Vortex Filament Drift

Classical inviscid point vortices rotating under mutual induced velocities, tracing complex filamentary chaotic orbits.

Playground

60 FPS • Canvas 2D

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Live Parameters

Tracer Count 1600

Number of fluid tracers

Vortex Core Radius (rc) 20

Vortex core smoothing width

Mathematical Formulation

45 chars medium

Analytical Equation

\mathbf{u}(\mathbf{x}) = \sum_{i=1}^{N} \frac{\Gamma_i}{2\pi} \frac{\mathbf{k} \times (\mathbf{x} - \mathbf{x}_i)}{\|\mathbf{x} - \mathbf{x}_i\|^2 + r_c^2}

Compact Formula

v_θ(r) = (Γ / 2πr) * (1 - exp(-r² / r_core²))

Renderer Logic

const dx = px[i] - vortexX[v];
const dy = py[i] - vortexY[v];
const dSq = dx * dx + dy * dy;
const factor = (vortexGamma[v] / (2 * Math.PI * (dSq + coreRSq))) * 12;
vx += -dy * factor;
vy += dx * factor;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#vortex #fluid #biot-savart #physics #turbulence #circulation

Author: Math Art Core Target: 60 FPS

Vortex Filament Drift

Live Parameters

Mathematical Formulation

Mathematical Tags

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