Augmented Lorenz Equations as Physical Model for Chaotic Gas Turbine

Motivated by the chaotic waterwheel subject to the Lorenz equations, which was invented by Malkus and Howard about 40 years ago, we have developed a chaotic gas turbine by mechanically simulating the Rayleigh-Bénard convection of fluids heated from below and cooled from above. The rotational motion of the turbine erratically reverses its direction similarly to the random reversal of large-scale circulation in turbulent thermal convection at high Rayleigh numbers. The nondimensionalized expression for the equations of motion of our gas turbine is represented as a starlike network of many Lorenz subsystems sharing the dimensionless angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We report the observed motion of the turbine and discuss its dynamical properties.