Cross-chirality transfer of kinetic energy and helicity in compressible helical turbulence

Abstract

As an underlying mechanism, cross-chirality transfer of kinetic energy and helicity plays an essential role in the turbulent dynamics, which is as important as cross-scale transfer especially in broken mirror-symmetry turbulence. The effects of helicity on the properties of turbulent flows in previous studies highlight the role of cross chirality, which may be developed into an efficient method of turbulence control. We numerically study the cross-chirality transfer of kinetic energy and helicity in this paper, particularly under the influence of compressibility in stationary helical homogeneous and isotropic turbulence. Through combining the Helmholtz decomposition and helical wave decomposition, a general helical wave decomposition is proposed to provide three orthogonal bases for velocity. Within the scope of chiral helicity, there also exists chiral kinetic energy based on chiral velocity. They are defined as the left- A nd right-chirality kinetic energy, and the remaining compressible component of velocity corresponds to free-chirality kinetic energy. Although there exists no difference in the definition of helicity in incompressible and compressible turbulence, its space-time evolution equation in compressible turbulence involves the compressible component of velocity. The compressibility has a great influence on the homochiral kinetic energy and helicity cascade, and it also plays an essential role in the chirality transfer process like cross-chirality kinetic energy and helicity transfer. The amplitude of cross-chirality kinetic energy transfer is comparable with cross-scale kinetic energy transfer at relatively large scales, and also with viscous dissipation at relatively small scales. The triple nonlinear interactions dominate the cross-chirality transfer relative to pairwise interaction of chiral modes, and it is less sensitive to compressibility. Relative to the compression, the expansion of fluid elements can lead to inverse chirality transfer and strengthen the lack of mirror symmetry. The only discrepancy of cross-chirality helicity transfer between incompressible and compressible turbulence lies in the medium role of the compressible component of velocity. The helicity transfer via the compressible component is weak, and even the kinetic energy of the compressible component relative to that of the other two chiral modes is highest. In addition, the inverse helicity transfer is always statistically associated with the compressible component of velocity via triple interaction extracted from nonlinear interactions.