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Gradual eddy-wave crossover in superfluid turbulence

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L'vov, V. S., Nazarenko, Sergey and Rudenko, Oleksii (2008) Gradual eddy-wave crossover in superfluid turbulence. Journal of Low Temperature Physics, Vol.153 (No.5-6). pp. 140-161. doi:10.1007/s10909-008-9844-0

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Official URL: http://dx.doi.org/10.1007/s10909-008-9844-0

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Abstract

We revise the theory of superfluid turbulence near the absolute zero of temperature and suggest a differential approximation model for the energy fluxes in the k-space, ε HD(k) and ε KW(k), carried, respectively, by the collective hydrodynamic (HD) motions of quantized vortex lines and by their individual uncorrelated motions known as Kelvin waves (KW). The model predicts energy spectra of the HD and the KW components of the system, ℰHD(k) and ℰKW(k), which experience a smooth crossover between different regimes of motion over a finite range of scales. For an experimentally relevant range of Λ≡ln (ℓ/a) (ℓ is the mean intervortex separation and a is the vortex core radius) between 10 and 15 the total energy flux ε=ε HD(k)+ε KW(k) and the total energy spectrum ℰ(k)=ℰHD(k)+ℰKW(k) are dominated by the HD motions for k<2/ℓ. In this region ℰ(k) follows the HD spectrum with constant energy flux ε≃ε HD=const.: ℰ(k)∝ k −5/3 for smaller k and tends to equipartition of the HD energy ℰ(k)∝ k 2 for larger k. This bottleneck accumulation of the energy spectrum is milder than the one predicted before in (L’vov et al. in Phys. Rev. B 76:024520, 2007) based on a model with sharp HD-KW transition. For Λ=15, it results in a prediction for the effective viscosity ν  ′≃0.004κ (κ is the circulation quantum) which is in a reasonable agreement with its experimental value in 4He low-temperature experiment ≈0.003κ (Walmsley et al. in Phys. Rev. Lett. 99:265302, 2007). For k>2/ℓ, the energy spectrum is dominated by the KW component: almost flux-less KW component close to the thermodynamic equilibrium, ℰ≈ℰKW≈const at smaller k and the KW cascade spectrum ℰ(k)→ℰKW(k)∝ k −7/5 at larger k.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Superfluidity, Turbulence, Quantum theory, Liquid helium, Wave mechanics
Journal or Publication Title: Journal of Low Temperature Physics
Publisher: Springer New York LLC
ISSN: 0022-2291
Official Date: December 2008
Dates:
DateEvent
December 2008Published
Volume: Vol.153
Number: No.5-6
Number of Pages: 22
Page Range: pp. 140-161
DOI: 10.1007/s10909-008-9844-0
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Description:

Paper presented at Symposium on Quantum Phenomena and Devices at Low Temperatures, Espoo, Finland, Mar 28-Aug 30, 2008

Conference Paper Type: Paper
Type of Event: Conference

Data sourced from Thomson Reuters' Web of Knowledge

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