2.3. The diffusion equation

The diffusion equation describes a molecular mixing process that, with time, distributes a parameter (e.g., salt, temperature, momentum) towards a state with smaller spatial gradients. If you wait long enough, the parameter is evenly distributed.

The diffusion equation for momentum \(u(x,t)\) is expressed:

\[\frac{\partial u}{\partial t}=\gamma\frac{\partial^2u}{\partial x^2},\]

where \(\gamma>0\) represents a diffusion coefficient, referred to as viscosity.