Hydrodynamics of superfluid turbulence

The equations of motion of superfluid helium, taking account of a chaotic cluster of vortex filaments (superfluid turbulence), are obtained by means of a method close to the Bekarevich-Khalatnikov theory. These equations are used for an investigation of the propagation of linear and nonlinear second sound in a supercritical helium countercurrent. A relation is obtained between the transit time of a nonlinear wave and the parameters of superfluid turbulence. This relation can be considered as a new method of probing the vortex cluster.