Dynamics of Small-Scale River Plumes in the Surf Zone: Idealized and Realistic Modeling

Abstract

River plumes transport freshwater, nutrients, and terrigenous materials (e.g., sediment, larvae, and contaminants) into the coastal ocean, significantly impacting nearshore water quality and coastal ecosystems. Despite the abundance and potentially significant combined fluxes of small-scale plumes with small discharge that are generated by narrow rivers and creeks, their dynamics and impacts remain poorly understood. Small rivers often exhibit complex behavior due to their vulnerability to morphological changes, climate changes, and human activities. Furthermore, the pollutants they carry may pose greater risks than those from larger discharges, as they are generally more difficult to monitor and tend to remain trapped within the surf zone. We use an idealized numerical model to investigate the dynamics and fate of a small river discharging into the surf zone. Our study reveals that the plume reaches a steady state, at which point the combined advective and diffusive freshwater fluxes from the surf zone to the inner shelf balance the river discharge. At steady state, the surf zone is well-mixed vertically due to wave-enhanced vertical turbulent diffusion and has a strong cross-shore salinity gradient. The horizontal gradient drives a cross-shore buoyancy-driven circulation, directed offshore at the surface and onshore near the bottom, which opposes the wave-driven circulation. Using a scaling analysis based on momentum and freshwater budgets, we determine that the steady state alongshore plume extent (Lp) and the fraction of river water trapped in the surf zone depend on the ratio of the near-field plume length to the surf zone width (Lnf/Lsz) across a wide range of discharge and wave conditions, and a limited set of tidal conditions. This scaling also allows us to predict the residence time and freshwater fraction (or dilution ratio) in the steady-state plume within the surf zone, which range from approximately 0.1 to 10 days and 0.1 to 0.3, respectively. These findings establish the basic dynamics and scales of an idealized plume in the surf zone, as well as estimates of residence times and dilution rates that may provide guidance to coastal managers. We then investigate the transport of the river plume at Los Penasquitos Lagoon (LPL), a small estuary in Southern California that discharges into an energetic surf zone. As a part of the Plumes in Nearshore Conditions (PiNC) project, we developed a quasi-realistic COAWST model incorporating in-situ bathymetry measurements and forced with realistic river discharge, tides, and waves. The model was validated by a comparison with the observed spectra of water surface elevation and the distribution of dye released from the estuary mouth, demonstrating its ability to effectively capture river transport patterns. The results show that at LPL, breaking waves generate alongshore convergent currents due to shoreline curvature, which dominate the volume budget within the surf zone. Freshwater ejection events at the surf zone edge are typically narrow (95% are less than 60 m wide) and are tidally modulated. These events are associated with bathymetry-driven rip currents during mid-tide and by alongshore convergent currents during low tide. Furthermore, sensitivity analysis suggests that uncertainty in the choice of horizontal mixing scheme significantly influences the modeled plume processes. Our findings offer a framework for understanding the wave-driven transport of small-scale river plumes discharging into the surf zone, which may contribute to improved predictions of spreading and dilution processes and help mitigate risks associated with poor coastal water quality. Finally, in order to generalize plume behavior that is complex due to an array of factors that influence nearshore currents, many of which are specific to individual river mouths, we utilized the quasi-realistic COAWST model to conduct a series of sensitivity tests examining the impacts of bathymetry, tides, waves, river discharge, and buoyancy on plume dynamics at LPL. Prior works have shown that breaking waves can fundamentally alter plume structure by preventing river water from directly discharging into the inner shelf. In this work, we find that wave-generated currents can also facilitate transport by inducing alongshore convergence in the presence of large-scale bathymetric features such as shoreline curvature. Small-scale bathymetric perturbations generate rip currents and surf zone eddies, which interact with large-scale surf zone circulation and lead to ejection events across the surf zone. Tidal forcing produces pronounced peaks and troughs in cross-shore freshwater transport, corresponding to ebbing and rising tides, because the magnitude of tidal discharge greatly exceeds that of the small-scale river, and tidal currents enhance offshore and onshore transport during ebbing and rising phases, respectively. Although buoyancy effects generally do not significantly affect freshwater transport patterns at LPL, they may shift the convergence point of alongshore currents and dampen peak export during ebbing tides. Additionally, we observe that the half-life of dye concentration at the river mouth is generally linearly related to the ratio of local Stokes and Eulerian mean velocities across a range of conditions. These findings provide a framework for assessing the relative contributions of various environmental forcings to the transport of small-scale river plumes discharging into the surf zone. The results may help improve predictions of the spreading and dilution of river water and its associated constituents under varying conditions, thereby supporting efforts to reduce human exposure to contaminated waters.