Mutagen Pollution: River Plume & Mutation-Frequency Simulator (2D)

Discharge Source

Discharge rate Q 55

River flow velocity v 0.90 m/s

Turbulent mixing D 0.18 m²/s

Degradation rate k 0.012 /s

Mutagenic sensitivity α 0.90

Live Readouts

Peak conc.

0.0 mg/L

Elapsed

0 s

Mean mutation freq.

0.0 %

Max mutation freq.

0.0 %

Clean water (C ≈ 0)

Moderate exposure

Peak plume concentration

Low mutation frequency

High mutation frequency

How it works

Top-down view of a river reach: x runs downstream, y runs across the channel. A mutagenic effluent enters at a fixed pipe cell and the concentration field C(x,y,t) is integrated every frame on a finite-difference grid using the 2‑D advection–diffusion–decay equation:

∂C/∂t = D·∇²C − v·∂C/∂x − k·C + S(x,y)

D = turbulent mixing coefficient (m²/s)
v = mean flow velocity (m/s)
k = degradation rate — photolysis + microbial breakdown (1/s)
S = continuous point source at the discharge cell

Every grid cell also accumulates a cumulative dose from the concentration it has been exposed to, and that dose is converted into a local mutation-frequency field MF(x,y,t) using a genuine dose–response curve — the same two families used to read out real Ames-test and epidemiological mutagenicity data:

dose(x,y,t) = ∫ C(x,y,τ) dτ

Linear (no-threshold):  MF = MF₀ + α · dose
Hill (saturating):      MF = MF₀ + MFmax · doseⁿ / (Kⁿ + doseⁿ)

MF₀   = spontaneous background mutation frequency
α     = mutagenic potency slope (linear model)
K, n  = half-saturation dose and cooperativity (Hill model)

Discharge rate Q — source strength at the pipe outfall; higher Q raises peak concentration and everything downstream of it.
Flow velocity v — how fast the river carries the plume; faster flow thins the plume but shortens contact time per unit distance.
Turbulent mixing D — lateral/longitudinal spreading; higher D dilutes the plume faster but widens the exposed corridor.
Degradation rate k — how quickly the mutagen breaks down chemically or biologically, shrinking the effective dose reaching the far bank.
Mutagenic sensitivity α — potency slope (linear model) or asymptote scale (Hill model); higher α means the same dose produces a larger jump in mutation frequency.
The downstream transect chart plots the concentration and mutation-frequency fields averaged across the channel width, at every distance from the outfall, so you can see the mutation-frequency curve is derived directly from the live concentration field, not scripted independently.

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