The Branching Hierarchy of Multiple Solutions in a Model of Moist Convection

The dynamics of two-dimensional, shallow moist convection is examined with the use of a six-component spectral model. Latent heating effects are incorporated by assuming that upward motion is moist adiabatic and downward motion is dry adiabatic. The resulting nondimensional system of equations has the same form as that for Benard convection, with the moist effects included by replacing the Rayleigh number with a modified form. The six-coefficient model contains a wide variety of multiple solutions with as many as 12 time-independent convective states and one conductive state occurring simultaneously. Temporally periodic solutions are also indicated, and some are found numerically that branch from stationary solutions at critical values of the external parameters. Only some of the solutions are linearly stable and, hence, observable, and a summary of the possible branching orders of these solutions is given. The development of moist convection proceeds in the model, by means of one of several available sequences of distinct transitions of the flow regime, to increasingly complex structures.