Abstract
The theory of wave processes tells us that the energy of waves of any nature propagates not with the phase velocity but with the group velocity
where ω(k) is the dispersion relation for waves of this nature, and ∇ k is the gradient operation in the k-space of wave numbers. The waves whose phase velocity does not coincide with the group velocity are called dispersion waves. So, for instance, are gravitational-gyroscopic waves with the dispersion relation (7.20), according to which they isotropically propagate in space.
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Dolzhansky, F.V. (2013). Resonant Interaction of Rossby Waves; Helmholtz and Obukhov Singular Vortices; The Kirchhoff Equations. In: Fundamentals of Geophysical Hydrodynamics. Encyclopaedia of Mathematical Sciences, vol 103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31034-8_8
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