane, the firsttwo spatial modes depict the surface vibration inducedreverse flow along the boundary, and its subsequentdeflection will change the flow structures in the horizontalcentral plane. Due to the strongly free surface distortion inthe near-field, the secondary vortex may appear in thisregion. The long-narrow structures in the fourth spatialmode shows the “squeeze effect” of the free surface on thelarge-scale structures. The convection of large-scale struc-tures reveals that the flow structures have up-and-downmotion due to the violent free surface vibration. The topol-ogy of the flow field in the horizontal central plane istotally changed by the unsteady up-and-down motion ofthe surface-parallel structures and the abovementionedsurface vibration induced reverse flow. The time-averagedflow field shows an obvious upwelling motion and themaximum velocity is located towards the free surface.

(ii) In the case of H/D¼ 4, dynamic structures in the verticalplane were investigated in two regions. In Part I, though




the time-averaged flow field shows that the jet reached thefree surface at around X/D¼ 24, the large-scale turbulentmotions are significantly changed, which is associatedwith the upwelling motion of some vortices in the jet andtheir subsequently downward entrainment due to the con-finement in the vertical plane. In Part II, the jet is fullyattached to the free surface, and the vortical structuresundergo a merging and restructured process in the upperhalf of the jet. In the horizontal central plane, dynamicstructures in the same streamwise region as Part I in thevertical plane were investigated. The flow structures arealso changed due to the abovementioned vortex in part I inthe vertical plane.

(iii) In the case of H/D¼ 6, dynamic structures in the samestreamwise regions as H/D¼ 4 were investigated. In PartI, the dominant structures are not significantly changedand show an approximately symmetric pattern. The domi-nant structures in the corresponding horizontal centralplane also show an approximately symmetric pattern. InPart II, the jet does not undergo a merging and restructuredprocess as shown in the case of H/D¼ 4, because the dis-tance from jet axis to the free surface increased and theinteraction became weaker. The rebounding vortex alsoshows the downward entrainment motion but does not sig-nificantly change the dominant structures.

Acknowledgment

This study was supported by the National Research Foundationof Korea (NRF) Grant funded by the Korea Government (MSIP)through GCRC-SOP (No. 2011-0030013) and KETEP(No. 20112010100030-12-2-300) and a Grant (No. 51176108) fromthe National Natural Science Foundation of China (NSFC).

Nomenclature

D ¼ nozzle diameterFOV ¼ field-of-view

H ¼ depth to jet axisL ¼ length of pipe

LDV ¼ laser Doppler velocimetryLIF ¼ laser induced fluorescencePIV ¼ particle image velocimetry

POD ¼ proper orthogonal decompositionUc ¼ local centerline velocityX ¼ streamwise coordinate

Y ¼ transverse coordinateZ ¼ vertical coordinate

References[1] Reed, A. M., Beck, R. F., Griffin, O. M., and Peltzer, R. D., 1990,

“Hydrodynamics of Remotely Sensed Surface Ship Wakes,” Trans. Soc. Nav.Archit. Mar. Eng., 98, pp. 319–363.

[2] Reed, A. M., and Milgram, J. H., 2002, “Ship Wakes and Their Radar Images,”Ann. Rev. Fluid Mech., 34, pp. 469–502.

[3] Evans, J. T., 1955, “Pneumatic and Similar Breakwaters,” Proc. R. Soc. Lon-don, Ser. A, 231, pp. 457–466.

[4] Rajaratnan, N., and Humphries, L. A., 1984, “Turbulent Non-Buoyant SurfacesJets,” J. Hydraul. Res., 22, pp. 103–115.

[5] Rajaratnan, N., and Subramanyan, S., 1985, “Plane Turbulent Buoyant SurfaceJets,” J. Hydraul. Res., 23, pp. 131–146.

[6] Swean, T. F., Ramberg, S. E., Plesniak, M. W., and Stewart, M. B., 1989,“Turbulent Surface Jet in Channel of Limited Depth,” J. Hydraul. Engng., 115,pp. 1587–1606.

[7] Bernal, L. P., and Kwon, J. T., 1989, “Vortex Ring Dynamics at a FreeSurface,” Phys. Fluids A, 1(3), pp. 449–451.

[8] Gharib, M., and Weigand, A., 1996, “Experimental Studies of Vortex Discon-nection and Connection at a Free Surface,” J. Fluid Mech., 321, pp. 59–86.

