Vortex fields and the Lamb–Stokes dissipation relation of fluid dynamics

Energy dissipation in Newtonian fluids containing a unified vortex field is shown to depend on −η∫V(ϖ2+λ2ζ2)dV, where η, ϖ   and ζ=u×ϖζ=u×ϖ are viscosity, vorticity and swirl. This term augments viscous dissipation where stream tube geometry is curved, e.g., in turbulent or helical flows.