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.