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Turbulence Measurements in a Submerged Jet Near a Free Surface D. Anthony, W. WilImarth, K. Madnia, A. Bernal (The University of Michigan, USA) ABSTRACT The results of two experimental investigations on the flow structure of a circular jet issuing beneath a free surface are presented. The mean flow scaling was determined from velocity measurements made with a hot- film anemometer. The free surface is shown to decrease the decay rate of the maximum velocity in comparison to a free jet. The similarity scaling of the flow is discussed based on a simple model. The mean flow and all components of the Reynolds stress tensor were measured with a three-component LDV system. Measurements beneath a clean free surface show that the mean flow spreads laterally in a shallow surface current, and the turbulent velocity fluctuations become anisotropic as the surface is approached. Flow visualization reveals that the surface current contains fluid structures ejected from the jet, and the current is suppressed with the addition of surface active agents. NOMENCLATURE cl d Similarity constant. Similarity constant. Jet exit diameter. h Jet centerline depth. hm Maximum velocity depth from the free surface. Jet momentum flux. Half velocity width. Streamwise velocity component. Horizontal velocity component. Vertical velocity component. x Streamwise coordinate, positive downstream. Go Streamwise location of virtual origin. Horizontal coordinate, positive for right-handed coordinate system. Vertical coordinate, positive upward. Water density. u w z Po c m z (subscript) Surface. (subscript) Half velocity width measured in y direction. (subscript) Half velocity width measured in z direction. Capital letters are used for mean qualities, primes to denote RMS fluctuations, and overlines to indicate Reynolds stresses, e.g., U. w', INTRODUCTION Synthetic Aperture Radar (SAR) images of ship wakes have generated a great deal of interest in the interaction of turbulent shear flows with a free surface. These images show a dark band along the track of the ship believed to be related, either directly or indirectly, to the interaction of turbulence in the wake with the free surface. The study of a turbulent jet beneath a free surface was undertaken to gain some insight on the interaction of turbulent shear flows with the free surface. The surface signature of a submerged turbulent jet was documented by Bernal and Madnia (19881. They found that the large scale structures in the jet cause surface deformations and the generation of surface waves as they interact with the free surface. Farther downstream, in the region of interaction of the turbulence in the jet with the free surface, persistent surface dimples are observed associated with vortex lines terminating at the free surface. This phenomenon has been studied in detail by Bernal and Kwon (1989) and Kwon (1989) for the case of a vortex ring interacting with a free surface. (subscript) Jet centerline. (subscript) Jet exit. (subscript) Profile maximum. In this investigation we consider the interaction of a submerged jet with the free surface. The flow geometry and coordinates system used is shown schematically in Figure 1. Here we focus on the velocity field beneath the surface. We discuss first the similarity scaling of the mean velocity profiles based on velocity measurements obtained with a hot-film anemometer at several jet 361

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z Ue ~~ - ~- - Figure 1. Schematic diagram of the flow geometry depths. In the second part of the paper the results of measurements of the mean flow and turbulence stresses are presented. These measurements were obtained with a three-component Laser Doppler Velocimeter. SCALING OF THE FREE SURFACE JET Rajaratnam and Humphries (1984) studied the mean flow characteristics of free surface jets when the free surface is located at the edge of the jet nozzle. In their investigation they did not study the free surface motion caused by the jet/free-surface interaction. However they reported a reduction of the mean velocity near the surface at high Froude numbers which was attributed to surface wave generation. Self-similarity was found for the mean velocity profiles. Rajaratnam and Humphries (1984) and more recently Ramberg et al. (1989) have studied two-dimensional free-surface jets. Ramberg et al. noted the pervasive effects of jet