Counter-flow Induced Decoupling in Super-Fluid Turbulence

Abstract

In mechanically driven superfluid turbulence the mean velocities of the normal- and superfluid components are known to coincide: ${\mathbf{U}}_{\text{n}}={\mathbf{U}}_{\text{s}}$. Numerous laboratory, numerical and analytical studies showed that under these conditions the mutual friction between the normal- and superfluid velocity components couples also their fluctuations: ${\mathbf{u}}_{\text{n}}^{\prime }(\mathbf{r},t)\approx {\mathbf{u}}_{\text{s}}^{\prime }(\mathbf{r},t)$ almost at all scales. In this paper we show that this is not the case in thermally driven superfluid turbulence; here the counterflow velocity ${\mathbf{U}}_{\text{ns}}\equiv {\mathbf{U}}_{\text{n}}-{\mathbf{U}}_{\text{s}}\ne 0$. We suggest a simple analytic model for the cross correlation function $⟨{\mathbf{u}}_{\text{n}}^{\prime }(\mathbf{r},t)\cdot {\mathbf{u}}_{\text{s}}^{\prime }({\mathbf{r}}^{\prime },t)⟩$ and its dependence on $U_{\text{ns}}$. We demonstrate that ${\mathbf{u}}_{\text{n}}^{\prime }(\mathbf{r},t)$ and ${\mathbf{u}}_{\text{s}}^{\prime }(\mathbf{r},t)$ are decoupled almost in the entire range of separations $|\mathbf{r}-{\mathbf{r}}^{\prime }|$ between the energy containing scale and intervortex distance.

References in corpus (3)

• Energy Spectra of Developed Turbulencein Helium Superfluids
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• Kelvin waves and the decay of quantum superfluid turbulence

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• Coexistence and interplay of quantum and classical turbulence in superfluid He-4: Decay, velocity decoupling and counterflow energy spectra
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• Statistics of turbulence and intermittency enhancement in superfluid ${}^4$He counterflow
• Counterflow-Induced Inverse Energy Cascade in Three-Dimensional Superfluid Turbulence
• Local and non-local energy spectra of superfluid ${}^3$He turbulence
• Theory of energy spectra in superfluid He-4 counterflow turbulence
• Strong anisotropy of superfluid ${}^4$He counterflow turbulence
• Statistics of Quantum Turbulence in Superfluid He
• Theory of anisotropic superfluid He-4 counterflow turbulence