Estuarine Stratification–Mixing Balance

Forcing

River discharge 0.50

Tidal current amplitude 0.60

Tidal period (s) 10.0

Water column state

Well-mixed

Tidal velocity U(t)

0.00

Surface−bottom ΔS

0.0 psu

Bulk Richardson Ri

0.00

Simpson–Hunter h/u³

0.0

How it works

The water column is split into 30 horizontal layers, each carrying a salinity S(z). Salinity spreads vertically by turbulent diffusion, opposed by buoyancy:

∂S/∂t = ∂/∂z( Kz(z,t) · ∂S/∂z )

Kz = K0·|U(t)| / (1 + 3.33·Ri)^1.5      (Munk–Anderson
                                          stability function)

Ri = g'·(ΔS/Δz) / U(t)²                 (gradient Richardson
                                          number: buoyancy vs
                                          tidal shear)

K0 is the raw turbulence input from the oscillating tidal current U(t) = U_tide·sin(2πt/T). The Richardson number Ri measures how strongly the density gradient resists that turbulence — when Ri is large, Kz collapses and the layer stops mixing (a real closure used in ocean/estuary mixing models). River discharge relaxes the top layer toward fresh water; the bottom layer is held near open-ocean salinity, so the two forcings compete every tidal cycle.

The particle drift also reproduces classic two-layer gravitational (estuarine) circulation: the fresher surface layer advects seaward while the saltier bottom layer creeps landward, and that residual flow strengthens with stratification — exactly the Hansen–Rattray mechanism that drives real estuarine exchange.

The readout h/u³ is the classic Simpson–Hunter stratification parameter (Simpson & Hunter, 1974): shallow, strongly-tidal water (small h/u³) mixes to uniform salinity; deep, weakly-tidal water (large h/u³) stays stratified — the same balance oceanographers use to locate real tidal mixing fronts.

River discharge — freshens the surface layer; higher values build a stronger, more persistent halocline.
Tidal current amplitude — sets the turbulence energy input; high values can erode the halocline entirely.
Tidal period — how fast the current oscillates between flood and ebb; mixing pulses twice per period, near slack water it briefly relaxes.
Reset — restores the initial linear salinity profile so you can compare regimes from the same starting point.

Fresh (river) water Saline (ocean) water

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.