confinement in their tank. These confinement effects have been studied by Kotsovinos (1976, 1978~. These effects can lead to breakdown of the similarity scaling laws because of the momentum flux associated with the entrained fluid. Experimental Apparatus The scaling experiments were conducted in a water tank facility consisting of a free surface tank and a jet tank. The free surface tank was made of glass and was 76.2 cm wide, 76.2 cm high and 167.6 cm long. The jet flow was generated by a jet tank located inside the free surface tank. The jet issues from a circular orifice 0.64 cm in diameter located on the side of the tank. A circular-arc-shaped nozzle with radius 1.27 cm provides a smooth transition from the side wall of the tank to the jet exit plane. For the data discussed here the exit velocity was 200 cm/s which gives a Reynolds number of 12,700. Velocity data were obtained using a constant temperature hot film anemometer. A standard TSI quartz coated cylindrical sensor was used in the measurements. The sensor length was 0.51 mm and the diameter 25 ,um. The sensor axis was positioned perpendicular to the flow direction and parallel to the free surface. The hot film was operated at the overheat ratio of 1.09. The output of the anemometer was DC shifted and amplified using a Tektronix AM501 operational amplifier wired as a differential amplifier with a gain of 2.6. The output of the differential amplifier was digitized using a Lecroy 8210 Transient Digitizer. Typical sampling rates used were between 200-800 Hz. The digitized output was then stored on permanent files using an IBM CS9OOO computer. Additional details on the facility and instrumentation can be found in Madnia (1989~. Scaling A simple model is proposed based on dimensional reasoning and similarity concepts which describes the scaling in the far field of the free surface jet. In this model we consider the momentum flux of the jet Jo as well as the momentum flux of an image jet above the surface as shown schematically in Figure 2. Thus the free surface is assumed to be a plane of symmetry for the flow. It is further assumed that the dominant length scale is h, the distance from the jet centerline to the free surface. The jet exit diameter plays an indirect role through its effect on the jet momentum Jo. l 14 ~ ~ Free Surface \ / UmN / Figure 2. Far field scaling of the free surface jet The similarity scaling in the far field of the turbulent axisymmetric jet has been discussed by several authors (e.g., Rajaratnam 1976~. If the jet momentum flux is constant, the linear growth of length scales with downstream distance implies that sufficiently far downstream compared to the jet exit diameter the mean centerline velocity, Um, can be written as: r ~ Po Um 362

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where pO is the fluid density and c is a constant. It follows that for the free surface jet at sufficiently large distance compared to the jet depth h, the maximum velocity Um is given by ~ I -= c (x - xO) Am where 2Jo is used instead of JO to account for the momentum of the image jet above the surface. The constant c should be the same as for the free jet while the location of the virtual origin xO depends on the geometry of the jet and consequently can not be expected to be the same as for the free jet. In order to verify this scaling arguments, the equation for the free surface jet can be written in terms of the jet exit parameters as follows Ued crux xO) Um h - ~2 (h - h J where we have used the relation JO ~ Po (Ue dj2. The same analysis applied to the free jet gives, Ue C (X TO: Thus, the constant cat can be determined from free let data, which gives cl- 0.162 (Madnia, 1989~. It should be noted that in order for the constant car to have the same value for a free jet as for a free surface jet it is required that the selfsimilar velocity profiles in both of these flows have the same shape. These arguments are based on the assumption that JO is a constant independent of x. As discussed bv Kotsovinos (1976,1978) this fails to account for the momentum flux of the entrained fluid which tends to reduce the momentum flux as the flow evolves downstream. Also in the free-surface jet problem, surface waves generated at the interaction will carry momentum away from the jet which will result in a lower effective value of JO. Another important effect is the presence of surface active agents which may contribute to a reduced