[9] Anthony, D. G., and Willmarth, W. W., 1992, “Turbulence Measurements in aRound Jet Beneath a Free Surface,” J. Fluid Mech., 243, pp. 699–720.

[10] Madnia, C. K., and Bernal, L. P., 1994, “Interaction of a Turbulent Round JetWith the Free Surface,” J. Fluid Mech., 261, pp. 305–332.

[11] Walker, D. T., Chen, C. Y., and Willmarth, W. W., 1995, “Turbulent Structurein Free-Surface Jet Flows,” J. Fluid Mech., 291, pp. 223–261.

[12] Walker, D. T., 1997, “On the Origin of the ‘Surface Current’ in Turbulent Free-Surface Flows,” J. Fluid Mech., 339, pp. 275–285.

[13] Tsai, W., and Yue, D. K. P., 1995, “Effects of Soluble and Insoluble Surfactanton Laminar Interactions of Vertical Flows With a Free Surface,” J. FluidMech., 289, pp. 315–349.

[14] Sarpkaya, T., 1996, “Vorticity, Free Surface, and Surfactants,” Ann. Rev. FluidMech., 28, pp. 83–128.

[15] Judd, K. P., Smith, G. B., Handler, R. A., and Sisodia, A., 2008, “The ThermalSignature of a Low Reynolds Number Submerged Turbulent Jet Impacting aFree Surface,” Phys. Fluids, 20(1), p. 115102.

[16] Shinneeb, A. M., Bugg, J. D., and Balachandar, R., 2011, “Coherent Structuresin Shallow Water Jets,” ASME J. Fluids Eng., 133(3), p. 011203.

[17] Tian, J. H., Roussinova, V., and Balachandar, R., 2012, “Characteristics of a Jetin the Vicinity of a Free Surface,” ASME J. Fluids Eng., 134(1), p. 031204.

[18] Kim, J. S., Kim, S. M., Kim, H. D., Ji, H. S., and Kim, K. C., 2012, “DynamicStructures of Bubble-Driven Liquid Flows in a Cylindrical Tank,” Exp. Fluids,53, pp. 21–35.

[19] Westerweel, J., Dabiri, D., and Gharib, M., 1997, “The Effect of a DiscreteWindow Offset on the Accuracy of Cross-Correlation Analysis of Digital PIVRecordings,” Exp. Fluids, 23, pp. 20–28.

[20] Yasuhiko, S., Nishio, Y., Okuno, T., and Okamoto, K., 2000, “A Highly Accu-rate Iterative PIV Technique Using a Gradient Method,” Meas. Sci. Technol.,11, pp. 1666–1673.

[21] Lumley, J. L., Holmes, P., and Berkooz, G., 1993, “The Proper OrthogonalDecomposition in the Analysis of Turbulent Flows,” Ann. Rev. Fluid Mech.,25, pp. 539–575.

[22] Sirovich, L., 1987, “Turbulence and the Dynamics of Coherent Structures PartI: Coherent Structures,” Quart. Appl. Math, 45, pp. 561–571.



http://dx.doi.org/10.1146/annurev.fluid.34.090101.190252

http://dx.doi.org/10.1098/rspa.1955.0187

http://dx.doi.org/10.1098/rspa.1955.0187

http://dx.doi.org/10.1080/00221688409499387

http://dx.doi.org/10.1080/00221688509499361

http://dx.doi.org/10.1061/(ASCE)0733-9429(1989)115:12(1587)

http://dx.doi.org/10.1063/1.857468

http://dx.doi.org/10.1017/S0022112096007641

http://dx.doi.org/10.1017/S0022112092002891

http://dx.doi.org/10.1017/S0022112094000352

http://dx.doi.org/10.1017/S0022112095002680

http://dx.doi.org/10.1017/S0022112097005181

http://dx.doi.org/10.1017/S0022112095001352

http://dx.doi.org/10.1017/S0022112095001352

http://dx.doi.org/10.1146/annurev.fl.28.010196.000503


http://dx.doi.org/10.1063/1.2981534

http://dx.doi.org/10.1115/1.4003194

http://dx.doi.org/10.1115/1.4005739

http://dx.doi.org/10.1007/s00348-011-1224-x

http://dx.doi.org/10.1007/s003480050082

http://dx.doi.org/10.1088/0957-0233/11/12/303


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