TY - JOUR

T1 - Impulsively generated Convection in a Semi-Infinite Fluid Layer above a Heated Flat Plate

AU - Bassom, Andrew

AU - Blennerhassett, P.J.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

U2 - 10.1093/qjmam/55.4.573

DO - 10.1093/qjmam/55.4.573

M3 - Article

VL - 55

SP - 573

EP - 595

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 4

ER -