A Model of the Disappearance of Time-Dependence in the Flow Pattern in the Taylor-Dean System

The transition to chaos in diverse physical systems far from thermodynamic equilibrium is one of the challenging problems of modern physics. The most commonly studied models in hydrodynamics are the Rayleigh-Benard thermal convection system and the Taylor-Couette instabilityl, 2, both of which have been intensively investigated during the last two decades. The transition to chaos has been characterized and various scenarios have been discovered experimentally and in numerical simulations of those systems3. These two systems possess several symmetries, the breaking of which gives rise to new patterns. However, the real world is far from these simple cases and an effort is underway to study more complicated systems such as thermal convection in superposed layers of immiscible fluids4, the horizontal Taylor-Couette system with a partially filled gap5, the flow in curved channel6 or the boundary layer flow over a concave wall2.