Viscous Gyre

Planetary boundary layer ocean circulation driven by non-linear wind stress curl, modeled via the Stommel double-gyre stream function.

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60 FPS • Canvas 2D

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Live Parameters

Current Tracers 1200

Particle count

Circulation Velocity 0.005

Advection timestep

Mathematical Formulation

49 chars medium

Analytical Equation

\psi(x, y) = -\frac{\tau_0}{\pi \rho H \beta} \sin(\pi x) \sin(2\pi y), \quad u = -\frac{\partial \psi}{\partial y}, \quad v = \frac{\partial \psi}{\partial x}

Compact Formula

u = 2π sin(πx) cos(2πy), v = -π cos(πx) sin(2πy)

Renderer Logic

const u = 2 * Math.PI * Math.sin(Math.PI * x) * Math.cos(2 * Math.PI * y + Math.sin(t) * 0.4);
const v = -Math.PI * Math.cos(Math.PI * x) * Math.sin(2 * Math.PI * y + Math.sin(t) * 0.4);
px[i] += u * speed;
py[i] += v * speed;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#oceanography #gyre #stream-function #fluid #geophysics

Author: Math Art Core Target: 60 FPS

Viscous Gyre

Live Parameters

Mathematical Formulation

Mathematical Tags

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