momentum flux. - In summ~y7 the similarity arguments presented above suggests that: (i) the proper velocity scale for the free-surface jet is Ued/h; (ii) the proper length scale for the interaction is h, the depth of the jet; and (iii) the maximum mean velocity an~rnache~ the. free c',rf~r`~ faith downstream distance. --a Errs _ vent Results and Discussion Figure 3 is a plot of UedlUmh as a function of xlh for free-surface jet data obtained at several values of hid. It is apparent that the proposed similarity scaling results in good collapse of the data throughout the interaction. Yet the slope of the data is somewhat smaller than the expected value of c/2=0.115. It is only when the values at xlh=24 and 32 are used to determine the slope that there is good agreement of the measured slope 0.114 with the calculated value. h/d=1 n h/d=3.5 h/d=1.5 Free Jet Data ~ h/d=2.5 7- 6- s 4 3 2 1 O /~ ~' '1 1 1 1 1 0 10 20 30 40 50 /: a / / o x/h Figure 3. Decay of maximum mean velocity. The collapse of the data in Figure 3 throughout the interaction region suggests that velocity profiles measured at the same value of xlh for different hid should collapse on a single similarity curve. Similarity profiles for various values of x/h are presented in Figures 4 and 5. In each figure, plot (a) presents the similarity profiles in the direction normal to the free surface and plot (b) presents the profiles parallel to the free surface. For a normalized distance of x/h-12, Figure 4(a) shows a significant reduction of the mean velocity close to the free surface (the free surface is located at zlLz al). The mean velocity profiles atxlh=24 and 32 are given in Figure 5. The profile in the direction perpendicular to the surface at xlh=24, Figure 5(a), shows that the maximum velocity occurs away from the surface. At xlh=32 the maximum occurs closer to the free surface. It is apparent that only downstream of xlh=32 do the similarity profiles of the free surface jet resemble those of a free jet. We expect that the far field slope c/2 can only be obtained downstream of this location. 363

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~ x/h_10.67 o x/h=12 ll 0.83 . _ 0.6 0.4 0.2 O- q 1~' -3 -2 ~e ~ x/h=13.33 1- 0.8 63 0.6 - 0.4 n'._ o_ ~. I . I . I -1 0 1 2 3 z/Lz (a) . a ~0 o of a . I I ~ ~ -10 1 2 3 Y~Y (b) Figure 4. Mean velocity similarity profiles. Ue=200 cm/s x/h = 10.67,12,13.3. (a) Profiles perpendicular to the surface. (b) Profiles parallel to the surface. The growth rate of the mean velocity profiles was characterized by the half velocity widths Lo, and Lz in the directions parallel and perpendicular to the free surface. These half velocity widths were determined with reference to the location of the maximum velocity in the profile. The similarity argument suggests that in the far field the maximum velocity should be found on the free surface, i.e. hm~0, and also Ly~Lz. Thus, in the far field Ly ~LZ+hm' where LZ+hm is a measure of the thickness of the high momentum region on the vertical symmetry plane. The normalized widths Lylh and (Lz +hm JIh are plotted in Figure 6 as a function of xlh for all values of hid. These results show that the high momentum region is deeper than it is wide throughout the interaction region. The asymmetry persists for large ~ _ 0.8 ~3 0.6 =) 0.4_ 0.2 0.8] Is 0.6 0.4 () 2_ 1 0 x/h=24 x/h=32 o n -2 0 zJLz (a) . I . I 2 4 o- g a a to to ._ 0 ~ ~on. -4-2 o y/Ly (b) Figure 5. Mean velocity similarity profiles. Ue=200 cm/s, x/h = 24, 32. (a) Profiles perpendicular to the surface. (b) Profiles parallel to the surface. 2 4 distances downstream. Only for xlh=32 the values of Ly and Lz +hm begin to converge toward each other as is expected in the far field. Both L'lh and (Lz +hm)lh grow almost linearly with x. The slope of these lines, 0.078, is in good agreement with the results for a free jet. This result is not consistent with reported measurements in free surface jets by Rajaratnam and Humphries (1984). The downstream evolution of the normalized mean surface velocity along the jet centerline, measured at a distance of approximately 2 mm below the surface, is shown in Figure 7. The mean surface velocity is very small for xlh ~ 5. The mean surface velocity reaches a maximum at x/hzl 1 and decreases downstream of this point. The solid line in this plot is a least squares curve fit through the normalized maximum mean velocity data 364

