Abstract
Laboratory measurements of decaying quasi-two-dimensional turbulence in thin fluid layers with various depths have been performed. It has been shown that decay at large Reynolds numbers corresponds to a non-linear bottom friction with the coefficient satisfying the law λ ∼ (ν/h 2)1/2|K|1/4 following from theoretical estimates, where K is the Okubo-Weiss function depending on the enstrophy and degree of ellipticity of vortices. It has been shown that the structure of the flow changes in the decay process.
Similar content being viewed by others
References
F. V. Dolzhanskii, V. A. Krymov, and D. Yu. Manin, Sov. Phys. Usp. 33, 495 (1990).
F. V. Dolzhanskii, Principles of Geophysical Fluid Dynamics (Fizmatlit, Moscow, 2011) [in Russian].
M. V. Nezlin and E. N. Snezhkin, Rossby Vortices, Spiral Structures, Solitons: Astrophysics and Plasma Physics in Shallow Water Experiments (Nauka, Moscow, 1990; Springer, New York, 1993).
N. N. Gor’kavyi and A. A. Fridman, Physics of Planetary Rings: Celestial Mechanics of Continuous Media (Nauka, Moscow, 1994; Springer, New York, 1999).
S. D. Danilov and D. Gurarii, Phys. Usp. 43, 863 (2000)
L. P. Graves, J. C. McWilliams, and M. T. Montgomery, Geophys. Astrophys. Fluid Dyn. 100, 151 (2006).
D. Suos, N. Bonnetona, and J. Sommeria, Phys. Fluids 16, 2886 (2004).
M. G. Shats, H. Xia, H. Punzmann, et al., Phys. Rev. Lett. 99, 164502 (2007).
G. Boffetta, A. Cenedese, S. Espa, et al., Europhys. Lett. 71, 590 (2005).
D. H. Kelley and N. T. Ouellette, Phys. Fluids 23, 045103 (2011).
S. D. Danilov, V. A. Dovzhenko, F. V. Dolzhanskii, et al., J. Exp. Theor. Phys. 95, 48 (2002).
H. J. H. Clercx, G. J. F. van Heijst, and M. L. Zoeteweij, Phys. Rev. E 67, 066303 (2003).
M. G. Shats, D. Birn, and H. Xia, Phys. Rev. Lett. 105, 264501 (2011).
H. P. Greenspan, The Theory of Rotating Fluid (Cambridge Univ. Press, Cambridge, 1968; Gidrometeoizdat, Leningrad, 1975).
R. E. Hewitt and M. Al-Azhari, J. Eng. Math. 63, 259 (2009).
M. P. Satin, A. W. Cense, R. Verzicco, et al., Phys. Fluids 13, 1932 (2001).
R. A. D. Akkermans, A. R. Cieslik, L. P. J. Kamp, et al., Phys. Fluids 20, 116601 (2008).
V. M. Ponomarev, A. A. Khapaev, I. G. Yakushkin, Izv. Atmos. Ocean. Phys. 44, 45 (2008).
A. R. Cieslik, L. P. J. Kamp, H. J. H. Clercx, et al., J. Hydro-Env. Res. 4, 89 (2010).
D. Elhmaidi, A. Provinzale, and A. Babiano, J. Fluid Mech. 257, 533 (1993).
S. V. Kostrykin, A. A. Khapaev, and I. G. Yakushkin, J. Exp. Theor. Phys. 112, 344 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.V. Kostrykin, A.A. Khapaev, I.G. Yakushkin, 2012, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 95, No. 10, pp. 583–588.
Rights and permissions
About this article
Cite this article
Kostrykin, S.V., Khapaev, A.A. & Yakushkin, I.G. On the decay law of quasi-two-dimensional turbulence. Jetp Lett. 95, 515–520 (2012). https://doi.org/10.1134/S0021364012100074
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364012100074