Waves propagation in turbulent superfluid helium in presence of combined rotation and counterflow

Abstract

A complete study of the propagation of waves (namely longitudinal density and temperature waves, longitudinal and transversal velocity waves and heat waves) in turbulent superfluid helium is made in three situations: a rotating frame, a thermal counterflow, and the simultaneous combination of thermal counterflow and rotation. Our analysis aims to obtain as much as possible information on the tangle of quantized vortices from the wave speed and attenuation factor of these different waves, depending on their relative direction of propagation with respect to the rotation vector. PACS number(s): 05.70.Ln, 67.40.Vs, 67.40.Bz, 47.27.2i A.M.S. Classification: 82D50

A mathematical model of counterflow superfluid turbulence describing heat waves and vortex-density waves

“…Note that in this special case, as in the previous case and in [9], only the longitudinal modes are present, so that the dispersion relation assumes the form 20) which is similar to equation (5.11). Now, the arguments suggested are the same to the previous situation, in fact, under the hypothesis (5.12), the dispersion relation (5.20) takes the form…”

Hydrodynamical Models of Superfluid Turbulence

“…(1,2) s , note that it is the same as the expression obtained when the vortices are assumed fixed (Jou & Mongiovì, 2006), (Peruzza & Sciacca, 2007), whereas the attenuation term k (3,4) s is the same as the second term of k (3,4) s of the first case (n parallel to q 0 ). As in , , in this case one has the propagation of two kinds of waves, namely heat waves and vortex density waves, which cannot be considered as propagating independently from each other.…”

“…It is observed that the first sound is not influenced by the thermal counterflow, while the velocity and the attenuation of the second sound are influenced by the presence of the vortex tangle. The results are (Peruzza & Sciacca, 2007):…”

“…If we perform in the field equations (15) the change of variables (47-48), we check immediately that the first three equations are identical to the ones of the two-fluid model for helium II, even in non-inertial frame (Peruzza & Sciacca, 2007). We concentrate therefore on the field equation for the heat flux.…”

“…These transversal modes are influenced from both dissipative and nondissipative contributions B, B ′ and B ′′ in the interaction between quasi-particles and vortex lines (Peruzza & Sciacca, 2007). Second case: n orthogonal to Ω.…”