Cascades of energy and helicity in axisymmetric turbulence

Aspectral analysis of strictly axisymmetric turbulence is performed. Both freely decaying and statistically steady flows are considered. In helical flows we identify a dual cascade, where energy is transferred towards the large scales and helicity to the smallest ones. It is shown that even in the absence of net helicity, a dual cascade persists, transferring energy backward and positively and negatively polarized helicity fluctuations forward.