The flume working section was seeded with approx-imately 0.5 cells mL 1 of P. fusiformis and the density of cells in the test section was checked after breaking events by pump sampling through a calibrated flow agitator (a device similar to a bathyphotometer that quantifies the number of photons emitted by bioluminescent organisms in a known volume [Widder et al., 1993]). The bioluminescence occur-ring during breaking was imaged at 30 frames s 1
with a video camera and image intensifier mounted on a motion-controlled sled allowing a single region of the breaking crest to be followed throughout its evolution.

The video images from the test experiment were analyzed using the model described above. To begin, the background noise level was estimated from a dark region of the images and subtracted. Then 5 video frames were averaged to match the camera light integration time with the flash duration of P. fusiformis, which is approximately 0.1 s. The cell path intensity appearing in equation (13) was estimated from the average sum of pixel values along ten selected cell tracks (i.e., Figure 1b). The anxiety parameter (for the pixel) was then calculated using equation (17) with = 0.17 s (the image integration time) and VC0 = 0.028 cells per pixel volume (estimated from manual cell counts of pump samples and the pixel sample volume).

This analysis produces a spatial map of l on pixel length scales. Although the images appear to contain information on these short scales (Figure 2b), the advection of flashing cells across the camera field of view places a fundamental limitation on the spatial resolution of the mapping. P. fusiformis has a bright and long-lasting ‘‘first’’ flash characteristics (up to 170 ms,) compared with other species, making it easy to image with an intensified video camera [Widder and Case, 1981], but is not an optimal choice for the measurement of stress on short temporal and spatial scales. To obtain a map of l on the spatial scales determined by cell advection required running the high-resolution image through a 2 dimensional spatial filter. We used a two dimensional Hanning window with a pixel width characteristic of a typical cell track length (75 pixels). The remaining step was to then relate the filtered estimates for l to shear stress. From the published decay rates [Latz et al., 1994; Rohr et al., 1997, 2002] for different constant stress levels for various dinoflagellates, including the genera Pyrocystis from which we can estimate l (see equation (15)). From their Table 2 [Latz et al., 1994], we estimate that
t •
0••••015
•
8••••2 Pa
•
18
•
for Pyrocystis. Equation (18) has been used to map our measured values of l to estimates of t and the resulting images are shown in Figure 2c. The measured shear stress ranges from about 0.2 to 1.0 Pa with peak values of 2.5 Pa. To put these shear stress levels into an oceanographic context, we note that shear stress of the order of 0.1 –1.0 Pa has been measured in wave-forced bottom shears in the surf zone [Rohr et al., 1997], and shear stress in the shallow 2 mm surface layer due to wind forcing is about 0.1 Pa [Cox et al., 1996]. Regions of high shear stress can be seen associated with the collapse of the overturning wave jet (top) and the turbulent eddy formed in the secondary splash-up in front of the wave crest (middle), which are consistent with expected high-stress regions imaged using traditional optics [Deane and Stokes, 1998, 2002].

 

Figure 1. Schematic of experimental setup and orientation of imaged volume relative to the camera. (a) Position of intensified camera system and motion-controlled sled exterior to a section of the glass-walled wave flume where wave packets constructively interfere and break (flume is more than 33 m long). A thin, opaque divider was placed in the flume in order to limit the imaging to a 10-cm slice of the wave. (b) Example intensified image frame collected during a breaking event. On the right, a subsection of the image is magnified to illustrate individual cell pathways illuminated during flashing and their position within the sample volume (10 cm thick). (c) Micrograph of a mature Pyrocystis fusiformis cell illustrating elongate spindle shape and central nucleus. Scale bar is 100 m m.

