A study of the asymmetric Malkus waterwheel: the biased Lorenz equations.

In this work, the asymmetric case of the Malkus waterwheel is studied, where the water inflow to the system is biasing the system toward stable motion in one direction, like a Pelton wheel. The governing equations of this system, when expressed in Fourier space and decoupled to form a closed set, can be mapped into a four-dimensional space where they form a quasi-Lorenz system. This set of equations is analyzed in light of analogues of the Rayleigh Bernard convection and conclusions are drawn.