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7;: h/d=2.5 0 h/d=3.5 1 ~ ' ~ ~ 2- do 1 ~ -e _.,~% . ~r a o . 1 0 10 20 30 40 50 x/h Figure 6. Evolution of half velocity width. Solid symbols, Ly/h; open symbols Lz/h+hm/h. presented in Figure 3. From Figure 7 it can be seen that the surface velocity approaches the maximum mean velocity in the profile for large values of xlh. It appears that the rate of decay of surface velocity is much slower than its initial rate of increase in the axial direction. This can have a significant effect in the dynamics of surface waves in this region. It is interesting to note that the location of the maximum velocity, x/in= 11, is downstream of the location of maximum surface activity as determined by surface curvature measurements, xlh~ 5tolO(Madnia, 1989). 0 in/d= 1 h/d=3.5 ~ hid- 1.5 0 h/d=2.5 0.6-1 - Um h/Ue d ~ ~1 ._ =, 0.4 ~ 0.3 con , 0.2 0.1 o 0 10 20 30 x/h Figure 7. Evolution of mean velocity near the surface. TURBULENCE MEASUREMENTS Experimental Apparatus Measurements of jet turbulence beneath a free surface were made using a three-component, underwater Laser Doppler Velocimeter (LDV) designed for wake measurements in a towing tank. The LDV used the three strongest lines, 514.5 nm (green), 488.0 nm (blue), and 476.5 nm (violet), of an Argon ion laser in a three-color, six-beam configuration. The green and blue beam pairs determined the velocity components in a plane, and the violet beams determined the component perpendicular to this plane (Figure 8~. The LDV used optical fibers to carry the transmitted beams to two watertight optical probes and to carry backscattered light from the probes to the photodetectors. The submerged probes were mounted oppositely in a cylindrical housing, and a pair of underwater mirrors folded the six beams to a crossing approximately 1.25 m from the housing axis. The measurement volume diameters were approximately .020 cm on all three components, and frequency shifting using Bragg cells was employed to allow discrimination of reversed flow of any component. The Doppler bursts t r.~ =. +Y Figure 8. Plan and side views of the three component LDV and jet nozzle. The LDV translates perpendicular to the jet and rotates about its own axis; the jet nozzle translates on its axis. 365

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were processed using counter-type processors, and the burst information from all three processors was tested for simultaneity or was rejected. The data were stored on an IBM PC. See Willmarth (1987) for a more complete description of the LDV design. The LDV was operated in a 2400-gallon small towing tank facility at the University of Michigan. The LDV probe was suspended from a carriage that allowed translation in one direction. A stepping motor attached to the underwater housing allowed the LDV to be rotated about its axis. The jet itself consisted of a brass nozzle attached to a pair of concentric PVC cylinders; within the cylinders were screens and honeycomb for turbulence management. The jet was suspended from the facility's towing carriage and was moved axially to provide the third axis of positioning. This 'free' jet arrangement allowed entrainment from all directions, in contrast to that used for the scaling measurements of Part I where the jet issued from a wall that spanned the facility. The jet exit diameter was .635 cm, and the jet exit velocity was 200 cm/s. Figure 8 shows the LDV probe, the jet, and the coordinate system. The water in the towing facility was continuously circulated and filtered when not taking measurements, so as to maintain a uniform temperature throughout the tank. A submersible pump drew from the towing tank, and the jet discharged back into the tank; in this manner, seeding uniformity between jet and ambient fluid could be assured. Titanium dioxide was added to the water to seed the fluid with scattering particles prior to taking measurements. Results and Discussion Three-component LDV measurements of the flow velocity in a submerged turbulent jet at depths of 60 and 2 diameters were made to quantify the behavior of turbulence beneath a free surface. The jet Reynolds number based on exit velocity and jet diameter was approximately 12,700. The data were obtained using a simultaneity window set equal to the time required for a scattering particle travelling with the measured mean speed to traverse the diameter of the measurement volume. Data rates tended to be low, around 30 Hi near