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.
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References
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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
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DOI: https://doi.org/10.1007/978-3-642-15942-8_8
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