The stability properties of two impulsively generated, time-dependent temperature profiles in an initially quiescent, isothermal Boussinesq fluid are examined using a combination of analytic and numerical techniques. Quasi-steady approximations are used to generate linear stability theory neutral curves whose large-time forms can be explained by rational asymptotic methods. For the temperature profile generated by a step change in the plate temperature only linear theory results are presented, while an asymptotic solution for strongly nonlinear roll-cell convection is given for the case of an impulsively applied heat flux at the plate. The main prediction of this strongly nonlinear solution is that the mean plate temperature remains proportional to the square root of time, even in the presence of the strong convective motion. The implications of this result for experimental investigations into the initiation of convection above an impulsively heated plate are discussed.
|Journal||Quarterly Journal of Mechanics and Applied Mathematics|
|Publication status||Published - 2002|