the jet centerline and less than 10 Hz at the jet edges. For the data reported here, at least 1000 individual measurements were recorded at each location; this number was chosen based on the appearance of the velocity histograms for each component. Ensemble averages were corrected for particle arrival bias using the reciprocal of the magnitude of the instantaneous velocity vector (McLaughlin and Tiederman, 1973) to weight the individual measurements. Measurements of the flowfield of a deep jet (h/d~60) were made as a baseline from which to compare measurements made in a shallow jet (h/d=2) beneath a free surface. The streamwise velocity component on the jet centerline is shown in Figure 9, plotted so as to reveal its inverse dependence on x, as expected from similarity considerations. The measured slope of this line gives Uc/Uc~6.3/(x/d), in agreement with that reported elsewhere, e.g. Rajaratnam (1976~. However, at 32 diameters downstream, the flow can still not be considered fully developed, in the sense that the turbulence quantities become self-similar. Wygnanski and Fiedler (1969) have shown that the turbulence ; o o o o o o ; 1'0 2'0 x/d o o , 30 40 Figure 9. Variation of jet centerline velocity with downstream distance, h/d~60. Scaling determined from straight line segment shown. quantities in an axisymmetric jet do not become self- preserving until about 80 diameters downstream. Profiles of mean velocity, RMS turbulent fluctuations, and Reynolds stresses were measured at downstream stations of 16, 24, and 32 diameters. Shown in Figs. lOa-d are profiles at x/d=32 for varying z at y=O; corresponding profiles for varying y at z=O, though not shown, are in excellent agreement and serve to verify that the jet is indeed axisymmetric. The profiles are plotted using similarity variables, normalizing the vertical coordinate z by the downstream distance x and the velocity components by Uc, the mean velocity on the jet centerline. The vertical mean velocity component W. shown in Fig. fob, shows outward flow near the jet centerline, and inward flow (entrainment) at the jet edges. This behavior is expected to differ when the jet discharges near a free surface, because of the restrictions the boundary places on the vertical growth of the jet and on the entrainment 366

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of fluid into the jet from above. The RMS turbulent fluctuations (Fig. lOc) show the horizontal and vertical fluctuations v' and w' to have the same magnitude, while the magnitude of the streamwise fluctuations u' is somewhat greater. By symmetry, the cross-stream mean velocity V(Fig. lOb) and the Reynolds stresses u v and v w (Fig. lOd) should be zero; to within the limits of experimental error, these terms are effectively zero. Shallow jet data (h/d=2) were obtained at x/d=32, for the same Reynolds number, and are presented in Figs. [la-d. The same similarity variables are used so that direct comparison between Figs. 10 and 11 is possible. Comparison of the streamwise mean velocity profiles (Figs. lea and lla) reveals that the location of maximum mean velocity approaches the surface, in agreement with the scaling results of Part I above. Fig. Fib shows a profile of the vertical mean velocity; near the jet centerline, the flow is again outward, and well below the centerline, the flow is entraining inward. The flowfield above the jet centerline shows the effects of the free surface, driving the vertical mean velocity to zero as it is approached. The RMS turbulent fluctuations, Fig. tic, reveal a distinctive behavior as the surface is approached: The fluctuations normal to the free surface are significantly diminished, while those parallel to the surface are enhanced. The Reynolds stresses are plotted in Fig. lid, showing that the principal stress uw diminishes to zero as the surface is approached. Measurements of turbulence beneath a free surface in inherently two-dimensional flows such as the channel flows reported by Komori, et. al. (1982) and Rashidi and Banerjee (1988), and the plane surface jet flow reported by Ramberg, et. al. (1989) have previously shown that the turbulent fluctuations become anisotropic beneath a free surface. Beneath a sheer-free plane surface as is appropriate to the image model outlined above, the vertical velocity and vertical fluctuations must go to zero as a consequence of the plane boundary. However, the interaction of the jet with a