Abstract
Cell patterns of the finite-amplitude Bénard-type convection in a shear flow with a curved vertical temperature profile are investigated near the critical state by means of the Landau amplitude equations. The steady solutions are obtained and their stability is discussed in relation to three parameters which represent the deviation of temperature from the linear profile, the magnitude of the shear of the basic flow and the deviation of the Rayleigh number from the critical value for the curved vertical temperature profile, (ΔR)*. The following results are obtained:
(1) The roll solution is unstable only in a narrow range of positive (ΔR)* when the magnitude of the shear is lesss than a critical value. When its magnitude exceeds the critical value, the solution becomes stable for all positive values of (ΔR)*.
(2) The solution which is reduced to a hexagonal one in the absence of the shear is modified to give a longitudinal one as the magnitude of the shear is increased. The solution becomes unstable when the magnitude of the shear exceeds a critical value.
