Observations of Giant Bursts Associated with Microscale Breaking Waves
Ira Leifer and Sanjoy Banerjeea)
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 Philips1). These bursts were only observed with microbreaking and are significantly different from turbulence
generated by wind stress at lower speeds. Both experiments (Rashidi and Banerjee2) 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 Banerjee2 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.
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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 Banerjee4. 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).
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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).
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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
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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.
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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 Banerjee14. 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 Okuda5, but with
insufficient resolution to visualize the structures. In addition, Okuda5 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
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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).
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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
2 Rashidi,
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