Observations of Giant Bursts Associated with Microscale Breaking Waves Ira Leifer and Sanjoy Banerjee a) Chemical Engineering Department, University of California, Santa Barbara, Santa Barbara, California, USA. I. INTRODUCTION The purpose of this abstract is to outline laboratory observations of large-scale bursts found associated with windstress-generated, microbreaking waves, i.e., relatively short-length waves breaking without air entrainment (Banner and Philips 1 ). These bursts were only observed with microbreaking and are significantly different from turbulence generated by wind stress at lower speeds. Both experiments (Rashidi and Banerjee 2 ) and direct numerical simulations (De Angelis et al. 3 ) had shown that at relatively low wind speeds (leading to non-breaking waves) the turbulence produced is similar to wall turbulence and scales with the shear rate. With microbreaking waves, however, a rapidly moving, surface layer of liquid was observed to move downwind with the wave crest. Structures similar to the windstress-generated bursts observed by Rashidi and Banerjee 2 were ejected downwards into the liquid from the free surface, but some of these bursts were nearly an order of magnitude larger and significantly more persistent. We call these giant bursts. It is this phenomenon that we discuss here. Similar phenomena were observed recently in the open ocean as part of our ongoing investigations, and will be reported separately. FIG. 1. Schematic of wind-wave channel set-up. FIG. 2. Wave profile and images for A) microbreaking wind waves and B) paddle-steepened wind waves. 1
II. OBSERVATIONS Investigations were conducted in a wind-wave channel to elucidate the flow structure of turbulence produced by microbreaking waves. The channel dimensions were 0.2 x 0.9 x 10 m, and a schematic is shown in Fig. 1. Air was blown through a wire grid into the channel. The channel was filled with filtered, fresh water to a depth of 0.1 m leaving 0.1 m for the airflow -. The channel water width to depth ratio was kept high to prevent secondary wind circulations near the center of the channel cross section, where the observations were made. Microbreaking waves were created by blowing air over the water stream using a bank of fans, and could be steepened with a paddle wavemaker positioned near the channel entrance. In these experiments, when used, the wavemaker produced waves comparable, in wavelength, to the wind stress-only wavelength at the observation window, and was located 4 m downwind from the fans. An anemometer in the center of the air space measured wind speeds. Examples of only (~4.3 m s -1 average wind speed) and paddle-steepened wind-waves are shown in Fig. 2. The rms wave height was measured directly from the profile shown (Fig. 2) and was ~2.5 cm while the wavelength was ~35 cm. Fluid motions were visualized with the help of neutrally buoyant 200-µm and 2000-µm polystyrene microspheres as well as ~50-µm microbubbles. Surface and subsurface motions were traced using the microspheres that were introduced onto the surface. The smaller diameter microspheres were entrained, and ejected downwards, by the fluid motions within the bursts, thus showing the physical extent of the burst. To aid in flow visualization, the image intensity was inverted, and for side images, the contrast was reduced for the portion of the images above the interface. Bursts were also visualized by microbubbles generated in vertical lines by applying high voltage pulses to a thin (50-µm diameter) platinum wire stretched vertically between the channel floor and ceiling. In these images, the top of the field of view just touched the wave trough, and the camera imaged perpendicular to the downwind direction. The pulse generator frequency could be varied, and for these experiments was set to 60 Hz. High-speed video images were taken at the observation window from the side of the channel the camera angled upwards at ~20, shutter speed - 1/1000s, frame rate 60 fps. A low light CCD camera (JVC LowLux) (shutter 1/1000 s, frame rate - 30 fps) was used to image microbubbles and surface motions. Microbubble lines were observed from the side with the camera level, while down-viewing videos were taken from 3 m above the channel, using a 25-mm lens to minimize distortion. A 2000-Watt incandescent spotlight underneath the channel provided illumination in a 2.5-cm thick light sheet. Flow velocity fields were determined from the video images by hierarchical digital particle imaging velocimetry (HDPIV) using the method described in Kumar and Banerjee 4. Vorticity fields were calculated from the velocity fields. Both incipient and microbreaking waves were observed, and show very similar profiles. The waves were three-dimensional and exhibited capillary waves in front of the wave crest. However, only microbreaking waves were accompanied by the movement of a surface layer of liquid at the crest speed (evident from the motion of the 200-µm particles at the surface) and there was generation of burst-like motions about a centimeter behind the wave crest. A small burst structure is shown using a sequence of microbubble lines in Figs. 3A 3F. These small bursts were shallow and short-lived. For example, the small burst shown had largely dissipated by ~ 1 s, changing little between the last two panels (Figs. 3E and 3F), and only penetrated ~ 2 cm below the interface. In Fig. 3, the brighter microbubble lines were associated with the passage of the wave crest where liquid velocities were greater. Giant turbulence bursts were also produced. These structures were much larger, developed faster, and persisted for many wave periods. An example of a giant burst is shown in Figs. 3G 3L. This structure was associated with the passing of the wave crest and continued to develop for the entire time it remained in the field of view, ~2.0 s, penetrating downwards more than 8 centimeters. The burst lifetime was significantly longer than for the small burst and also much longer than the wave period. Giant bursts were also highly three dimensional, as shown by the apparent advection of bubble lines in the spanwise direction (e.g., Fig. 3K). 2
FIG. 3. Images of turbulence bursts visualized by microbubble lines for microbreaking wave conditions. The line to the left of each image is the platinum wire used to generate the bubble lines. A) F) show a sequence for a small burst, H)-L) shows a giant turbulence burst produced under identical experimental conditions. Size scale and times are indicated on the figure. The zero time was arbitrary and was chosen for a relatively quiescent flow field (i.e., microbubble lines were largely parallel). 3
FIG. 4. Sequence showing a giant turbulence burst. Images of the burst are shown in A) E), the velocity field in F) J), and the vorticity field in K) - O). Time zero was set for when the microbreaking wave crest entered the field of view. Gray area in velocity fields shows areas of high particle concentration. Velocity and vorticity fields are only shown for subsurface flow, and the image contrast above the interface has been reduced. Time, position, velocity scale, and vorticity contours indicated on the figure. Giant bursts were formed close to the interface. This is clear from the side view image sequence and calculated flow and vorticity fields shown in Fig. 4 for paddle-steepened waves and a wind speed of 4.3 m s -1. Time was set to zero when the crest entered the field of view. The wave crest can be seen at horizontal positions of 1.5 and 7.5 cm in 4
Figs. 4A and 4B, respectively. Particles were collected and transported by this wave crest, a phenomenon shown more clearly in Fig. 5. The burst enters from the top left (Fig. 4A, 4F, and 4K) and descended downwards with an initial velocity of ~20 cm s -1 in the lab frame of reference at an injection angle of ~30 from the horizontal. Motions with about double this velocity were observed within the burst itself, but due to the complexity of the motion, more work is needed to resolve these. Turbulence associated with the second burst can be seen in the flow and vorticity fields extending a centimeter or two deeper and in front of the area highlighted by the dense cloud of particles (e.g., Figs. 4B, 4C, 4G, 4H, and 4K, 4L). A second giant burst, slightly smaller, was created at horizontal position of 6 cm in Fig. 4A, and generated the region of turbulence motions visible after t = 0.136 s. With time the burst grew downward and at maximum penetration (Fig. 4E) was descending almost vertically. The patch of turbulence associated with the giant burst is still easily identifiable at 0.5 s in the image (Fig. 4E) and vorticity (Fig. 4O) fields, and persisted for several wave periods. The burst was associated with persistent upwelling flows that were observed on the interface from above as a divergence of fluid behind the crest, as discussed later. The surface fluid velocity can be calculated from Figs. 4A and 4B. Particles were collected and transported downwind with the crest which