ИСТИНА

As is known, the alpha effect in the dynamo theory is responsible for the generation of the large-scale magnetic fields by turbulence. In terms of cascade phenomena, this corresponds to the inverse cascade of the energy, when the energy of small-scale motions is transformed into the energy of a large-scale magnetic field. However, inverse energy cascade exists even in a simpler systems without a magnetic field. Thus, in 2D turbulence, two cascades are simultaneously observed: the inverse cascade of kinetic energy and the direct cascade of enstrophy [1]. The inverse cascade of kinetic energy is also observed in 3D rotating turbulence, where instead of the cascade of enstrophy, a cascade of the kinetic helicity, which is also direct, is considered [2]. To the moment, a large number of confirmations of this phenomenon have appeared both in numerical simulations [2] as well as in a physical experiment [3]. We present analogue of the Fjortoft theorem for 3D rapidly rotating turbulence is proposed [4], which gives a simple explanation of the both cascades if the rapidly rotating turbulence. The considered regimes are typical for the planetary cores and rapidly rotating convective zones of the stars.