Chaotic gas turbine subject to augmented Lorenz equations

Inspired by the chaotic waterwheel invented by Malkus and Howard about 40 years ago, we have developed a gas turbine that randomly switches the sense of rotation between clockwise and counterclockwise. The nondimensionalized expressions for the equations of motion of our turbine are represented as a starlike network of many Lorenz subsystems sharing the angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We show qualitative similarities between the statistical properties of the angular velocity of the turbine rotor and the velocity field of large-scale wind in turbulent Rayleigh-Bénard convection reported by Sreenivasan et al. [Phys. Rev. E 65, 056306 (2002)]. Our equations of motion achieve the random reversal of the turbine rotor through the stochastic resonance of the angular velocity in a double-well potential and the force applied by rapidly oscillating fields. These results suggest that the augmented Lorenz model is applicable as a dynamical model for the random reversal of turbulent large-scale wind through cessation.