Shock formation and viscous dissipation in 1D flow
t = 0.000 | max shock steepness: 0
0.005
5
The Burgers equation ∂u/∂t + u·∂u/∂x = ν·∂²u/∂x² is the simplest PDE combining nonlinear advection with viscous diffusion. The nonlinear term steepens gradients → shock formation (in finite time for ν=0). Viscosity regularizes shocks: the steady shock profile is u(x) = −tanh(x/2ν). Exact solution via the Cole-Hopf transformation: u = −2ν·∂ₓlog(φ), where φ satisfies the heat equation. Reynolds number Re = UL/ν. Burgers is a 1D toy model for the Navier-Stokes equations.