# Viscous Burgers equation physical meaning

The viscous Burgers' equation: $$q_{t}+q\:q_{x}~=~\nu\:q_{xx}, \mbox{ where } \:\:\nu >0,$$ combines the nonlinear propagation of $q(x,t)$ and the diffusion.

• What is this equation for? (in modelling context)

• What is so special about it? (other than if $\nu=0$ then the solution can form a shockwave)

• I think it also provides one of the ways the Reynolds number is derived, or at least physically demonstrated. For the form shown in the OP, R = $\frac{ q \ q_{x} }{ \nu \ q_{xx} }$, which shows that the Reynolds number can represent the ratio of steepening to viscosity (or in KdV equations, viscosity is replaced by dispersion). Oct 31, 2014 at 18:17
The convection-advection equation resembles the mathematical structure of Burgers equation. Despite differences (convection-advection has an "extra" variable $c(x,t)$) you can think that Burgers describes compressible material fluid transportation by means of advection (the $\vec{v} \cdot \nabla$ term) and diffusion (the $D \nabla^2$ term) without mechanical pressure gradients applied.