Equilibrium and non-equilibrium time-reversible dynamical ensembles relevant to chiral turbulence

Ideas and theories of turbulence based on modifying the Navier-Stokes equation, to obtain equilibrium and non-equilibrium time-reversible dynamical ensembles relevant to helical turbulence, are presented. Discussions of controlling helicity to control the aerodynamic force, heat and noise are presented, together with the compressible turbulence relevant statistical mechanics analysis. A helical time-reversible system for nonequilibrium dynamical ensemble is constructed. Applications are also remarked.