Vertical Transport of Nearly-buoyant Particles in a Free-surface Boundary Layer

Abstract

This dissertation investigates the vertical transport of nearly buoyant, finite-sized particles in a wind-driven free-surface boundary layer, where surface waves and turbulence coexist and interact. Predicting the transport of buoyant particles in these environments is important to many environmental systems, including microplastics in the upper ocean. Vertical transport depends on turbulent mixing and particle rise velocity, both of which are influenced by wave-driven motions, turbulence intensity, and particle properties such as buoyancy, size, and shape. Quantifying the separate and coupled effects of these processes is therefore essential for predicting particle fate and informing effective monitoring and remediation strategies. To begin addressing this challenge, our first study focuses on separating wave and turbulence effects from Eulerian velocity measurements. We begin with Eulerian measurements because a fixed sensor samples the flow at a known location without any particle effects (i.e., particle drift, inertia, and buoyancy), providing a simpler setting for developing and validating our separation method. Even in this setting, however, separating waves and turbulence from Eulerian data is an ongoing challenge because surface wave motion and turbulence fluctuations can occur at overlapping frequencies. While advanced decomposition techniques have been developed, they often entail restrictive assumptions about the wave and turbulence interactions, require synchronized measurements, and/or only decompose the signal spectrally without a time series reconstruction. To address this problem, we first develop a Dynamic Mode Decomposition-based algorithm to separate wave-coherent and turbulent contributions in Eulerian velocity data with minimal assumptions about the waves and turbulence. Our method is validated against synthetic, field, and laboratory signals, and it successfully reconstructs both components. Moreover, our algorithm outperforms state-of-the-art mode-based separation methods. The decomposition provides a practical tool for isolating wave and turbulence effects in time series, which we use throughout this dissertation. In our second study, we quantify the combined effects of waves and turbulence on particle vertical transport. We evaluate the two key vertical transport parameters predicted by existing models for particles in a wind-driven free-surface boundary layers: the vertical turbulent diffusivity (turbulent mixing) and the effective particle rise velocity (particle buoyancy). Current transport models, adapted from sediment transport theory, typically rely on assumptions of a quiescent rise velocity and gradient diffusion with an unconstrained Schmidt number. Thus, we test these types of models against experiments by studying the vertical mixing of near-neutrally buoyant, finite-sized spheres, rods, and disks in a wind-driven, wavy free-surface flow, measuring their diffusivity directly from particle trajectories and comparing against concentration-based estimates. We also use the wave-turbulence separation technique we developed in our first study to characterize the influence of waves relative to turbulence in the flow. We find that particle buoyancy is the main control on the diffusivity while particle shape and finite-size effects are secondary. Furthermore, the diffusivity decreases as particle rise velocity grows relative to the turbulent fluctuations, consistent with the crossing-trajectories theory, even for finite-sized, non-spherical particles in a wavy flow. In contrast, we find that inferring the diffusivity from concentration profiles, assuming a still-water rise velocity, overestimates the diffusivity by up to $80\%$, consistent with an effective rise velocity lower than the quiescent value. We also find our turbulent Schmidt numbers to be greater than unity. Together, these results show that standard model closures can have biases in both their diffusivities and rise velocities when applied to buoyant particles at the ocean surface. Having evaluated the assumptions in existing transport closures under both waves and turbulence, we next examine the separate contributions of these processes to particle dispersion. In our third study, we combine Lagrangian measurements of particle positions and velocities with Eulerian velocity measurements for the same range of wind speeds, particle rise velocities, shapes, and sizes considered in our second study. To separate wave and turbulent motions, we use a two-component model for the Lagrangian vertical-velocity autocorrelation, capturing turbulence as a decorrelating process in time and waves as a damped oscillation with its own decorrelation time. The model reproduces the measured autocorrelations and provides estimates of the wave and turbulent contributions to the velocity variance, integral time scale, and diffusivity. The model fits show that the Lagrangian turbulent correlation time, relative to the Eulerian value, decreases with increasing particle buoyancy, consistent with the crossing-trajectories effect. In contrast, the wave decorrelation time is generally longer in the Lagrangian measurements than in the Eulerian measurements, suggesting that particles sample the wave field differently from a fixed observer. Although waves dominate the velocity variance near the free surface, their contribution to the net long-time diffusivity is relatively small, with turbulence being responsible for most of the mixing. Diffusivities estimated from the autocorrelation model agree closely with independent estimates from particle mean-square displacement, and both decrease with increasing particle rise velocity, again, consistent with the crossing-trajectories effect. Together, these results show that turbulence controls the long-time effective diffusivity of near-buoyant particles, while surface waves primarily influence the near-surface velocity variance. These results are the first of its kind to demonstrate that wave and turbulent contributions can be separated in Lagrangian measurements of particle transport in a vertically inhomogeneous free-surface boundary layer, including conditions with wave breaking.