The salt wedge position in a bar-blocked estuary subject to pulsed inflows

A series of laboratory experiments were carried out to investigate the response of a bar-blocked, saltwedge estuary to the imposition of both steady freshwater inflows and transient inflows that simulate storm events in the catchment area or the regular water releases from upstream reservoirs. The trapped salt water forms a wedge within the estuary, which migrates downstream under the influence of the freshwater inflow. The experiments show that the wedge migration occurs in two stages, namely (i) an initial phase characterized by intense shear-induced mixing at the nose of the wedge, followed by (ii) a relatively quiescent phase with significantly reduced mixing in which the wedge migrates more slowly downstream.<br /><br />Provided that the transition time t_T between these two regimes satisfies t_T>g′h⁴L/q³α, as was the case for all our experiments and is likely to be the case for most estuaries, then the transition occurs at time t_T=1.2(gα³L⁶/g′³q²)^1/6, where g′=gΔρ/ρ0 is the reduced gravity, g the acceleration due to gravity, Δρ the density excess of the saline water over the density ρ₀ of the freshwater, q the river inflow rate per unit width, and L and α are the length and bottom slope of the estuary, respectively.<br /><br />A simple model, based on conversion of the kinetic energy of the freshwater inflow into potential energy to mix the salt layer, was developed to predict the displacement xw over time t of the saltwedge nose from its initial position. For continuous inflows subject to t<t_T, the model predicts the saltwedge displacement as x_w/h=1.1 (t/τ)^1/3, where the normalizing length and time scales are h=(q²/g)^1/3 and τ=g′α²h4L/q³, respectively. For continuous inflows subject to t>tT, the model predicts the displacement as xw/h=0.45N1/6(t/τ)1/6/α, where N=q²/g′h²L is a non-dimensional number for the problem. This model shows very good agreement with the experiments. For repeated, pulsed discharges subject to t<t_T, the saltwedge displacement is given by (xw/h)3−(x0/h)(xw/h)2=1.3t/τ, where x₀ is the initial displacement following one discharge event but prior to the next event. For pulsed discharges subject to t>t_T, the displacement is given by (xw/h)⁶−(x0/h)(xw/h)⁵=0.008N(t/τ)/α⁶. This model shows very good agreement with the experiments for the initial discharge event but does systematically underestimate the wedge position for the subsequent pulses. However, the positional error is less than 15%.<br />