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.

 

Figure 2. Image montage showing an example breaking wave (left), bioluminescence intensity images (center), and shear stress (right) calculated from the cell firing model. Intensity images and shear stress images have been averaged over 5 video frames. The wave in the image is moving from left to right. Regions of high shear stress are 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

 

Conclusion
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. Ultimately, 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].