In this detailed study of inhomogeneous superfluid turbulence created in a spatially nonuniform flow, we measure the turbulent dissipation produced by thermal counterflow in a nonuniform rectangular channel. The width of the channel increases linearly with position r along the channel length to impose a known spatial nonuniformity on the velocity in the flow direction, V\ensuremath{\propto}Q\ifmmode \dot{}\else \.{}\fi{}/r, where Q\ifmmode \dot{}\else \.{}\fi{} is the heat current. Because the channel widens gradually, this divergence is weak, producing a small deviation from uniform flow. Probes embedded in the channel walls allow access to the local temperature at several positions r. We employ sensitive differential thermometry to measure the temperature difference between any two of these locations to high precision. The single turbulent state we observe is clearly the analog of the T-II state of fully developed, homogeneous turbulence present in uniform flows. Making an approximation of local uniformity, we attempt to extend the theoretical description of turbulence in uniform flows to our results by replacing the uniform velocity with the local velocity in the expression for the temperature gradient. When applied locally, the Schwarz model of homogeneous turbulence, so successful in describing the T-II state in uniform flows, has the wrong dependence on both r and Q\ifmmode \dot{}\else \.{}\fi{} to characterize our results. The Geurst three-fluid model, which extends to situations where a gradient is present in the line density in an otherwise uniform flow, likewise does not agree with our observations when used in the local approximation.We therefore find that even a small perturbation imposed on a uniform flow radically changes the nature of the T-II state, and the inhomogeneous T-II state we observe is markedly different from that of homogeneous turbulence. This rather surprising result points to the need for a proper theory, or direct numerical simulation, of inhomogeneous turbulence in nonuniform flow. By introducing a substantial modification to the Schwarz line density, we identity a modified line density that constitutes a three-parameter fit yielding excellent agreement with our results. Finally, we find that the transition from laminar to turbulent flow occurs at a stationary front. Observations of the location of this front as a function of Q\ifmmode \dot{}\else \.{}\fi{} show that the critical condition for maintaining turbulence is more consistent with a minimum line density than a critical velocity.In this detailed study of inhomogeneous superfluid turbulence created in a spatially nonuniform flow, we measure the turbulent dissipation produced by thermal counterflow in a nonuniform rectangular channel. The width of the channel increases linearly with position r along the channel length to impose a known spatial nonuniformity on the velocity in the flow direction, V\ensuremath{\propto}Q\ifmmode \dot{}\else \.{}\fi{}/r, where Q\ifmmode \dot{}\else \.{}\fi{} is the heat current. Because the channel widens gradually, this divergence is weak, producing a small deviation from uniform flow. Probes embedded in the channel walls allow access to the local temperature at several positions r. We employ sensitive differential thermometry to measure the temperature difference between any two of these locations to high precision. The single turbulent state we observe is clearly the analog of the T-II state of fully developed, homogeneous turbulence present in uniform flows. Making an approximation of local uniformity, we attempt to extend the theoretical description of turbulence in uniform flows to our results by replacing the uniform velocity with the local velocity in the expression for the temperature gradient. When applied locally, the Schwarz model of homogeneous turbulence, so successful in describing the T-II state in uniform flows, has the wrong dependence on both r and Q\ifmmode \dot{}\else \.{}\fi{} to characterize our results. The Geurst three-fluid model, which extends to situations where a gradient is present in the line density in an otherwise uniform flow, likewise does not agree with our observations when used in the local approximation.We therefore find that even a small perturbation imposed on a uniform flow radically changes the nature of the T-II state, and the inhomogeneous T-II state we observe is markedly different from that of homogeneous turbulence. This rather surprising result points to the need for a proper theory, or direct numerical simulation, of inhomogeneous turbulence in nonuniform flow. By introducing a substantial modification to the Schwarz line density, we identity a modified line density that constitutes a three-parameter fit yielding excellent agreement with our results. Finally, we find that the transition from laminar to turbulent flow occurs at a stationary front. Observations of the location of this front as a function of Q\ifmmode \dot{}\else \.{}\fi{} show that the critical condition for maintaining turbulence is more consistent with a minimum line density than a critical velocity.

Physical review. B, Condensed matterDec 1, 199410 citations

Visualization of the normal-fluid turbulence in counterflowing superfluid He4

Alexander Marakov, J. Gao, Wei Guo +4 more

We describe a technique, using thin lines of triplet-state $\mathrm{He}_{2}^{*}$ molecular tracers created by femtosecond-laser field ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid $^{4}\mathrm{He}$ , together with its application to thermal counterflow in a channel. We show that, at relatively small velocities, where the superfluid is already turbulent, the flow of the normal fluid remains laminar, but with a distorted velocity profile, while at a higher velocity there is a transition to turbulence. The form of the structure function in this turbulent state differs significantly from that found in types of conventional turbulence. This visualization technique also promises to be applicable to other fluid dynamical problems involving cryogenic helium.We describe a technique, using thin lines of triplet-state $\mathrm{He}_{2}^{*}$ molecular tracers created by femtosecond-laser field ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid $^{4}\mathrm{He}$, together with its application to thermal counterflow in a channel. We show that, at relatively small velocities, where the superfluid is already turbulent, the flow of the normal fluid remains laminar, but with a distorted velocity profile, while at a higher velocity there is a transition to turbulence. The form of the structure function in this turbulent state differs significantly from that found in types of conventional turbulence. This visualization technique also promises to be applicable to other fluid dynamical problems involving cryogenic helium.

arXiv:1412.1890Physical Review BMar 6, 201599 citations

Hydrodynamics of superfluid turbulence

Sergey K. Nemirovskii, Vladimir V. Lebedev

Journal of Experimental and Theoretical PhysicsMay 1, 198310 citations

Counterflow-Induced Inverse Energy Cascade in Three-Dimensional Superfluid Turbulence

Juan Ignacio Polanco, Giorgio Krstulovic

Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a nonzero-mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi-two-dimensional system exhibiting a split cascade, is observed. The findings of this work could motivate new experimental settings to study quasi-two-dimensional superfluid turbulence in the bulk of three-dimensional experiments. They might also find applications beyond superfluids in systems described by more than one fluid component.Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a nonzero-mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the emergence of a counterflow-induced inverse energy cascade in three-dimensional superfluid flows by performing extensive numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. As the intensity of the mean counterflow is increased, an abrupt transition, from a fully three-dimensional turbulent flow to a quasi-two-dimensional system exhibiting a split cascade, is observed. The findings of this work could motivate new experimental settings to study quasi-two-dimensional superfluid turbulence in the bulk of three-dimensional experiments. They might also find applications beyond superfluids in systems described by more than one fluid component.

arXiv:2005.10106Physical Review LettersDec 17, 202011 citations

We describe a technique, using thin lines of triplet-state

\mathrm{He}_{2}^{*}

molecular tracers created by femtosecond-laser field ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid

^{4}\mathrm{He}

, together with its application to thermal counterflow in a channel. We show that, at relatively small velocities, where the superfluid is already turbulent, the flow of the normal fluid remains laminar, but with a distorted velocity profile, while at a higher velocity there is a transition to turbulence. The form of the structure function in this turbulent state differs significantly from that found in types of conventional turbulence. This visualization technique also promises to be applicable to other fluid dynamical problems involving cryogenic helium.