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Modeling Kelvin wave cascades in superfluid helium

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Boffetta, G., Celani, A., Dezzani, D., Laurie, Jason and Nazarenko, Sergey. (2009) Modeling Kelvin wave cascades in superfluid helium. Journal of Low Temperature Physics, Vol.156 (No.3-6). pp. 193-214. ISSN 0022-2291

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Official URL: http://dx.doi.org/10.1007/s10909-009-9895-x

Abstract

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics
Q Science > QC Physics

Divisions:

Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Turbulence -- Mathematical models, Liquid helium, Superfluidity, Quantum statistics, Hydrodynamics

Journal or Publication Title:

Journal of Low Temperature Physics

Publisher:

Springer New York LLC

ISSN:

0022-2291

Official Date:

September 2009

Dates:

Date	Event
September 2009	Published

Volume:

Vol.156

Number:

No.3-6

Number of Pages:

Page Range:

pp. 193-214

Identification Number:

10.1007/s10909-009-9895-x

Status:

Peer Reviewed

Access rights to Published version:

Open Access

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