free surface shows considerable surface activity, including the generation of surface waves, and the vertical fluctuations need not go to zero as the surface is approached. Recent research investigating the dynamics of vortex rings at a free surface (Bernal and Kwon, 1989) revealed a process of vortex reconnection to the free surface. The vortex lines comprising the rings were found to disconnect and become attached to the surface, resulting in open vortex lines beginning and terminating at the free surface. We suggest that the physical mechanism acting to redistribute the turbulent energy from the vertical to lateral fluctuations is a process whereby vortex filaments in turbulence become attached to the free surface. Lateral velocity profiles were taken between the jet centerline z=0 and the free surface z=h, again at x/d=32. Those points nearest the free surface were within 1 mm of the undisturbed surface and were as close to the surface as was possible without the measurement volume being interrupted by surface deformations. Though not shown, these data reveal a significant increase in the jet width as the surface is approached. The flow is inward at the jet edges on and just above the jet centerline, corresponding to entrainment, but is outward in a thin layer just beneath the surface that extends laterally to several jet widths from the jet centerline. We refer to this thin layer as the surface current. To investigate this surface current, the LDV was operated without requiring simultaneity among the three components; this allows determination of the mean velocities, but sacrifices the turbulence quantities in favor of a higher data acquisition rate. The data shown in Figs. 12a-d are averages of at least 2000 individual measurements per channel at each location, and are not corrected for bias. Shown are vector plots of the mean velocity components V and W at various downstream stations. At x/d=16, the data show the beginnings of the surface current in the data taken at the surface, but not in that taken below it. Proceeding downstream to 24 and 32 diameters, the current is seen to develop, growing significantly wider than the turbulent jet flow beneath it, but remaining confined to a shallow layer just beneath the surface. At 48 diameters downstream, the surface current dominates the flowfield, the velocity components throughout the jet having diminished with increasing distance downstream. Near the jet centerline, the mean flow has a component outward (as the jet grows wider downstream), and well below the jet centerline, the flow is inward as ambient fluid is entrained. In the current layer, a strong outward flow causes the entraining flow below it to be turned outward. One might attribute such turning to the action of a streamwise vortex lying just outboard of the jet, as the flowfield is suggestive of a vortex pair lying just beneath and parallel to the free surface. A similar flow pattern appears in wake data taken behind surface ships, and this pattern is sometimes attributed to the action of large streamwise vortices shed from the stern or bilges of the ship. In the case of the jet, stretching of ring-like or helical vertical structure within the jet could yield streamwise structure in the mean. Far from the free surface, there should be no preferred azimuthal position for these structures, but in close proximity to the surface, a stable configuration of streamwise vorticity could develop. This feature might be characteristic of the interaction between a three-dimensional turbulent shear flow and a free surface. 367

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1.00 0.80 0.60 0.20 of - o o U o 0.30 o ~ o o o 0.20 o o o o o o o o o 0.00 - Go Oo -0.20 -0. 10 0.00 0.10 0.20 Z/X Figure lOa. Profile of streamwise mean velocity component, x/d=32, h/d~60. 0.10; 0.05 0.00 -0.05 oo U' o V' o I' o 8 o it, 0 ~ ~ ~ [; 0 0 i,\ 0 o r' ~ 0 o8 0.00 1 , , , ~ -0.20 -0. 10 0.00 0.10 0.20 Z/X Figure lOc. Profiles of RMS turbulent fluctuations, x/d=32, h/d~60. 0.025 V o C`2 W ~o o O a O C O o U ~ A O C C O ~O A ~ 0.000 ~ ~ ~ear, UV O veer 0 ^~^ US O Oo O ~ ~ 8 ~ ~ ~ ~ 0 0 O8 of o8g gone ~ -0.10~, , , , -0025 1 , . . . 