Abstract
The statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution 8192 × 8192) in the presence of pumping and viscous-like damping. It is shown that quasi-shocks of vorticity and their Fourier partnerships in the form of jets introduce an essential influence in turbulence leading to strong angular dependencies for correlation functions. The energy distribution as a function of modulus k for each angle in the inertial interval has the Kraichnan behavior, ~k –4, and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum E k = C Kη2/3k–3, where η is the enstrophy flux and the Kraichnan constant C K ≃ 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S L3 which, as for the isotropic turbulence, gives the same scaling with respect to the separation length R and η, S L3 = C 3ηR 3, but the average over the angles and time differs from its isotropic value.
Similar content being viewed by others
References
R. Kraichnan, Phys. Fluids 11, 1417 (1967).
D. K. Lilly, J. Fluid Mech. 45, 395 (1971).
J. C. McWilliams, J. Fluid Mech. 146, 21 (1984).
S. Kida, J. Phys. Soc. J. 54, 2840 (1985).
M. E. Brachet, M. Meneguzzi, and P. L. Sulem, Phys. Rev. Lett. 57, 683 (1986).
M. E. Brachet, M. Meneguzzi, and P. L. Sulem, J. Fluid Mech. 194, 333 (1988).
R. Benzi, S. Patarnello, and P. Santangelo, Europhys. Lett. 3, 811 (1986).
B. Legras, B. Santangelo, and R. Benzi, Europhys. Lett. 5, 37 (1988)
B. Santangelo, R. Benzi, and B. Legras, Phys. Fluids A 1, 1027 (1989).
K. Okhitani, Phys. Fluids A 3, 1598 (1991).
E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Phys. Fluids 19, 105110 (2007).
P. G. Saffman, Stud. Appl. Math. 50, 49 (1971).
W. Wolibner, Math. Z. 37, 698 (1933)
V. I. Yudovich, 3, 1407 (1963)
T. Kato, Arch. Rat. Mech. Anal. 25, 189 (1967).
E. A. Kuznetsov, V. Naulin, A. H. Nielsen, and J. J. Rasmussen, Theor. Comput. Fluid Dyn. 24, 253 (2010).
A. N. Kudryavtsev, E. A. Kuznetsov, and E. V. Sereshchenko, JETP Lett. 96, 699 (2013).
E. A. Kuznetsov, JETP Lett. 80, 83 (2004).
T. Gotoh, Phys. Rev. E 57, 298491 (1998).
N. Schorghofer, Phys. Rev. E 61, 657277 (2000).
E. Lindborg and K. Alvelius, Phys. Fluids 12, 945 (2000).
E. Lindborg and A. Vallgren, Phys. Fluids 22, 091704 (2010).
U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge Univ. Press, Cambridge, UK, 1995).
D. Bernard, Phys. Rev. E 60, 618487 (1999).
E. Lindborg, J. Fluid Mech. 388, 259 (1999).
V. Yakhot, Phys. Rev. E 60, 5544 (1999).
G. Boffetta and R. E. Ecke, Annu. Rev. Fluid Mech. 44, 427 (2012).
E. A. Kuznetsov and V. P. Ruban, JETP Lett. 67, 1076 (1998), Phys. Rev. E 61, 831 (2000).
E. A. Kuznetsov, JETP Lett. 76, 346 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Kuznetsov, E.A., Sereshchenko, E.V. Anisotropic characteristics of the kraichnan direct cascade in two-dimensional hydrodynamic turbulence. Jetp Lett. 102, 760–765 (2015). https://doi.org/10.1134/S0021364015230083
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364015230083