 

........It is necessary to create a context for these estimates of spatially and time varying dissipation before comparing them with previous work. Prior estimates of energy dissipation in wave crests do not include temporal and spatial information; they consist of fractional dissipation measured as the ratio of the surface displacement variance down-stream and upstream of the breaking events [i.e., Lamarre and Melville, 1991; Loewen and Melville, 1991; Melville, 1994], and dissipation inferred from bubble size distribution measurements [Deane and Stokes, 2002]. It is not possible to make a direct comparison with the results of Melville and coworkers because their measurements of the fractional dissipation are an average over the entire breaking event, which potentially includes multiple plume injections occur-ring at the beginning and end of the event. We can however, compare our data with that obtained by Deane and Stokes [2002], which represents an estimate of the turbulent dissipation rate within a primary plume injection during the air entrainment phase. This corresponds to the spatially averaged dissipation rate within the crushing cavity and overturning jet and lasts for about 200 ms for these laboratory waves. The average dissipation rate inferred from the scale of the smallest bubble subject to turbulent frag-mentation (the Hinze scale), is reported to be 12 W kg 1

Light Scattering and Absorption by Bubbles
One of the main sources of bias in the images collected using this visualization technique to measure shear stress within wave crests is the scattering and absorption of photons by the bubbles entrained by breaking. A plate illustrating the effects of scattering is shown in Figure 4. The figure is plotted in false color to emphasize light level contours. The white and blue elongated regions correspond to the tracks of light produced by flashing dinoflagellates as they moved past the camera. The red granular regions surrounding the plankton tracks are the result of light scattered from microbubbles in the wave crest. These low levels of light do not occur in regions where microbubbles are absent. For example, the tracks in the box ‘‘A’’ (Figure 4) are behind the actively breaking wave crest in a region with few bubbles [Deane and Stokes, 2002], and do not exhibit low-light granularity. The effects of scattering are removed by subtracting the mean scattering intensity from the images (thresholding). This is a subjective procedure: the intensity level used here was determined by examining a number of imagesand selecting a level that removed most of the granular region. This same threshold level was applied to all images includ-ing those used to calibrate the cell emission intensity. The result of thresholding is shown in the right hand plate in Figure 4. The effects of light absorption by bubbles depends on the transmission path length through the bubbly mixture. An opaque divider was added to the wave flume specifically to limit the length of the transmission path and minimize the effects of absorption by bubble occlusion (see Figure 1a). [26] These measures combined with the reasonable agree-ment between quantitative analysis of shear stress levels and those expected to exist on the basis of the work of ourselves and others, albeit for a limited data set, helps justify our treatment of scattering and absorption. A more rigorous evaluation of bubble effects could be made by imaging a calibrated light source inside a breaking wave crest and this will be done in future experiments.

Concluding Remarks
The formulation of a statistical model of dinoflagel-late cell firing behavior and the development of a calibration technique (bioluminescence imaging) has allowed us to produce quantitative images of the evolving fluid shear stress field within breaking wave crests. The images show high rates of turbulent energy dissipation in the jet/wave face interaction region consistent with earlier optical observations. The technique is based on two parts: a statistical model for single cell flashing behavior and its relationship to fluid shear, and a calibration methodology for analyzing images. The fundamental assumption in the statistical model is expressed by equation (1), which states that over some small time interval, the probability that a cell flashes is proportional to time. An additional assumption is that cells produce a detectable flash only once (a good assumption for some, but not for all species). When applied to populations of cells, the statistical model produces results consistent with available biological data for the special case of constant shear stress; the case of time-varying shear remains to be examined. Cells flash in response to many kinds of stimulation; the focus here is on stimulation induced by fluid shear. The model we have adopted relating the anxiety parameter to shear includes a known thresholding effect, but does not account for any effects caused by rate of change of fluid shear or cell memory. In principle, these effects could be included in equation (15), but the experiments required to understand their importance have not yet been undertaken. Finally, the calibration methodology presented here has only partially accounted for the effects of bubble absorption and scattering. Again, further measurements are required to better eliminate these biases. Bioluminescence imaging has the potential to significantly impact a broad range of hydrodynamic research areas, including transient, turbulent, two-phase flows. Ulti-mately, it may be possible to use cell bioluminescence to study wave turbulence in the open ocean and surf zone by calibrating the statistical model using bioluminescent species common to coastal red tides. In principle, aerial observations of flow-induced bioluminescence offer an unprecedented advantage to point measurements and would provide an instantaneous, synoptic view of highly dissipa-tive events over large areas of the ocean surface [Rohr et al., 2002].

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