Passive tracer advected by a 2D flow field plus molecular diffusion. Click to inject dye. Watch striation, stretching, and the Batchelor scale where diffusion beats stirring.
Advection-diffusion: ∂c/∂t + u·∇c = κ∇²c. The Péclet number Pe=UL/κ measures advection vs diffusion. High Pe: tracer forms thin filaments (Batchelor scale η_B = √(κ/γ̇)) before diffusing. Relevant to ocean mixing, pollutant dispersion, and microfluidics.