Two-layer hydraulics at the river–ocean interface

Abstract

Liftoff is the hydraulically forced detachment of buoyant freshwater from the channel bottom or seabed that occurs as river water discharges into the coastal ocean. It is a key feature of strongly stratified systems, occurring well upstream in the channel or seaward of the river mouth under sufficiently strong forcing. We present a two-layer hydraulic solution for the river–ocean interface that considers the river, estuary and near-field river plume as a single interlinked system, extending previous work that considered them separately. This unified approach provides a prediction of the liftoff location and free-surface profile for a wide range of forcing conditions, which are characterized in terms of the freshwater Froude number $F_{f}\equiv Q/b_{0}\sqrt{g_{0}^{\prime }h_{0}^{3}}$. Here, $Q$ is the river discharge, $b_{0}$ is the channel width, $g_{0}^{\prime }\equiv (\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}_{0}/\unicode[STIX]{x1D70C}_{2})g$ is the reduced gravitational acceleration, $\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}_{0}$ is the density contrast between fresh and ocean water and $h_{0}$ is the total water depth at the river mouth. The solution is validated with laboratory experiments using an experimental apparatus consisting of a long, sloping river channel that discharges into a deep, wide saltwater basin. The experiments simulate the full range of hydraulic behaviours predicted by the model, from saltwater intrusion to offshore liftoff. For $F_{f}<1$, liftoff occurs in the estuary channel and our results show that the relationship between intrusion length and $F_{f}$ depends on the channel slope. For $F_{f}>1$, corresponding to flood conditions in many natural systems, liftoff is forced outside the river mouth and the hydraulic coupling between the channel and shelf becomes more important. For these conditions and for intermediate to steeply sloped shelves, the offshore liftoff distance varies linearly with $F_{f}-1$, a particularly simple scaling given the nonlinearity and relative complexity of the governing equations. The model and experimental results support a conceptual description of the river–ocean interface that relates the liftoff location, free-surface elevation and the spreading rate of the buoyant river plume.

The Propagation of Fluvial Flood Waves Through a Backwater‐Estuarine Environment

“…For example, during high flow events water level consistently peaked at Main Pass before the rest of the bay (Figures and a). This is likely associated with the hydrodynamics of Main Pass, which may generate supercritical flow (Noble et al, ), a process that lowers the water level as flow increases (Poggioli & Horner‐Devine, ).…”

River Plume Liftoff Dynamics and Surface Expressions

“…Thus, each thick solid line in Figure 8 was computed with a single value of κ , which ranges from −0.18 to 0.22. The κ values were also entered into the Poggioli and Horner‐Devine (2018) hydraulic model to compute the L lo and the predictions agree well with those of Equation (Figure 8). In section 6.2 we determine the spreading rate from the ROMS salinity fields directly and show that the values of κ from these fits are consistent with the observed spreading.…”

“…The dependence of the liftoff length on discharge, α and R A is explored in Figure 8, which shows dimensionless liftoff lengths computed from ROMS output compared with analytical model predictions of Equations and , and the Poggioli and Horner‐Devine (2018) hydraulic model. Note that the Poggioli and Horner‐Devine (2018) model returns no prediction for some high Fr f values because no hydraulic solution exists. For all values of α and R A , liftoff occurs further offshore as Fr f increases, consistent with the expectation that liftoff is further away from the mouth as discharge increases (Jones et al., 2007; Geyer & Ralston, 2011; Poggioli & Horner‐Devine, 2018; Safaie, 1979).…”

“…The river has a bottom slope of 0.0001 and empties into an ocean with a constant shelf slope, vertical coastal wall, and 30 S layers with resolution focused near the surface and the bottom (Figure 3d). Shelf slopes of 0.001, 0.002, and 0.005 were chosen for comparison with previous studies, for example, Yankovsky and Chapman (1997) and Poggioli and Horner-Devine (2018). Sensitivity studies were conducted to determine the minimum resolution necessary to resolve the dynamics of plume liftoff and spreading near the mouth.…”

“…Recently, Poggioli and Horner‐Devine (2018) used a two‐layer hydraulic model of the river, estuary, and near‐field river plume to study liftoff and included lateral plume spreading due to buoyancy. The model is hydrostatic, with the density and velocity assumed to be uniform in each layer and the velocity in the lower layer assumed to be negligible.…”