The long wavelength instability of high Prandtl number convective flow Original Research Article

This 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 → ∞.