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We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT)that describes the dynamics of finite temperature superfluids. The superfluidcomponent is described by the vortex filament method while the normal fluid isgoverned by a modified Navier-Stokes equation. The superfluid vortex lines andnormal fluid components are fully coupled in a self-consistent manner by thefriction force, which induces local disturbances in the normal fluid in thevicinity of vortex lines. The main focus of this work is the numerical schemefor distributing the friction force to the mesh points where the normal fluidis defined and for evaluating the velocity of the normalfluid on the Lagrangiandiscretization points along the vortex lines. In particular, we show that ifthis numerical scheme is not careful enough, spurious results may occur. Thenew scheme which we propose to overcome these difficulties is based on physicalprinciples. Finally, we apply the new method to the problem of the motion of asuperfluid vortex ring in a stationary normal fluid and in a turbulent normalfluid.

A new self-consistent approach of quantum turbulence in superfluid helium