20 -0.10 0.00 0.10 0.20 -0 20 -0.10 0.00 0.10 0.20 Z/X Z/X Figure fob. Profiles of horizontal and vertical mean Figure led. Profiles of Reynolds stresses, x/d=32, velocity components, x/d=32, h/d~60. h/d~60. The surface current does not obviously follow from the considerations of Part I for a shallow submerged jet merging with its image above the surface, although the concept of image vorticity is essential to understanding the surface current. To understand the origin of the surface current, flow visualization using laser-induced fluorescence (LIE) was used. A small amount (3 ppm) of fluorescein dye was added to the reservoir supplying the jet, and a cross-stream plane (x/d=32), normal to the free surface and the axis of the jet, was illuminated with a laser light sheet. The boundary of the jet was observed to be very uneven and unsteady, appearing to emit puffs of dyed, vertical fluid in random directions; these puffs initially propagated outward and away from the jet. The puffs that were emitted downward slowed rapidly and were rarely observed to propagate far from the jet boundary. However, those that were ejected near the surface, having little downward velocity, were observed to 368

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l. o.8 0.60 c, 0.40 0.20 0.00- 00 , . . . -0.20 -0. 10 o.oo o. 10 0.20 z/x Figure 11a. Profile of streamwise mean velocity component, x/d=32, h/d=2. o 'it. o to U o o o o o o 0.10 0.05 c, 0.00 - c, 0 0 ~ ~ ~ -0.05 o. 100 20 -o. to o.oo o. to 0.20 z/x Figure lib. Profiles of horizontal and vertical mean velocity components, x/d=32, h/d-2. continue to propagate parallel to the surface away from the jet boundary. These emissions persisted to several jet half-widths hom the boundary in a thin layer just below the surface. The average of many such emissions and their subsequent propagation outward gives rise to a mean outward flow which is observed as a surface current. 0 30 ~ - ~ 0.20 - - ~n 1n a Coo 0 0 ~ ~ ~ B o o U' O V' O in' 0-00- -0.20 -0.10 o.oo 0.10 0.20 z/x Figure 11c. Profiles of RMS turbulent fluctuations, x/d=32, h/d=2. 0.025 v ~C`2 w ~ ~ 0.000 1> 1> car 1= uv 0 veer 0 user ~ oo 28 8~~ ~ AL -0.025 l l l l -0.20 -0. 10 o.oO 0.10 0.20 z/x Figure 11d. Profiles of Reynolds stresses, x/d=32, h/d=2. Using a horizontal light sheet, planes parallel to the surface were illuminated. With the sheet just beneath the surface, a plan view of the surface current was obtained. The layer appears to originate near x/d=16 for a jet depth h/d=2. Ibe current layer shows puffs of dyed fluid ejected from the jet propagating outward at an angle of about 35 degrees to the jet axis, whereas the jet flow itself spreads at about 12 degrees. 369

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2 o' z/d -2 4 yld 0 2 4 6 ~10 12 0 .h .~.1 ~ ~1 1 1 1 , ~ ~ - ~ + ~ 9 ,.^ an____` %~_4~` _ , , _~ t t ~ ~ ~ 10 cm/s Figure 12a. Vector plot of horizontal and vertical mean velocity components, x/d=16, h/d=2. Shaded circle shows jet nozzle, shaded triangle shows location of free surface. y/d o 4 1 ~ b ~ ~ t Figure 12b. Vector plot of horizontal and vertical mean velocity components, x/d=24, h/d--2. The ejected structures remained relatively coherent, and high concentrations of dye in the ejected fluid suggest that turbulent mixing is greatly reduced within the layer. Illuminating a plane through the jet centerline, z=O, reveals characteristic deep jet behavior up to approximately 24 diameters, at which distance the structures emitted in the surface layer have grown in scale sufficiently to intercept the sheet from above, well outboard of the 12 degree jet boundary. In a plane beneath the jet, z/d=-1, the only evidence of the layer comes from the few structures large enough to reach the light sheet. y/d 2 4 6 8 10 12 Lit 1 ~ __ _ ~ _ - 4 10 cm/s Figure 12c. Vector plot of horizontal and vertical mean velocity components, x/d=32, h/d=2. ~U 2 z/d -2 -4 ma. ~ 10 cm/s , 370 ~ . 10 cm/s Figure 12d. Vector plot of horizontal and vertical mean velocity components, x/d=48, h/d=2. Although we have not directly measured the vorticity, the fact that the surface puffs continue to propagate away from their origin near the jet boundary indicates that they consist of vertical fluid. The dye concentration of the fluid carried with the surface puffs indicates that this fluid has not mixed with the surrounding (non-dyed) fluid as the puffs propagate outward along the surface. The recent work of Bernal, et. al. (1989) and Hirsa (1990) in determining the behavior of a vortex pair

