Turbulent dissipation anomaly (${\lim }_{\nu \to 0}ϵ>0$)

Although the local viscous dissipation is $2\nu S_{ij}{S}_{ij}$, increasingly intense velocity gradients can compensate for vanishing kinematic viscosity. A Burgers vortex illustrates this mechanism: its radius shrinks while its excess integrated viscous dissipation remains finite. Such a local model does not by itself prove the zeroth law of turbulence for a whole flow.