Abstract
Now it is time for our theory to bear fruit and for us to harvest. In this chapter we shall recollect the results concerning specific physical systems and shall obtain some new results by specializing general approaches from the previous chapters. We shall try to describe most hitherto known facts with regard to the spectra of developed weak turbulence. The general model of wave turbulence adopted in this book is based on the detailed consideration of the wave-wave interaction. The interaction with the external environment was described by the function Γ(k) specifiying the decrement of wave attenuation or the growth-rate of wave instability. Nature is naturally more complex (for example, the interaction of water waves with wind and currents or wave-particle interactions in plasmas). Nevertheless, we believe the following fomulas and interpretations to provide a good basis for the further development of the theory of wave turbulence in various systems each of which might require a separate monograph for an adequate detailed description.
... a time to gather stones together
Ecclesiastes
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
V.I. Ozhogin: Bull. Acad. Sci. USSR Phys. Series 42, 48 (1978)
V.E. Zakharov, S.L. Musher, A.M. Rubenchik: Physics Reports 129, 285–366 (1985)
V.L. Gurevich: Kinetics of Phonon System (Nauka, Moscow 1980) [In Russian]
V.E. Zakharov: Sov. Phys. JETP 24, 455 (1967)
G.E. Falkovich, A.V. Shafarenko: Sov. Phys. JETP 68, 1393–1397 (1988)
V.E. Zakharov, S.L. Musher: Sov. Phys. Dokl. 18, 240 (1973)
G.E. Falkovich, A.V. Shafarenko: Preprint 393 Inst. Automation and Electrometry Novosibirsk (1987); J. Nonlinear Science 1, 457–480 (1991)
V.S. L’vov, G.E. Falkovich: Sov. Phys. JETP 53, 2 (1981)
W. Rudin: Principles of Mathematical Analysis (McGraw-Hill, New York 1964)
A.M. Balk, V.E. Zakharov: “Stability of Weak Turbulence Kolmogorov Spectra”, in Plasma Theory and Nonl. and Turb. Processes in Physics (World Scientific, Singapore 1988) pp. 359–376;
A.M. Balk, V.E. Zakharov: “Stability of Weak Turbulence Kolmogorov Spectra”, in Integrability and Kinetic Equations for Solitons, (Naukova Dumka, Kiev 1990) pp. 417–472 [in Russian]
V.S. L’vov, G.E. Falkovich, A.V. Shafarenko: in Problems of Nonlinear Acoustics, Proc. 11th IUPAP, IUTAM Symp. on Nonlinear Acoustics (Nauka, Novosibirsk 1987)
V.S. L’vov, G.E. Falkovich: Zh. Eksp. Teor. Fiz. 95, 2033–2037 (1989) [English: Sov. Phys. JETP]
G.E. Falkovich: Sov. Phys. JETP 66 (1), 97–100 (1987)
S.L. Musher: private communication (1987)
G.E. Falkovich, A.V. Shafarenko: Physica 27D, 399–411 (1987)
S.V. Volotskii, A.V. Kats, V.M. Kontorovich: Dokl. Akad. Nauk Ukr. SSR A11, 64–67 (1980) [in Ukrainian]
M. Lesieur Turbulence in Fluids (Kluwer Acad. Publ., Dordrecht 1990)
G. Falkovich, S. Medvedev: Europhys. Letters 19 (1992)
V.E. Zakharov, N.N. Filonenko: Zh. Prikl. Mekh. Tekh. Fiz, 5, 62 (1967) [English: J.Appl. Mech. Tech. Phys.]
B.N. Breizman, Yu.M. Rosenraukh: Preprint, Nucl. Phys. Inst. Novosibirsk (1984)
G.T. Lleonart, D.R. Blackman: J. Fluid Mech. 97, 455–79 (1980)
K. Hasselman: J. Fluid Mech. 12, 481 (1962)
V.E. Zakharov, N.N. Filonenko: Dokl. Akad. Nauk SSSR, 170, 1292–1295 (1967)
V.E. Zakharov, M.M. Zaslavskii: Izv. Akad. Nauk USSR, Atm. Ocean. Phys. 18, 970 (1982)
O.M. Phillips: J. Fluid Mech. 156, 505–31 (1985)
G.Z. Forristall: J. Geophys. Res. 86, 8075–84 (1981)
A.V. Kate, V.M. Kontorovich: Zh. Prikl. Mekh. Tekh. Fiz. 6, 97 (1974) [English: J. Appl. Mech. Tech. Phys.]
G.E. Falkovich, M.D. Spector: Phys. Letters (to be published).
V.E. Zakharov: Sov. Phys. JETP 35, 908 (1972)
A. Newell, B. Pushkarev, V. Dyachenko, V. Zakharov: Physica D (to be published)
G. Falkovich, I. Ryzhenkova: Phys. Fluids B 4, 594–598 (1992)
V.S. Lutovinov, V.R. Chechetkin: Zh. Eksp. Teor. Fiz 76, 223 (1979) [English: Sov. Phys. JETP]
E.A. Kuznetsov: Zh. Eksp. Teor. Fiz. 62, 584 (1972) [English: Sov. Phys. JETP]
A.A. Kanashov: Preprint 175 Inst. of Automation Novosibirsk (1982) [In Russian]
E.A. Kuznetsov: Preprint 81–73 Inst. Nucl. Phys., Novosibirsk (1973)
A.G. Sazontov: in Fine Structure and Synoptic Variations of the Sea, 147–152 (Nauka, Tallinn 1980) [In Russian]
A.S. Monin, L.I. Piterbarg: Dokl. Akad. Nauk SSSR, 295, 816 (1987) [English: Sov. Phys. Dokl.]
V.E. Zakharov, A.M. Balk, S.V. Nazarenko: Proc. Int. Symp. “Generation of Large-Scale Structures”, 33 (Nauka, Moscow 1990)
S.V. Novakovskii, A.B. Mikhailovskii, O.G. Onischenko: Phys. Lett. A132, 33 (1988)
V.E. Zakharov, A.M. Balk, S.V. Nazarenko: Zh. Eksp. Teor, Fiz. 97 (1990) [English: Sov. Phys. JETP 71 249 (1990)]
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Zakharov, V.E., L’vov, V.S., Falkovich, G. (1992). Physical Applications. In: Kolmogorov Spectra of Turbulence I. Springer Series in Nonlinear Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50052-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-50052-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-50054-1
Online ISBN: 978-3-642-50052-7
eBook Packages: Springer Book Archive