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beneath a free surface revealed the importance of surface-active agents in determining the vortex trajectories and the generation of secondary vorticity beneath surfaces contaminated with such agents. Discrete vortices travelling toward a free surface propagate outward beneath the surface when the surface is relatively free of surfactant, but rebound from the surface when surfactant is present. The rebounding is caused when secondary vorticity of opposite sign to the primary vortices is generated beneath a surfactant covered surface. Oleyl alcohol, an insoluble surface- active agent for which the constitutive relation between surface pressure and concentration is known, was added to the free surface, and the LIF flow visualizations were repeated. The surface current did not form, and vertical ejections from the jet, emitted near and parallel to the free surface, were confined laterally through interaction with secondary vorticity generated beneath the surfactant layer. Acknowledgements This work is supported at the University of Michigan by the Office of Naval Research University Research Initiative Program in Ship Hydrodynamics, Contract Number N000184-86-K-0684 and at the David Taylor Research Center by the ONR Surface Ship Wake Consortium, Contract Number N0001490-WX- 22034. References Bernal, L. P. and Kwon, J. T., (1989), "Vortex Ring Dynamics at a Free Surface," Physics of Fluids A, Vol. 1, No. 3, pp. 449-451. Bernal, L. P., Hirsa, A., Kwon, J. T., and Willmarth, W. W., (1989), "On the Interaction of Vortex Rings and Pairs with a Free Surface for Varying Amounts of Surface Active Agent," Physics of Fluids A, Vol. 1, No. 12, pp. 2001-2004. Hirsa, A., (1990), "An Experimental Investigation of Vortex Pair Interaction with a Clean or Contaminated Free Surface," Ph.D. Thesis, The University of Michigan, Ann Arbor, MI. Komori, S., Ueda, H., Ogino, F., and Mizushima, T., (19823, "Turbulence Structure and Transport Mechanism at the Free Surface in an Open Channel Flow," Internation Journal of Heat and Mass Transfer, Vol. 25, No. 4, pp. 513-521. Kotsovinos, N.E. (1976), "A note on the spreading rate and virtual origin of a plane turbulent jet", I. Fluid Mech, Vol. 77, 305-311 Kotsovinos, N.E. (1978), "A note on the conservation of the axial momentum of a turbulent jet", J. Fluid Mech., Vol. 87, 55-63. Kwon, J.T. (1989) "Expenmental study of vortex ring interaction with a free surface", Ph.D. Thesis, University of Michigan. Madnia, K. (1989) "Interaction of a turbulent round jet with the free surface," PhD Thesis, The University of Michigan. McLaughlin, D. K. and Tiederman, W. G., (1973), "Biasing Correction for Individual Realization of Laser Anemometer Measurements in Turbulent Flows," Physics of Fluids, Vol. 16, No. 12, pp. 2082-2088. Rajaratnam, N., (1976), Turbulent Jets, Elsevier Scientific Publishing Co., New York, NY. Rajaratnam, N. and Humphries, J.A., (1984) "Turbulent Non-Buoyant Surface Jets," Journal of Hydraulic Research, Vol. 22, No. 2, pp. 103-115 Ramberg, S. E., Swean, T. F., and Plesnia, M. W., (1989), "Turbulence Near a Free Surface in a Plane Jet," NRL memorandum Report 6367, Naval Research Laboratory, Washington, DC. Rashidi, M. and Banerjee, S., (1988), "Turbulence Structure in Free-Surface Channel Flows," Physics of Fluids, Vol. 31, No. 9, pp. 2491-2503. Willmarth, W. W., (1987), "Design of Three Component Fiber Optic Laser Doppler Anemometer for Wake Measurements in a Towing Tank," Proceedings of the International Towing Tank Conference. Wygnanski, I. and Fiedler, H., (1969), "Some Measurements in the Self-Preserving Jet," Iou~nal of Fluid Mechanics, Vol. 38, Part 3, pp. 577-612. 371

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DISCUSSION John P. McHugh The University of New Hampshire, USA Did you notice any pattern on the free surface near the jet? Were there any distinct streamwise or transverse waves visible? AUTHORS' REPLY Under the conditions investigated, the interaction of the jet flow with the free surface led to the generation of surface waves near the jet centerline. These waves, generated continually and apparently at random by the large-scale structures in the jet flow, were observed to coalesce and to propagate in a direction almost perpendicular to the jet axis. Measurements of the wavelength and wavespeed from shadowgraph images of the free surface showed the waves to be gravity-capillary waves of wavelengths between 1 and 4 cm, travelling with approximately the minimum wavespeed, 23 cm/s, attainable on deep water having a clean free surface. 372