Theory of energy spectra in superfluid He-4 counterflow turbulence

Abstract

In the thermally driven superfluid He-4 turbulence, the counterflow velocity $U_{\mathrm{ns}}$ partially decouples the normal and superfluid turbulent velocities. Recently we suggested [J. Low Temp. Phys. 187, 497 (2017)] that this decoupling should tremendously increase the turbulent energy dissipation by mutual friction and significantly suppress the energy spectra. Comprehensive measurements of the apparent scaling exponent nexp of the 2nd-order normal fluid velocity structure function $S_2(r)\propto r^{n_{\exp }}$ in the counterflow turbulence [Phys.Rev.B 96, 094511 (2017)] confirmed our scenario of gradual dependence of the turbulence statistics on the flow parameters. We develop an analytical theory of the counterflow turbulence, accounting for a twofold mechanism of this phenomenon: i) a scale-dependent competition between the turbulent velocity coupling by the mutual friction and the $U_{\mathrm{ns}}$-induced turbulent velocity decoupling and ii) the turbulent energy dissipation by the mutual friction enhanced by the velocity decoupling. The suggested theory predicts the energy spectra for a wide range of flow parameters. The mean exponents of the normal fluid energy spectra $⟨m_n{⟩}_{10}$, found without fitting parameters, qualitatively agree with the observed $n_{\exp }+1$ for $T\gtrsim 1.85$K

14 pages, 7 figures

References in corpus (10)

• Bottleneck crossover between classical and quantum superfluid turbulence
• Visualization study of counterflow in superfluid helium-4 using metastable helium molecules
• Energy Spectra of Developed Turbulencein Helium Superfluids
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• Dissipation of Quasiclassical Turbulence in Superfluid ${}^4$He
• Coexistence and interplay of quantum and classical turbulence in superfluid He-4: Decay, velocity decoupling and counterflow energy spectra
• Turbulent statistics and intermittency enhancement in coflowing superfluid ${}^4$He
• Coexistence of quantum and classical flows in quantum turbulence in the $T=0$ limit
• Local and non-local energy spectra of superfluid ${}^3$He turbulence
• Statistics of Quantum Turbulence in Superfluid He

Cited by in corpus (5)

• ${}^4$He Counterflow Differs Strongly from Classical Flows: Anisotropy on Small Scales
• Statistics of turbulence and intermittency enhancement in superfluid ${}^4$He counterflow
• Double accumulation and anisotropic transport of magneto-elastic bosons in yttrium iron garnet films
• Strong anisotropy of superfluid ${}^4$He counterflow turbulence
• Theory of anisotropic superfluid He-4 counterflow turbulence