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arXiv:0909.2936

Comment on "Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades" [arXiv:0905.0159] by J. Yepez, G. Vahala, L.Vahala and M. Soe

Victor S. L’vov, Sergey Nazarenko

Published Sep 16, 2009• 0 citations
arXivHTMLPDF

Abstract

Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be done for the interpretation of the important numerical results obtained by the authors. A way to do this is suggested.

DOI
10.48550/arxiv.0909.2936

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Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be done for the interpretation of the important numerical results obtained by the authors. A way to do this is suggested.
In this comment we point out that the high wavenumber k−3k^{-3}k−3 power-law observed by the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] is an artifact stemming from the definition of the kinetic energy spectra and is thus not directly related to a Kelvin wave cascade. We also clarify a confusion about the wavenumber intervals on which Kolmogorov and Kelvin wave cascades are expected to take place.
We comment on the paper by Sonin [Phys. Rev. B 85, 104516 (2012)] with most statements of which we disagree. We use this option to shed light on some important issues of a theory of Kelvin-wave turbulence, touched on in Sonin's paper, in particular, on the relation between the Vinen spectrum of strong and the L'vov-Nazarenko spectrum of weak turbulence of Kelvin waves. We also discuss the role of explicit calculation of the Kelvin-wave interaction Hamiltonian and ``symmetry arguments'' that have to resolve a contradiction between the Kozik-Svistunov and the L'vov-Nazarenko spectrum of weak turbulence of Kelvin waves.
The main topological feature of a superfluid is a quantum vortex with an identifiable inner and outer radius. A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a Bose-Einstein condensate superfluid described by the Gross-Pitaevskii equation on grids up to 5760(3). For the first time, an accurate power-law scaling for the quantum Kelvin wave cascade is determined: k(-3). The incompressible kinetic energy spectrum exhibits very distinct power-law spectra in 3 ranges of k space: a classical Kolmogorov k(-(5/3)) spectrum at scales greater than the outer radius of individual quantum vortex cores and a quantum Kelvin wave cascade spectrum k(-3) on scales smaller than the inner radius of the quantum vortex core. The k(-3) quantum Kelvin wave spectrum due to phonon radiation is robust, while the k(-(5/3)) classical Kolmogorov spectrum becomes robust on large grids.
As long as vorticity quantization remains irrelevant for long-wave physics, superfluid turbulence supports a regime macroscopically identical to the Kolmogorov cascade of a normal liquid. At high enough wave numbers, the energy flux in wavelength space is carried by individual Kelvin-wave cascades on separate vortex lines. We analyze the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, revealing a chain of three distinct intermediate cascades supported by local-induction motion of the vortex lines and distinguished by specific reconnection mechanisms. The most prominent qualitative feature predicted is unavoidable production of vortex rings of a characteristic size.