Vortex dynamics in rotating counterflow and plane Couette and Poiseuille turbulence in superfluid helium

An equation previously proposed to describe the evolution of vortex-line density in rotating counterflowturbulent tangles in superfluid helium Phys. Rev B 69, 094513 2004 is generalized to incorporate nonvanishingbarycentric velocity and velocity gradients. Our generalization is compared with an analogous approachproposed by Lipniacki Eur. J. Mech. B Fluids 25, 435 2006, and with experimental results bySwanson et al. Phys. Rev. Lett. 50, 190 1983 in rotating counterflow, and it is used to evaluate the vortexdensity in plane Couette and Poiseuille flows of superfluid helium.