from horizontal positions, 1.5 to 7.5 cm, respectively. This translates into an interface speed of ~55 cm s -1. Only slightly below (~3 mm), fluid velocity was much less, ~30 cm s -1 (see Fig. 4F at x = 2.0 cm). This strongly supports the existence of a shear layer in the region of the microbreaking wave crest. Images, surface flow fields, and divergence fields for a different microbreaking wave are shown in Fig. 5. Particles can be seen transported downwind with the wave crests as was also shown in Fig. 4. This suggests transport of surface liquid with microbreaking waves. Microbreaking began shortly before Fig. 5A, and in the shaded regions outlined in Figs. 5B and 5C, which correspond to where most of the particles lie in Fig. 5A, there appeared to be a small upwelling as evidenced in the surface divergence field, shown in Fig. 5C. A short time later, the same wave showed that this upwelling region had become larger as evidenced by the growth of the region of positive surface divergence shown in Fig. 5F. FIG. 5. Downward looking images, velocity fields, and divergence fields for a microbreaking wave at 0.37 s in A) C), respectively, and for 0.50 s, in D) F). Note the particle transport at the wave crest. Velocity and divergence fields blanked where insufficient particles. Zero time is arbitrary. Time, position, velocity scale, and divergence contours indicated on the figure. 5
III. DISCUSSION and CONCLUSIONS Bursts generated near the air-water interface under microbreaking conditions have several interesting aspects. They appear to result from a different generation mechanism than those at lower wind speeds. The small turbulence structure shown in Fig. 3A 3G was similar to structures at lower wind speeds (with no microbreaking) reported in Rashidi and Banerjee 14. Microbreaking waves were associated with a thin liquid layer that traveled downwind at near the crest speed, collecting and transporting floating particles. In addition to small bursts, giant bursts that were associated with high levels of turbulence were occasionally produced by microbreaking waves. The downward injection of near surface fluid under microbreaking waves was reported in the same region by Okuda 5, but with insufficient resolution to visualize the structures. In addition, Okuda 5 also reported microbreaking was associated with strong and persistent upwelling flows. The location of these upwelling flows coincides with previous observations of thermal disruptions and surface renewals (e.g., Jessup et al. 6 ) behind the crest of microbreaking waves. Thus giant bursts are a potential mechanism for increases in surface renewal rates with the onset of microbreaking. This increase has been associated with increased mass transfer rate (Komori et al. 7 ). The mechanism responsible for the generation of giant bursts remains unclear. We speculate that the thin, intense shear layer found near the free surface during microbreaking provides a potential mechanism for the generation of giant bursts. Coherent structures emanating from this shear layer could lead to the large structures shown in this paper. ACKNOWLEDGMENTS This work has been performed with the support of the Department of Energy, Grant No. DE-F603-85ER-13314. REFERENCES 1 Banner M.L. and O.M. Phillips, On the incipient breaking of small scale waves, J. Fluid Mech. 65, 647 (1974). 2 Rashidi, M., and S. Banerjee, Streak characteristics and behavior near wall and interface in open channel flows, J. Fluid Engineering. 112, 164 (1990). 3 De Angelis, V., P. Lombardi, and S. Banerjee, Direct numerical simulation of turbulent flow over a wavy wall, Phys. Fluids 9, 2429 (1997). 4 Kumar, S. and S. Banerjee, Development and Application of a hierarchical system for digital particle image velocimetry to free-surface turbulence, Phys. Fluids 10, 160 (1998). 5 Okuda, K., Internal flow structure of short wind waves Part I. On the internal vorticity structure, J. Oceanogr. Soc. Jpn. 38, 28 (1982). 6 Jessup, A.T., C.J. Zappa, and H. Yeh, Defining and quantifying microscale wave breaking with imagery, J. Geophys. Res., 102, (no.c10), 23145 (1997). 7 Komori, S., R. Nagaosa and Y. Murakami, Turbulence structure and mass transfer across a sheared air-water interface in wind-driven turbulence, J. Fluid Mech., 249, 161 (1993). a) Author to who correspondence should be addressed. Permanent address: Chemical Engineering Department, University of California, Santa Barbara, California, 93106-5080. Electronic mail: banerjee@engineering.ucsb.edu 6