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1. Data from: Dynamics and scaling of a small river discharging into the surf zone

   https://doi.org/10.5061/dryad.2280gb608  

   Lou, Yingzhong; Horner-Devine, Alexander; Derakhti, Morteza; Giddings, Sarah; Spydell, Matthew; Rodriguez, Angelica; Simpson, Alexandra (January 2025, Dryad)

   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 a 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. Our 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. # Data from: Dynamics and scaling of a small river discharging into the surf zone [https://doi.org/10.5061/dryad.2280gb608](https://doi.org/10.5061/dryad.2280gb608) The present dataset includes the [COAWST model](https://www.usgs.gov/centers/whcmsc/science/coawst-a-coupled-ocean-atmosphere-wave-sediment-transport-modeling-system) outputs used to describe the dynamics and scaling of a small river discharging into the surf zone. ## File structure The data are structured as follows: 1. plume_scale.mat - Data of plume scales of all the cases, where * Hs: significant wave height [m] * Q: river discharge [m^3 s^-1] * L_nf: near-field plume length [m] * L_p: alongshore plume extent [m] * h_sz: water depth at the surf zone edge [m] * x_sz: surf zone width [m] * S_in: inflow salinity [PSU] * g_p: reduced gravity at the river mouth [m s^-2] * g_p*_*0: reduced gravity at the river mouth calculated using the density difference between river inflow and ambient ocean water [m s^-2] * Eta_0: water surface elevation anomaly at the river mouth [m] * V_sz: total volume of freshwater trapped in the surf zone [m^3] * T: the time required for the plume to reach a steady state [day] * L_t: plume turning distance [m] * S_bar: averaged salinity in the plume [PSU] 2. DepthAveraged.mat - Depth-averaged flow fields. DepthAveraged_BaseCase.mat, DepthAveraged_Case1.mat, DepthAveraged_Case3.mat, DepthAveraged_Case4.mat, DepthAveraged_Case6.mat, DepthAveraged_Case7.mat, DepthAveraged_Case8.mat, DepthAveraged_Case9.mat, DepthAveraged_Case16.mat, DepthAveraged_Case17.mat, DepthAveraged_Case18.mat, DepthAveraged_Case19.mat includes the results of the base case, cases 1, 3, 4, 6-9, and 16-19, respectively. In these files: * Wetdry_mask: wet/dry mask on RHO-points [binary] * Wetdry_mask_u: wet/dry mask on U-points [binary] * Wetdry_mask_v: wet/dry mask on V-points [binary] * Z: free-surface [m] * S: surface salinity [PSU] * Hs: significant wave height [m] * U: vertically integrated u-momentum component [m s^-1] * U_st: vertically-integrated u-Stokes drift velocity [m s^-1] * V: vertically integrated v-momentum component [m s^-1] * V_st: vertically-integrated v-Stokes drift velocity [m s^-1] 3. FullField_BaseCase.mat - 3D flow fields for the base case, where * Z: free-surface [m] * S: salinity [PSU] * Hs: significant wave height [m] * Lw: mean wavelength [m] * U: u-momentum component [m s^-1] * U_st: u-Stokes drift velocity [m s^-1] * V: v-momentum component [m s^-1] * V_st: v-Stokes drift velocity [m s^-1] * W: w-momentum component [m s^-1] * W_st: w-Stokes drift velocity [m s^-1] * Aks: salinity vertical diffusion coefficient [m^2 s^-1] * Akv: vertical viscosity coefficient [m^2 s^-1] * Cs_r: S-coordinate stretching curves at RHO-points [-] * Cs_w: S-coordinate stretching curves at W-points [-] 4. FreshwaterTrace_BaseCase.mat - Time series of freshwater volume and fluxes for the base case, where * i_sz: XI-index of the location of the surf zone edge [-] * i_shore: XI-index of the location of the shoreline [-] * Vsz: volume of freshwater in the plume in the surf zone [m^3] * Vis: volume of freshwater in the plume in the inner shelf [m^3] * Vsz_total: total volume of freshwater in the surf zone [m^3] * Vis_total: total volume of freshwater in the inner shelf [m^3] * R2SZ_flux: freshwater flux discharging into the surf zone [m^3 s^-1] * Vchannel: volume of freshwater in the plume in the river channel [m^3] * Vchannel_total: volume of freshwater in the river channel [m^3] * SBoundary_flux_SZ: the freshwater fluxes through the southern domain boundaries of the surf zone [m^3 s^-1] * SBoundary_flux_IS: the freshwater fluxes through the southern domain boundaries of the inner shelf [m^3 s^-1] * NBoundary_flux_SZ: the freshwater fluxes through the northern domain boundaries of the surf zone [m^3 s^-1] * NBoundary_flux_IS: the freshwater fluxes through the northern domain boundaries of the inner shelf [m^3 s^-1] * WBoundary_flux: the freshwater fluxes through the westhern domain boundary [m^3 s^-1] 5. DepthAveraged_XDiagnostic.mat - Depth-averaged diagnostic output of cross-shore momentum terms. DepthAveraged_XDiagnostic_BaseCase.mat includes the results of the base case at the steady state, and DepthAveraged_XDiagnostic_0day_1mWave.mat includes those at the start of river flow. In these files: * ubar_xadv: time-averaged 2D u-momentum, horizontal XI-advection term [m s^-2] * ubar_yadv: time-averaged 2D u-momentum, horizontal ETA-advection term [m s^-2] * ubar_xvisc: time-averaged 2D u-momentum, horizontal XI-viscosity term [m s^-2] * ubar_yvisc: time-averaged 2D u-momentum, horizontal ETA-viscosity term [m s^-2] * ubar_prsgrd: time-averaged 2D u-momentum, pressure gradient term [m s^-2] * ubar_zqsp: time-averaged 2D u-momentum, quasi-static pressure [m s^-2] * ubar_zbeh: time-averaged 2D u-momentum, Bernoulli head [m s^-2] * ubar_bstr: time-averaged 2D u-momentum, bottom stress term [m s^-2] * ubar_wbrk: time-averaged 2D u-momentum, wave breaking term [m s^-2] 6. DepthAveraged_YDiagnostic_BaseCase.mat - Depth-averaged diagnostic output of alongshore momentum terms, where * vbar_xadv: time-averaged 2D v-momentum, horizontal XI-advection term [m s^-2] * vbar_yadv: time-averaged 2D v-momentum, horizontal ETA-advection term [m s^-2] * vbar_xvisc: time-averaged 2D v-momentum, horizontal XI-viscosity term [m s^-2] * vbar_yvisc: time-averaged 2D v-momentum, horizontal ETA-viscosity term [m s^-2] * vbar_prsgrd: time-averaged 2D v-momentum, pressure gradient term [m s^-2] * vbar_zqsp: time-averaged 2D v-momentum, quasi-static pressure [m s^-2] * vbar_zbeh: time-averaged 2D v-momentum, Bernoulli head [m s^-2] * vbar_bstr: time-averaged 2D v-momentum, bottom stress term [m s^-2] * vbar_wbrk: time-averaged 2D v-momentum, wave breaking term [m s^-2] 7. grid.zip - Model grid file. * This grid file is designed for use with [ROMS](https://www.myroms.org/index.php), the hydrodynamic module of the COAWST modeling system. A diagram illustrating how the variables are placed on the grid and where the boundaries lie relative to the grid is available on [WikiROMS](https://www.myroms.org/wiki/Grid_Generation). * This grid file is in NetCDF format, which can be opened and used by a wide range of application software such as MATLAB, Python, and Panoply. For more detailed information, please refer to its [official website](https://www.unidata.ucar.edu/software/netcdf/). ## Code/Software All the post-processing scripts and data are prepared by MATLAB. 

