Remember Me
Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:

OpenAIRE is about to release its new face with lots of new content and services.
During September, you may notice downtime in services, while some functionalities (e.g. user registration, login, validation, claiming) will be temporarily disabled.
We apologize for the inconvenience, please stay tuned!
For further information please contact helpdesk[at]openaire.eu

fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Laurie, Jason; L'vov, Victor S.; Nazarenko, Sergey; Rudenko, Oleksii (2009)
Languages: English
Types: Article
Subjects: Nonlinear Sciences - Chaotic Dynamics, Physics - Fluid Dynamics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Condensed Matter - Superconductivity
We argue that the physics of interacting Kelvin Waves (KWs) is highly non-trivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbulence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a new Local Nonlinear (partial differential) Equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable Local Induction Approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Secondly, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak non-locality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [7] R. J. Donnelly, Quantized Vortices in He II (Cambridge University Press, Cambridge, 1991)
    • [8] Quantized Vortex Dynamics and Super uid Turbulence, ed. by C. F. Barenghi et al., Lecture Notes in Physics 571 (Springer-Verlag, Berlin, 2001)
    • [9] K.W. Schwarz, Phys. Rev. B 31, 5782 (1985), DOI: 10.1103/PhysRevB.31.5782, and 38, 2398 (1988), DOI: 10.1103/PhysRevB.38.2398.
    • [10] B.V. Svistunov, Phys. Rev. B 52, 3647 (1995), DOI: 10.1103/PhysRevB.52.3647.
    • [11] R.J. Arms and F.R. Hama, Phys. Fluids 8, 553 (1965).
    • [12] H. Hasimoto, Journal of Fluid Mech. 51, 477-485 (1972), DOI: 10.1017/S0022112072002307.
    • [13] G. Bo etta, A. Celani, D. Dezzani, J. Laurie and S. Nazarenko, Journal of Low Temp. Phys. 156, 193-214 (2009), DOI: 10.1007/s10909-009-9895-x.
    • [14] V.E. Zakharov, V.S. L'vov and G.E. Falkovich. Kolmogorov Spectra of Turbulence, (Springer-Verlag, 1992).
    • [15] R. Kraichnan, Phys. Fluids, 10 1417 (1967), DOI: 10.1063/1.1762301.
    • [16] R. Kraichnan, J. Fluid Mech, 47 525 (1971), DOI: 10.1017/S0022112071001216.
    • [17] S.V.Nazarenko, JETP Letters 84, 585-587 (2007), DOI: 10.1134/S0021364006230032.
    • [18] V.E. Zakharov and E.I. Schulman, Physica D: Nonlinear Phenomena 4, 270-274 (1982), DOI: 10.1016/0167- 2789(82)90068-9.
    • [19] I. Gradstein and I. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York (1980).
    • [20] The limit of three small wave numbers is not allowed by the resonance conditions. Indeed, putting three wave numbers to zero, we get a 1 $ 2 process which is not allowed in 1D for ! k2.
    • [21] Here, we evoke a quantum mechanical analogy as an elegant shortcut, allowing us to introduce KE and the respective solutions easily. However, the reader should not get confused with this analogy and understand that our KW system is purely classical. In particular, the Plank's constant ~ is irrelevant outside of this analogy, and should be simply replaced by 1.
    • [22] It is evident for the approximation Eq. (31). For the full expression Eq. (29a) it was con rmed by symbolic computation with the help of Mathematica.
    • [23] It is appropriate to remind the reader, that we use the bold face notation of the one-dimensional wave vector for convenience only. Indeed, such a vector is just a real number, k 2 R.
  • No related research data.
  • Discovered through pilot similarity algorithms. Send us your feedback.

Share - Bookmark

Funded by projects


Cite this article

Cookies make it easier for us to provide you with our services. With the usage of our services you permit us to use cookies.
More information Ok