Optical measurements of breaking wave turbulence Print

With the development of DPIV techniques that provide improved spatio-temporal coverage measurements, we considered it timely to once again return to a study of the unsteady breaking of individual waves. In this study we use DPIV techniques to measure the velocity and vorticity fields under breaking waves in the laboratory. We use the dispersive focussing technique to generate intermediate or long packets of deep-water waves. Thus the conditions of the experiments could correspond to the breaking of wind waves and swell on the continental shelf, where the depth is not directly important for the individual waves but may be for the long waves forced by the modulation of the carrier waves. Despite the spatial coverage provided by imaging techniques like DPIV, we found that we could not cover the full dynamic range and spatial extent of the flow in one image frame. While the desire to directly measure the smallest turbulent (Kolmogorov) scaleswould have required frame sizes of O(1) cm, the desire to image the whole flow would have required frames of O(1) m. We concluded that detailed studies at the Kolmogorov scales were premature before the overall kinematics of the flow were measured, and so we decided to conduct a series of measurements designed to characterize the larger coherent structures in the flow and look at the integral properties of the flow based on the energy bearing scales.

Figure 1 A) Mean velocity under a breaking wave at different times after the breaking event. Note the mean vortex propagating downstream. B) Streamline of the mean flow presented in A). C)turbulent kinetic energy density of the turbulence. The high levels of turbulence initially generated quickly dissipate.

Even with this decision it was not possible to image the whole flow with sufficient spatial resolution and we decided to build up a ``picture'' of the whole flow with a ``mosaic'' of individual frames. Since each realization of the flow is unique, such a scheme depends on our ability to build up the coherent features of the flow and the statistics through ensemble averaging.

Figure 1 shows ensemble average of the mean velocity vectors, the streamlines (along with the magnitude of the velocity) and the turbulent kinetic energy were the turbulent velocity is calculated as the departure from the ensemble mean.

We have shown that an overall description of the turbulence and coherent structures generated by breaking waves in the laboratory can be studied using a mosaic of smaller DPIV images. The advances in imaging systems since these experiments were conducted would permit a finer resolution of the velocity field with fewer fields of view, but it is likely that this mosaic approach will still be required to fully represent the flows associated with breaking waves of large Reynolds numbers.

We find that the coherent vortex generated by the breaking wave advects slowly in the wave propagation direction with a speed of approximately 0.01C, for at least 50 periods after breaking. This is consistent with the speed induced by an image line vortex above the free surface. The speed of the vortex corresponds to the speed at which the fields of turbulent kinetic energy and vorticity propagate downstream. We show that this vortex, through well-established mechanisms of wave-current interaction, may lead to a persistent region of smooth water at the site of breaking in the field.

Our measurements of the kinetic energy and vorticity, and the Reynolds stress, show that they decay like t-1, consistent with the earlier measurements of Rapp and Melville (1990) and the recent numerical modelling by Chen et al. (1999).

Measurements of the Reynolds stress, along with the hypothesis of Reynolds number independence for large R, can be used to estimate the momentum flux from breaking waves into the water column. These estimates are consistent with our earlier measurements described in Melville (1994), but are an order of magnitude less than those implied by the quasi-steady breaking measurements of Duncan (1981,1983), and an order of magnitude larger than those estimated by Phillips et al. (1999) on the basis of field measurements of microwave scattering by breaking waves. These discrepancies need to be resolved.

 
 
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