Estuary Cross-Section: Longitudinal Salt-Wedge Model

Forcing

River discharge 0.50

Tidal current amplitude 0.60

Tidal period (s) 10.0

Channel state

Well-mixed

Tidal velocity U(t)

0.00

Mean vertical ΔS

0.0 psu

Bulk Richardson Ri

0.00

Salt intrusion length

How it works

This is the 2D longitudinal-vertical counterpart to the 3D estuary model. Instead of one vertical salinity column repeated uniformly along the channel, this solves a real 2D field S(x,z,t) on a 90×24 grid spanning the river head (x=0) to the open-ocean mouth (x=L):

∂S/∂t = −u(x,z,t)·∂S/∂x + ∂/∂z( Kz·∂S/∂z ) + Kx·∂²S/∂x²

Kz = K0·|U(t)| / (1 + 3.33·Ri)^1.5      (same Munk–Anderson
                                          closure as the 3D model)
Ri = g'·(∂S/∂z) / U(t)²

u(x,z,t) = u_river + U(t) + u_grav(x,z)

The vertical mixing closure is identical to the 3D model's — turbulence collapses whenever the local Richardson number is high. What's new here is the horizontal transport: u_grav(x,z) = k·(∂S̄/∂x)·(1−2z*) is the classic Hansen–Rattray gravitational circulation, driven by the real, locally-computed longitudinal salinity (density) gradient ∂S̄/∂x at every point along the channel — not a single global stratification number substituting for it, as the 3D model necessarily uses since it has no along-channel dimension. The river's freshwater boundary condition sits at x=0, the ocean's fixed salinity at x=L, and the salt wedge that forms between them — its shape, its reach upstream, and how far the tide pushes it back — all emerge from the same coupled PDE, not from a pre-set profile.

The readout salt intrusion length is the new headline number this 2D geometry makes possible: the fraction of the channel, measured from the ocean mouth, over which the depth-averaged salinity stays above the river/ocean midpoint. High river discharge shortens it (fresh water pushes the wedge seaward); strong tidal mixing can extend it by homogenizing the whole channel toward marine salinity.

River discharge — sets the freshening strength at the landward boundary; higher values shrink the salt intrusion and build a persistent, sharply stratified wedge.
Tidal current amplitude — the turbulence energy input (uniform along the channel, as tides are barotropic); high values erode vertical stratification everywhere.
Tidal period — how fast the current oscillates between flood and ebb.
Reset — restores the initial linear-in-x salinity field (uniform with depth) so regimes can be compared from the same start.

Fresh (river) water Saline (ocean) water

← river head ocean mouth →