Modes of Tropical Variability under Convective Adjustment and the Madden–Julian Oscillation. Part II: Numerical Results

Abstract

Abstract Convective interaction with dynamics (CID) dictates the structure and behavior of the eigenmodes of the tropical atmosphere under moist convective adjustment (MCA) when the convective adjustment time scale, τc, is much smaller than dynamical time scales, as examined analytically in Part I. Here, the modes are reexamined numerically to include the effects of finite τc, again for a primitive equation model with the Betts-Miller MCA parameterization. The numerical results at planetary scales are consistent with the analytical approach, with two well-separated classes of vertical modes: one subset evolves at the cumulus time scale, while the other subset evolves at a time scale set by the large-scale dynamics. All modes are stable for homogeneous basic states in the presence of simple mechanical damping effects. Thus, there is no CISK at any scale under MCA. However, the finite τc effect has the property of selectively damping the smallest scales while certain vertical modes at planetary scales decay...