Transition to doubly diffusive chaos

Doubly diffusive convection driven by horizontal gradients of temperature and salinity is studied in a three-dimensional enclosure of square horizontal cross section and large aspect ratio. Previous studies focused on the primary instability and revealed the formation of subcritical branches of spatially localized states. These states lose stability because of their twist instability, thereby precluding the presence of any related stable steady states beyond the primary bifurcation and giving rise to spontaneous temporal complexity for supercritical parameter values. This paper investigates the emergence of this behavior. In particular, chaos is shown to be produced at a crisis bifurcation located close to the primary bifurcation. The critical exponent related to this crisis bifurcation is computed and explains the unusually abrupt transition. The construction of a low-dimensional model highlights that only a few requirements are necessary for this type of transition to occur. As a consequence, it is believed to be observable in many other systems.