Pis’ma v ZhETF, vol. 111, iss. 10, pp. 707 - 708

May 25

Reply to Comment on “Amplitude of waves in the Kelvin-wave cascade”

(Pis’ma v ZhETF 111, 462 (2020))

V. B. Eltsov⁺¹⁾, V. S. L’vov^∗

⁺Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Finland

^∗Department of Chemical Physics and Biological Physics, Weizmann Institute of Science, 7610001 Rehovot, Israel

Submitted 14 April 2020

Resubmitted 16 April 2020

Accepted 16 April 2020

This is a Reply to Sonin’s Comment [arXiv preprint arXiv:2003.09912, 2020] on Eltsov and L’vov [Pis’ma

v ZhETF 111, 462 (2020)] in which we provide relation of the energy flux carried by the cascade to the

amplitude of the excited Kelvin waves, important for analysis of future experiments.

DOI: 10.31857/S1234567820100110

In his Comment, Sonin used our paper [1] as an ex-

tude of Kelvin waves. We stress that the target of the ini-

cuse to return to a rather old dispute on the theoretical

tial experiments would be to discriminate between dissi-

models of the Kelvin-wave cascade. This dispute was ini-

pation originating from the Kelvin-wave cascade versus

tiated by the controversy between the Kozik-Svistunov

other dissipation mechanisms like acoustic or tunneling

[2] and the L’vov-Nazarenko [3, 4] energy spectra of the

two-level system damping. Here we hope that our order-

cascade. The discussion also included other contribu-

of-magnitude estimation of the expected amplitudes will

tions [5, 6], in particular from the author of the Com-

be useful as well as pointing out two important parame-

ment, whose arguments were criticized in [7, 8]. Numer-

ters, the energy flux and the starting wave vector of the

ical simulation efforts intended to resolve the contro-

cascade k_min, which preferably should be controlled in

versy were built up as well. The authors of the latest

the experiment independently. The focus of the initial

published numerical works known to us [9, 10] claim

experiments will probably not be on verifying particu-

that their results support the L’vov-Nazarenko spec-

lar models of the cascade. In fact, we agree with the

trum [4], including the numerical prefactor. Remarkably,

author of the Comment that in an experiment which

these calculations were performed using different numer-

probes only the longest energy-containing length scales,

ical approaches (Gross-Pitaevskii formalism in [9] and

the discrimination between different cascade models is

vortex-filament method in [10]). We should say from the

unlikely.

outset that our paper has nothing to contribute to this

We think therefore that our paper [1] should not

extended discussion and its focus is on a different topic.

serve as a reason for reanimating the old debate. Of

Independently of the details of the theoretical mod-

course, we do not have in mind to preclude others

els, the generally accepted picture of quantum turbu-

from continuing discussions, preferably finding new ar-

lence includes the Kelvin-wave cascade as an essential

guments. One interesting development for proponents

component in the low-temperature limit. There is, how-

of other theoretical models of the cascade would be to

ever, no experimental evidence so far for the existence

make alternative predictions for observables in single-

of such cascade. The relevant difficulties are mentioned

vortex dynamics and to suggest possible experimental

both in our paper and in the Comment. With recent

realizations where the difference between cascade mod-

progress in experimental techniques we hope that stud-

els becomes potentially resolvable.

ies of the dynamics of nearly straight vortices, not hin-

dered by the hydrodynamic energy cascade and recon-

1. V. B. Eltsov and V. S. L’vov, Pis’ma v ZhETF 111, 462

nections, will become possible in near future. The pur-

(2020).

pose of our paper is to facilitate interpretation of the

2. E. Kozik and B. Svistunov, Phys. Rev. Lett. 92, 035301

results of such potential experiments by providing a par-

(2004).

ticular relation between the energy flux and the ampli-

3. J. Laurie, V. S. L’vov, S. Nazarenko, and O. Rudenko,

Phys. Rev. B 81, 104526 (2010).

4. V. S. L’vov and S. Nazarenko, Pis’ma v ZhETF 91, 464

¹⁾e-mail: vladimir.eltsov@aalto.fi

(2010).

Письма в ЖЭТФ том 111 вып. 9 - 10

2020

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