Sparse sampling of intermittent turbulence generated by breaking surface waves

We examine how Eulerian statistics of wave breaking and associated turbulence dissipation rates in a field of intermittent events compare with those obtained from sparse Lagrangian sampling by surface following drifters. We use a polydisperse two-fluid model with large-eddy simulation (LES) resolution and volume-of-fluid surface reconstruction (VOF) to simulate the generation and evolution of turbulence and bubbles beneath short-crested wave breaking events in deep water. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. Eulerian statistics are obtained from the numerical results, which are available on a fixed grid. Next, we sample the LES/VOF model results with a large number of virtual surface-following drifters that are initially distributed in the numerical domain, regularly or irregularly, before each breaking event. Time-averaged Lagrangian statistics are obtained using the time series sampled by the virtual drifters. We show that convergence of statistics occurs for signals that have minimum length of approximately 1000-3000 wave periods with randomly spaced observations in time and space relative to three-dimensional breaking events. We further show important effects of (i) extent of measurements over depth and (ii) obscuration of velocity measurements due to entrained bubbles, which are the two typical challenges in most of the available in situ observations of upper ocean wave breaking turbulence. An empirical correction factor is developed and applied to the previous observations of Thomson et al. Applying the new correction factor to the observations noticeably improves the inferred energy balance of wind input rates and turbulence dissipation rates. Finally, both our simulation results and the corrected observations suggested that the total wave breaking dissipation rates have a nearly linear relation with active whitecap coverage.