A numerical simulation of transient near-shore natural convection induced by ramped iso-flux cooling

The present study numerically investigates the unsteady natural convection in a triangular domain induced by ramped iso-flux cooling at the water surface. The simulations indicate that, although the ramped cooling does not alter the final state of the flow for a given steady state flux, it may change the developing path towards the final state as well as slow down the development of the flow. The ramped cooling delays or completely suppresses the onset of a Rayleigh-Bénard type (RBT) instability during the developing process. As a consequence, a transitional stage characterized by the appearance and disappearance of the RBT instability at intermediate Rayleigh numbers does not occur if the ramp time is significantly long. Both qualitative and quantitative information is presented to demonstrate the effects of the ramp time on the transient behaviour of the flow at different Rayleigh numbers. A time scale for the onset time of the RBT instability under ramped cooling is also proposed and verified by the numerical results. The local instantaneous Rayleigh number at different parameters is calculated and its time history confirms the observed transient flow behaviours.