### Abstract

A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simple-fluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k^{?5/3} regime, a sub-turbulence, low Reynolds number, fluctuating k^{?2.2} regime, and an intermediate, viscous k^{?6} range that connects the two. The k^{?2.2} regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k^{?3} range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k^{?5/3} regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k^{?1} range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale.

Language | English |
---|---|

Article number | 105105 |

Number of pages | 15 |

Journal | Physics of Fluids |

Volume | 26 |

Issue number | 10 |

Early online date | 22 Oct 2014 |

DOIs | |

Publication status | E-pub ahead of print - 22 Oct 2014 |

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### Keywords

- rotating flows
- Kelvin waves
- Reynolds stress modeling
- viscosity
- superfluid flow

### Cite this

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*Physics of Fluids*, vol. 26, no. 10, 105105. https://doi.org/10.1063/1.4898666

**Energy spectra of finite temperature superfluid helium-4 turbulence.** / Kivotides, Demosthenes.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Energy spectra of finite temperature superfluid helium-4 turbulence

AU - Kivotides, Demosthenes

N1 - Copyright (2014) AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Kivotides, D. (2014). Energy spectra of finite temperature superfluid helium-4 turbulence. Physics of Fluids, 26(10), [105105]. 10.1063/1.4898666 and may be found at http://www.dx.doi.org/10.1063/1.4898666

PY - 2014/10/22

Y1 - 2014/10/22

N2 - A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simple-fluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k?5/3 regime, a sub-turbulence, low Reynolds number, fluctuating k?2.2 regime, and an intermediate, viscous k?6 range that connects the two. The k?2.2 regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k?3 range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k?5/3 regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k?1 range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale.

AB - A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simple-fluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k?5/3 regime, a sub-turbulence, low Reynolds number, fluctuating k?2.2 regime, and an intermediate, viscous k?6 range that connects the two. The k?2.2 regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k?3 range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k?5/3 regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k?1 range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale.

KW - rotating flows

KW - Kelvin waves

KW - Reynolds stress modeling

KW - viscosity

KW - superfluid flow

UR - http://www.scopus.com/inward/record.url?scp=84910071762&partnerID=8YFLogxK

U2 - 10.1063/1.4898666

DO - 10.1063/1.4898666

M3 - Article

VL - 26

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

M1 - 105105

ER -