Estuarine Circulation Evaluator

U_res = U_river + U_wind + U_coastal

U_river = Q_r / (W × H)

U_wind = τ_w × C_d / (ρ × H)

τ_w = ρ_air × C_d × U₁₀²

Where: Q_r=river discharge, W=width, H=depth, τ_w=wind stress

M = (E_tidal + E_wind) / (1 + N²)

E_tidal = U_tidal³

E_wind = U₁₀³ / F

N² = (g/ρ) × (∂ρ/∂z)

Where: N²=buoyancy frequency, F=fetch length, g=gravity

CI = (U_res × M) / (1 + ∂ρ/∂z)

∂ρ/∂z ≈ β × (S_bottom - S_surface) / H

β = 0.78 kg/m³/psu (haline contraction)

Where: β=haline contraction coefficient, S=salinity

T_f = V_estuary / Q_exchange

V_estuary = W × H × L

Q_exchange = Q_river + Q_tidal

Q_tidal = U_tidal × W × H

Where: L=estuary length, Q=volumetric flow rate