CRITICAL SELF-TUNING - THE EXAMPLE OF ZERO PRANDTL NUMBER CONVECTION

We present a new type of bifurcation scenario where nonlinear saturati on of a stationary instability takes place only because of the competi tion with an oscillatory one. This is shown on the example of convecti on at zero Prandtl number between stress-free boundaries. We show with direct numerical simulations that time-dependent wavy rolls are gener ated at the onset of convection. Using a Galerkin model, are analyze t he nonlinear interactions between rolls and waves and find that they m aintain the system in the vicinity of the oscillatory instability onse t, thus preventing the blow-up Of the growing nonlinear roll solution. An interesting feature of this type of dynamics is that the system is self-tuned in the vicinity of a transition point.