Chiral turbulence: Equilibrium and non-equilibrium ensembles for time-reversible systems

Ideas and theories together with a new model, based on modifying the Navier-Stokes equation to obtain helical equilibrium and non-equilibrium time-reversible dynamical ensembles, of turbulence are presented. Discussion of controlling helicity to control the aeroacoustic noise and the aerodynamic force and heat follow the compressible turbulence relevant statistical mechanics analysis. Non-equilibrium dynamical ensembles with energy-helicity constraints are constructed by introducing chirality-dependent "viscosity" parameters. Applications in wall-bounded turbulence, mutual supports with Bose-Einstein condensates/quantum acoustics and the analogy with the plasma heating and acceleration in corona and solar wind are also remarked.