Breaking Surface

I know, I know; A woman trapped underwater during a diving expedition? Groundbreaking! And yes, this might sound like a familiar plot. However, this time around there are no sharks. Time is their only real enemy.

Breaking Surface

The relation of surface roughness length to wave parameters is tested with data at the approximate free surface through combination of Eqs. (2) and (3). Gray circles show 5-min averages of unscaled turbulent length q3/ε, and blue circles show log mean averages with one standard deviation in log space. Orange diamonds show the log mean averages estimated with structure-function-derived TKE dissipation rates. The solid line shows the slope for , while the dashed line shows the slope with wavenumber-scaled roughness length .

Observations of surface waves, currents, and turbulence at the Columbia River mouth are used to investigate the source and vertical structure of turbulence in the surface boundary layer. Turbulent velocity data collected on board freely drifting Surface Wave Instrument Float with Tracking (SWIFT) buoys are corrected for platform motions to estimate turbulent kinetic energy (TKE) and TKE dissipation rates. Both of these quantities are correlated with wave steepness, which has previously been shown to determine wave breaking within the same dataset. Estimates of the turbulent length scale increase linearly with distance from the free surface, and roughness lengths estimated from velocity statistics scale with significant wave height. The vertical decay of turbulence is consistent with a balance between vertical diffusion and dissipation. Below a critical depth, a power-law scaling commonly applied in the literature works well to fit the data. Above this depth, an exponential scaling fits the data well. These results, which are in a surface-following reference frame, are reconciled with results from the literature in a fixed reference frame. A mapping between free-surface and mean-surface reference coordinates suggests 30% of the TKE is dissipated above the mean sea surface.

The surface flux of turbulence is difficult to prescribe at river inlets, where wave breaking is different from purely wind-driven whitecapping or depth-limited surf. At river inlets, strong currents and gradients in currents can shoal and refract surface waves, often causing breaking in intermediate depth (Zippel and Thomson 2017). Indeed, even wave dissipation (distinct from the turbulent dissipation) in such environments is still an active area of research (e.g., Rapizo et al. 2017).

In addition to the magnitude of the TKE surface flux from wave breaking, the vertical fate of this turbulence remains an active research area. Many studies agree that the decay scale is set by the significant wave height Hs and that the vertical decay is a power law. However, measurements have yet to converge on a single decay exponent λ for TKE dissipation rate. Estimates are typically constrained to 1

There is a lack of consensus, then, on the appropriate surface flux of TKE and its vertical decay at river inlets. This has, in part, lead to difficulty in understanding how wave-breaking turbulence influences such regions and whether wave-breaking turbulence has distinct properties in these regions. Certainly, the bathymetry and currents at river inlets can enhance wave breaking, but once the waves have broken, the resulting turbulence may not be any different than it is in the open ocean. There is a small, growing body of work on how wave-breaking turbulence might interact with buoyant layers. For example, Gerbi et al. (2013) modeled a buoyant river plume during upwelling-favorable winds and found that the inclusion of wave-breaking turbulence increased plume thickness. Using field measurements, Thomson et al. (2014) showed large wave energy flux gradients across a plume front and observed wave-breaking turbulence levels at the surface that were as large as published turbulence values at the subsurface plume interface. Further studies have investigated surface boundary layer effects where buoyancy is relevant (Vagle et al. 2012; Gerbi et al. 2015).

Currently, there is no clear consensus on how to map measurements from the coordinate frame to coordinates referenced to the mean sea surface; that is to say, mapping from to . Both Gemmrich (2010) and Thomson et al. (2016) did it directly, using raw time series of η. Without a general coordinate transform, it is difficult to fully interpret comparisons of the various field measurements and model predictions. It is also important to note the change from (z/z0 + 1) in the analytic solution to (z/Hs) in the scaling, which can give similar functional values near the surface for different values of λ and z0/Hs.

Here, we present field measurements of turbulence and waves from the mouth of the Columbia River to examine the validity of these surface turbulence models under a wide range of wave conditions. The uniqueness of the river mouth, relative to the open ocean, remains an open question, but the practical effect is to provide a natural laboratory with ample wave breaking. We focus in particular on determining an appropriate model roughness length and length-scale decay constant for the surface turbulence. A description of the field site, the dataset, and wave and turbulence processing techniques are presented in section 2. Data processing includes a method for correcting buoy velocities for platform motion and compares two methods for estimating TKE dissipation rates. Field measurements are compared with existing open-ocean turbulence models in section 3, along with a limited exploration of the interaction of surface turbulence with the subsurface stratification. Section 4 discusses the choice of model constants, and the implications of the measurement reference frame on the results. The results are summarized in section 5.

The drifting platform primarily tracks with the free surface, such that velocity contamination by wave orbital motions is small. However, measured along-beam velocities ubeam(z, t) are contaminated by buoy motions, both translational (bobbing) and rotational (tilting) motions. We remove these motions from the time-domain-measured velocity as follows.

Zippel and Thomson (2017) showed that wave steepness is a strong indicator of wave breaking at river inlets, and that the relevant steepness is between the deep-water formula for whitecaps and the shallow-water formula for surf. The turbulence results suggest that this wave breaking is the dominant source of near-surface turbulence throughout the Columbia River mouth. Figure 5 shows a strong correlation of depth-averaged TKE and TKE dissipation rates with wave steepness. The strong correlation of turbulence values with wave steepness holds for estimates from both the spectral method and the structure function method. Appendix A evaluates non-wave-breaking sources of turbulence, including shear production, buoyancy, surface convergence, and bottom stress; the conclusion is that wave breaking is the dominant forcing for turbulence in the upper 0.5 m. 041b061a72