Hydrodynamic impulse and energy of vortex tangle in superfluid turbulent He-II

The average hydrodynamic impulse (or Lamb impulse) JV in the counter flowing, superfluid, turbulent He-II and the kinetic energy E, which is associated with the chaotic vortex filaments, are calculated. These quantities are defined as averages of the classical quantities taken over the stochastic vortex loop distribution. The averaging procedure was performed by using the Gaussian model of the chaotic vortex tangle elaborated earlier. Calculations show that the quantity JV has an only a component in the direction of external counterflow velocity (created, e.g., by a heater). As for the energy, it is shown that besides the usual local contribution, the quantity E includes additional terms due to a long-range interaction. Some dynamic properties of the turbulent He-II due to the impulse and energy of the vortex configuration, such as suppression of the superfluid density and decrease in the velocity of the second sound that propagates in the superfluid turbulent He-II, are discussed