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2. Dynamics and Scaling of a Small River Discharging into the Surf Zone

   https://doi.org/10.1175/JPO-D-24-0072.1  

   Lou, Yingzhong; Horner-Devine, Alexander R; Derakhti, Morteza; Giddings, Sarah N; Spydell, Matthew S; Rodriguez, Angelica R; Simpson, Alexandra J (August 2025, Journal of Physical Oceanography)

   Abstract 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 a 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 (L_p) 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 (L_nf/L_sz) 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 ranges from approximately 0.1 to 10 days and from 0.1 to 0.3, respectively. Our 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. Significance StatementSmall rivers and estuaries often carry pollutants, sediments, and larvae into the coastal ocean, where wave action in the surf zone can trap them near the shore. This process can play an important role in the flux of material into and out of the nearshore ecosystem and presents a potential risk to swimmers when materials are harmful. The present study uses a numerical model to investigate the fate of freshwater discharged from small rivers into the surf zone and the processes through which trapped riverine freshwater escapes from the surf zone. These results establish a basis for predicting the fate of river-borne materials from coastal rivers and understanding the exchange between the surf zone and the inner shelf. Additionally, this work provides a theoretical framework for predicting the residence time and concentration of river-borne material trapped in the surf zone. 

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3. Perspectives on Northern Gulf of Alaska salinity field structure, freshwater pathways, and controlling mechanisms

   https://doi.org/10.1016/j.pocean.2024.103373  

   Reister, Isaac; Danielson, Seth; Aguilar-Islas, Ana (December 2024, Progress in Oceanography)

   The biologically productive Northern Gulf of Alaska (NGA) continental shelf receives large inputs of freshwater from surrounding glaciated and non-glaciated watersheds, and a better characterization of the regional salinity spatiotemporal variability is important for understanding its fate and ecological roles. We here assess synoptic to seasonal distributions of freshwater pathways of the Copper River discharge plume and the greater NGA continental shelf and slope using observations from ship-based and towed undulating conductivity-temperaturedepth (CTD) instruments, satellite imagery, and satellite-tracked drifters. On the NGA continental shelf and slope we find low salinities not only nearshore but also 100–150 km from the coast (i.e. average 0–50 m salinities less than 31.9, 31.3, and 30.8 in spring, summer, and fall respectively) indicating recurring mid-shelf and shelfbreak freshwater pathways. Close to the Copper River, the shelf bathymetry decouples the spreading river plume from the direct effects of seafloor-induced steering and mixing, allowing iron- and silicic acid-rich river outflow to propagate offshore within a surface-trapped plume. Self-organized mapping analysis applied to true color satellite imagery reveals common patterns of the turbid river plume. We show that the Copper River plume is sensitive to local wind forcing and exerts control over water column stratification up to ~100 km from the river mouth. Upwelling-favorable wind stress modifies plume entrainment and density anomalies and plume width. Baroclinic transport of surface waters west of the river mouth closely follow the influence of alongshore wind stress, while baroclinic transport east of the river mouth is additionally modified by a recurring or persistent gyre. Our results provide context for considering the oceanic fate of terrestrial discharges in the Gulf of Alaska. 

