Transfers of energy and helicity in helical rotating turbulence

Helical rotating turbulence is a chiral and anisotropic flow. The energy and helicity transfers of helical rotating turbulence are studied in this paper. First, we discuss the antisymmetry and conservation of energy and helicity transfers. There are three expressions for helicity transfers due to the commutability of differential operators. The first expression is derived here. The second expression violates antisymmetry, and the third one introduces non-physical effects. The relations of these expressions are discussed in detail, including those about the sum of all triads and partial triads, as well as those about helical wave decomposition. Through direct numerical simulations, we find that helicity can reduce inverse energy cascades. The inhibition is mainly associated with transhelical energy fluxes and the interactions of two-dimensional modes. The inverse cascades of decomposed energy fluxes are related to the two-dimensionalization. For helicity, rotation does not affect the total helicity flux but generally suppresses the decomposed helicity fluxes. Positive homochiral and negative heterochiral helicity fluxes are associated with corresponding positive anisotropic transfers. Notably, the transhelical helicity fluxes increase the amplitudes of both positive and negative helicity, which is related to the chirality polarization.