A Conceptual Model of a River Plume in the Surf Zone

Abstract

We use observations from the Quinault River, a small river that flows into an energetic surf zone on the West Coast of Washington state, to investigate the interaction between river and wave forcing. By synthesizing data from moorings, drifters, and Unmanned Aerial System video, we develop a conceptual model of this interaction based on three length scales: the surf zone width, L SZ ; the near-field plume length, L NF ; and the cross-shore extent of the channel, L C . The relationships between these length scales show how tidal variability and bathymetric effects change the balance of wave and river momentum. The most frequently observed state is L SZ > L NF . Under these conditions the surf zone traps the outflowing river plume and the river water's initial propagation into the surf zone is set by L NF . When the river velocity is highest during low water, and when wave forcing is low, L NF > L SZ and river water escapes the surf zone. At high water during low wave forcing, L C > L SZ , such that minimal wave breaking occurs in the channel and river water escapes onto the shelf. Based on the discharge, wave, and tidal conditions, the conceptual model is used to predict the fate of river water from the Quinault over a year, showing that approximately 70% of the river discharge is trapped in the surf zone upon exiting the river mouth.Plain Language Summary Small rivers are an important source of sediment, nutrients, and pollutants to the coastal ocean, but they are less well studied than their larger siblings. The coastal discharge from small rivers often meets large breaking waves in the surf zone. Our work investigates the effect of the large waves present at the mouth of one such river, the Quinault River in Washington State. We find that the fate of Quinault River water is determined by the relative importance of river, wave, and depth effects, all of which are modulated by the tide. When wave forcing dominates, river water is trapped in the surf zone. When river forcing dominates, river water escapes the surf zone. The difference in depth between the offshore channel and the rest of the beach can also allow river water to escape the surf zone by reducing the effect of the wave forcing. When we apply our conceptual model to 1 year of wave, river, and tide data, we predict that 70% of Quinault River discharge is trapped in the surf zone. The sediment and pollutants carried by this trapped river water can thus have important impacts on beach erosion, public health, and local ecology.Small river mouths are often unengineered, allowing surf zone wave breaking to occur near or at such outflows. In regions with higher population densities, engineered structures such as jetties are present at most river mouths, preventing wave breaking and the influence of surf zone dynamics on buoyancy and

Long‐Distance/Time Surf‐Zone Tracer Evolution Affected by Inner‐Shelf Tracer Retention and Recirculation

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The transport and dilution of shoreline released tracers, such as pathogens (e.g., Boehm, 2003) or larvae (e.g., Morgan et al, 2018), is important to coastal ecosystems and human health (Boehm et al, 2017). The surf-zone can entrain shoreline released tracers and discharges from small-scale and low-flow rivers, estuaries and out-falls (Kastner et al, 2019;Rodriguez et al, 2018;Wong et al, 2013). Surf-zone released tracers have been detected in coastal community aerosols (Pendergraft et al, 2021), indicating potential for pathogen and toxin exposure without direct coastal water contact (e.g., Kirkpatrick et al, 2010).

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River Plume Modulation by Infragravity Wave Forcing

“…where U 0 is river velocity at the mouth (variable in a tidal cycle), Q is river discharge, g′ is the reduced gravity (based on density differences between the plume and ocean), and 𝐴𝐴 𝐴𝐴𝑒𝑒 is an entrainment velocity defined to represent the mixing of density and momentum from the lower ocean layer into the upper river plume layer (Hetland, 2010), and has typical values in the range 1-8 mm/s (Kastner et al, 2019;MacDonald & Geyer, 2004). The cross-flow length is determined by the discharge momentum and the alongshore velocity in the surfzone (Jones et al, 2007;Wong et al, 2013)…”

“…L NF predicts the region in which the momentum of a jet, rather than its buoyancy, controls the flow (Hetland, 2010;Kastner et al, 2019), while L a can be interpreted as the characteristic length scale for the outflow jet to become bent by the cross-flow (Jones et al, 2007;Wong et al, 2013). The relative magnitude of these two discharge length scales compared to the surfzone width provides a framework to predict the fate of the river water in the coastal system (Kastner et al, 2019;Wong et al, 2013). Kastner et al (2019) proposed that if L NF > L SZ the river water exits the surfzone as its momentum overcomes the breaking wave forcing.…”

“…Conceptual models that predict the fate of freshwater in the surfzone use length scales to characterize river and wave momentum, and the presence of alongshore currents (e.g., Kastner et al., 2019; Wong et al., 2013). The three primary length scales are: the surfzone width ( L SZ ), the near‐field plume length ( L NF ) and the cross‐flow length ( L a ).…”

Modeling Untreated Wastewater Evolution and Swimmer Illness for Four Wastewater Infrastructure Scenarios in the San Diego‐Tijuana (US/MX) Border Region

“…The oceanic transport and dispersion of untreated wastewater is important for determining shoreline pathogen concentrations. Tracer released from small coastal inlets can be surfzone entrained or jet offshore onto the shelf (Feddersen et al., 2016; Kastner et al., 2019; Olabarrieta et al., 2014; Rodriguez et al., 2018; Wong et al., 2013). Surfzone tracer is often alongshore transported 10 km d −1 (Grant et al., 2005; Grimes et al., 2020, 2021), driven by obliquely incident breaking waves.…”