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4. Freshwater Composition and Connectivity of the Connecticut River Plume During Ambient Flood Tides

   https://doi.org/10.3389/fmars.2021.747191  

   Whitney, Michael M.; Jia, Yan; Cole, Kelly L.; MacDonald, Daniel G.; Huguenard, Kimberly D. (October 2021, Frontiers in Marine Science)

   The Connecticut River plume interacts with the strong tidal currents of the ambient receiving waters in eastern Long Island Sound. The plume formed during ambient flood tides is studied as an example of tidal river plumes entering into energetic ambient tidal environments in estuaries or continental shelves. Conservative passive freshwater tracers within a high-resolution nested hydrodynamic model are applied to determine how source waters from different parts of the tidal cycle contribute to plume composition and interact with bounding plume fronts. The connection to source waters can be cut off only under low-discharge conditions, when tides reverse surface flow through the mouth after max ambient flood. Upstream plume extent is limited because ambient tidal currents arrest the opposing plume propagation, as the tidal internal Froude number exceeds one. The downstream extent of the tidal plume always is within 20 km from the mouth, which is less than twice the ambient tidal excursion. Freshwaters in the river during the preceding ambient ebb are the oldest found in the new flood plume. Connectivity with source waters and plume fronts exhibits a strong upstream-to-downstream asymmetry. The arrested upstream front has high connectivity, as all freshwaters exiting the mouth immediately interact with this boundary. The downstream plume front has the lowest overall connectivity, as interaction is limited to the oldest waters since younger interior waters do not overtake this front. The offshore front and inshore boundary exhibit a downstream progression from younger to older waters and decreasing overall connectivity with source waters. Plume-averaged freshwater tracer concentrations and variances both exhibit an initial growth period followed by a longer decay period for the remainder of the tidal period. The plume-averaged tracer variance is increased by mouth inputs, decreased by entrainment, and destroyed by internal mixing. Peak entrainment velocities for younger waters are higher than values for older waters, indicating stronger entrainment closer to the mouth. Entrainment and mixing time scales (1–4 h at max ambient flood) are both shorter than half a tidal period, indicating entrainment and mixing are vigorous enough to rapidly diminish tracer variance within the plume. 

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5. The Cross-Shelf Regime of a Wind-Driven Supercritical River Plume

   https://doi.org/10.1175/JPO-D-23-0012.1  

   Yankovsky, Elizabeth; Yankovsky, Alexander (February 2024, Journal of Physical Oceanography)

   Abstract River plumes are a dominant forcing agent in the coastal ocean, transporting tracers and nutrients offshore and interacting with coastal circulation. In this study we characterize the novel “cross-shelf” regime of freshwater river plumes. Rather than remaining coastally trapped (a well-established regime), a wind-driven cross-shelf plume propagates for tens to over 100 km offshore of the river mouth while remaining coherent. We perform a suite of high-resolution idealized numerical experiments that offer insight into how the cross-shelf regime comes about and the parameter space it occupies. The wind-driven shelf flow comprising the geostrophic along-shelf and the Ekman cross-shelf transport advects the plume momentum and precludes geostrophic adjustment within the plume, leading to continuous generation of internal solitons in the offshore and upstream segment of the plume. The solitons propagate into the plume interior, transporting mass within the plume and suppressing plume widening. We examine an additional ultra-high-resolution case that resolves submesoscale dynamics. This case is dynamically consistent with the lower-resolution simulations, but additionally captures vigorous inertial-symmetric instability leading to frontal erosion and lateral mixing. We support these findings with observations of the Winyah Bay plume, where the cross-shelf regime is observed under analogous forcing conditions to the model. The study offers an in-depth introduction to the cross-shelf plume regime and a look into the submesoscale mixing phenomena arising in estuarine plumes. Significance StatementIn this study, we characterize a novel regime of freshwater river plumes. Rather than spreading near to or along the coast, under certain conditions river plumes may propagate away from the coast and remain coherent for tens to over 100 km offshore. Cross-shelf plumes provide a mechanism by which freshwater and river-borne materials may be transported into the open ocean, especially across wide continental shelves. Such plumes carry nutrients critical for biological productivity offshore and interact with large-scale oceanic features such as the Gulf Stream. We use high-resolution numerical modeling to examine how the cross-shelf regime arises and support our findings with observational evidence. We also study the mixing phenomena and fluid instabilities evolving within such plumes. 

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