The long wavelength instability of high Prandtl number convective flow

AbstractThis paper considers the stationary instability of convective flow between heated vertical planes in the limit of high Rayleigh number, A → ∞. This limit is of practical importance in applications. The planes are held at temperatures that increase linearly with height and differ horizontally by a constant amount. This allows an exact solution of the Boussinesq equations whose nature depends on the value of a convective parameter γ. The lower branch of the neutral stability curve is obtained for general values of γ and large Prandtl numbers, σ, revealing a dramatic change in the stability properties of the system in the limit as σ → ∞