Ocean Plastic Cleanup - 2D Gyre Drift Map and Barrier Capture Rate

Controls

Live readouts

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Numerical check

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Performance graph

How to use

A patch of floating plastic (2400 tracer particles) drifts and spreads in a wind-assisted ocean gyre in a 6 km x 4 km window. A V-shaped floating barrier is towed through the water at a set speed, pursuit heading towards the centre of the remaining debris, so relative to the barrier the water carries debris into the V and towards the apex pocket, where it is collected (green graph).

The skirt draft matters: plastic is mixed down by waves, so the deeper the skirt, the less of it slips underneath. Higher wind mixes particles deeper, so the escape fraction rises. Use the heading offset to make the barrier approach the patch from the side.

Try: draft 0.5 m versus 3 m; wind 0 versus 12 m/s; barrier length 300 versus 1000 m; set the gyre to 0.02 m/s so water is nearly still and the capture rate follows the swept-area formula shown in the numerical check.

The science

Particles are passive tracers advected by the flow and spread by eddy diffusion: dx = u(x) dt + √(2 D dt) ξ. The gyre is a closed circulation from a streamfunction, which makes it exactly incompressible:

ψ = ψ₀ sin(πx/Lₓ) sin(πy/L_y), u = ∂ψ/∂y, v = −∂ψ/∂x, ∇·u = 0

Floating debris also feels wind: leeway of about 3% of the wind speed is added to the water velocity. A barrier towed at speed v_r through the water sweeps a strip of width W = 2 L sin α, so with debris surface density n the encounter rate is Ṅ = n W v_r (1 − p_escape).

Escape underneath is modelled as the share of the mixed layer below the skirt: p_escape = exp(−d / h_p), h_p = 0.4 + 0.12 U₁₀ (m) where d is the skirt draft and h_p the mean mixing depth of the particles.

Honest simplifications: 2-D surface plane, steady idealised gyre (no tides, eddies or Ekman spiral), a single particle class (no size, buoyancy or biofouling), one barrier with a simplified capture rule (reflection along the arms, collection in an apex pocket), no waves overtopping, no vessel dynamics or catch removal logistics. Not a calibrated model of any real clean-up system.

Keyboard, touch and accessibility

Space pauses or resumes the simulation.
R resets it to its initial state.
C re-runs the numerical check.
All sliders are native range inputs and work with arrow keys, Home and End; on touch devices drag on the canvas where the sim supports pointer input.
Rendering is capped at a device pixel ratio of 2 so phones stay smooth; the frame-time graph above shows the cost of the current settings (green line is 16.7 ms, i.e. 60 frames per second).

What is checked and why you can trust it

Every time the page loads, and whenever you press Re-run check, the simulation evaluates its own mathematics against an independent reference, such as a closed-form formula, a finite-difference derivative or an exhaustive count. Each line above reports PASS or FAIL together with the measured numbers, so you can see by how much it agrees. Results are also published on window.__msChecks for automated testing. The check never uses the same code path as the animation it validates, otherwise it would only confirm itself.

How to read a failure: a FAIL line means the measured discrepancy exceeded the stated tolerance for the current slider values. Try Reset, then move the sliders back toward their defaults; if a check still fails at the defaults it is a bug worth reporting. Tolerances are chosen from the numerical method itself, never tuned to make a test pass: round-off level (1e-9) for exact algebra, about 1e-3 for finite differences and Monte Carlo estimates with a few hundred thousand samples, and a documented margin for stochastic learning runs.

Reproducibility: the particle and pen simulations use the browser random generator for initial positions, so exact pixels differ between visits, but the checks depend only on mathematics and not on those positions. Fixed wave tables (curl noise) and fixed grammars (L-system) are deterministic.

This is an educational model. It shows the mechanism clearly, but it is deliberately simplified; the science panel lists what was left out.