A linear stability analysis of two-layer moist convection with a saturation interface

Abstract

The linear convective instability of a mixture of dry air, water vapour and liquid water, with a stable unsaturated layer residing on an unstable saturated layer, is studied. It may serve as a prototype model for understanding the instability that causes mixing at the top of stratocumulus cloud or fog. Such a cloud-clear air interface is modelled as an infinitely thin saturation interface where radiative and evaporative cooling take place. The interface position is determined by the Clausius–Clapeyron equation, and can undulate with the evolution of moisture and temperature. In the small-amplitude regime two physical mechanisms are revealed. First, the interface undulation leads to the undulation of the cooling source, which destabilizes the system by superposing a vertical dipole heating anomaly on the convective cell. Second, the evolution of the moisture field induces non-uniform evaporation at the interface, which stabilizes the system by introducing a stronger evaporative cooling in the ascending region and vice versa in the descending region. These two mechanisms are competing, and their relative contribution to the instability is quantified by theoretically estimating their relative contribution to buoyancy flux tendency. When there is only evaporative cooling, the two mechanisms break even, and the marginal stability curve remains the same as the classic two-layer Rayleigh–Bénard convection with a fixed cooling source.