Abstract
In this Chapter, conservation laws of Wave Turbulence single- and multi-mode closures are presented: the energy, the momentum and the waveaction. Conditions for presence of extra invariants are derived. Relations between the statistical and the dynamical invariants are discussed. Directions of the turbulent cascades in the k-space are found via a generalised Fjørtoft’s argument (originally used in 2D hydrodynamic turbulence). The Petviashvilli drift-wave model is discussed as an example, including its extra invariant, zonostrophy, and its role in forming anisotropic turbulent cascades and generation of zonal flows.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Nazarenko, S.V.: Physical realisability of anisotropic spectra of wave turbulence and structure of the Rossby/drift turbulence, PhD thesis, Landau Institute for Theoretical Physics AN USSR, Chernogolovka (1990)
Balk, A.M., Nazarenko, S.V., Zakharov, V.E.: On the structure of the Rossby/drift turbulence and zonal flows. In: Proceedings of the International Symposium “Generation of Large-Scale Structures in Continuous Media”, June 11–20, 1990, Perm-Moscow, USSR, pp. 34–35
Balk, A.M., Nazarenko, S.V., Zakharov, V.E.: New invariant for drift turbulence. Phys. Lett. A 152, 5, 6, 276 (1991)
Balk, A.M.: A new invariant for Rossbywave systems. Phys. Lett. A 155(1), 20 (1991)
Nazarenko, S., Quinn, B.: Triple cascade behaviour in QG and drift turbulence and generation of zonal jets. Phys. Rev. Lett. 103(11) (2009), Article Number: 118501; Extended version on arxiv.org: nlin.CD arXiv:0905.1314
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nazarenko, S. (2011). Conserved Quantities in Wave Turbulence and their Cascades. In: Wave Turbulence. Lecture Notes in Physics, vol 825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15942-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-15942-8_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15941-1
Online ISBN: 978-3-642-15942-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)