Counter-flow Induced Decoupling in Super-Fluid Turbulence

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}$}(\mathbf r,t) \approx \mathbf u’{$\text{s}$}(\mathbf r,t)$ 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 $\left\langle \mathbf u’{$\text{n}$}(\mathbf r,t) \cdot \mathbf u’{$\text{s}$}(\mathbf r’,t)\right \rangle$anditsdependenceon$U_{$\text{ns}$}$\mathrm{.}Wedemonstratethat$\mathbf u’{$\text{n}$}(\mathbf r,t)$and$ \mathbf u’{$\text{s}$}(\mathbf r,t)$ are decoupled almost in the entire range of separations $\mathrm{\mid }\mathbf{r}-{\mathbf{r}}^{\mathrm{\prime }}\mathrm{\mid }$ between the energy containing scale and intervortex distance.