Specific heat of the Kelvin modes in low temperature superfluid turbulence

Turbulence in superfluid helium~II is a tangle of quantized vortex lines which interact via the classical Biot-Savart law. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonloc...

The present article reviews the recent developments in the physics of quantum turbulence. Quantum turbulence (QT) was discovered in superfluid $^4$He in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that i...

On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $\alpha(T) \ll 1$, responsible for the cutoff. The curve $\ln L(\ln \alpha)$ is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wavenumber re...

We review the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) equations for superfluid Helium turbulence and discuss their implications for recent measurements of superfluid turbulence decay. A new Hamiltonian formulation of these equations renormalizes the vortex line velocity to incorporate finite temperature effects. These effects also renormalize the coupling constant in the mutual friction force between the superfluid and normal fluid components by a factor of rho_s / \rho (t...

The article considers implications of tilt symmetry (symmetry with respect to tilting of the coordinate axis with respect to which vortex motion is studied) in the non-linear dynamics of Kelvin waves. The conclusion is that although the spectrum of Kelvin wave is not tilt-invariant, this does not compromise tilt invariance of the Kelvin-wave cascade vividly argued now in the theory of superfluid turbulence. The article investigates the effect of strong kelvon interaction on t...

We present experimental, numerical and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasi-classical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation is temperature- and mutual frict...

Numerical calculations of Helium-II hydrodynamics show that a dense tangle of superfluid vortices induces in an initially stationary normal fluid a highly dissipative, complex, vortical flow pattern ("turbulence") with a -2.2 energy spectrum scaling exponent and fluctuations Reynolds number of order unity. In this normal fluid flow the effects of mutual friction excitation from the superfluid vortices and those of viscous stresses are of the same order. The results suggest th...

The problem of the statistics of a set of chaotic vortex lines in a counterflowing superfluid helium is studied. We introduced a Langevin-type force into the equation of motion of the vortex line in presence of relative velocity $\mathbf{v_{ns}}$. This random force is supposed to be Gaussian satisfying the fluctuation-dissipation theorem. The corresponding Fokker-Planck equation for probability functional in the vortex loop configuration space is shown to have a solution in t...

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re=UR/\nu in classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re >> 1 ...

Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the...