Reply to a Comment by A. van Delden

Abstract

I am grateful that A. van Delden has pointed out some inadequacies of mesoscale entrainment instability (MEI) as an explanation for mesoscale cellular convection (MCC). I agree that the MEI model for MCC suffers because of the requirement that lateral diffusion acts as the large wavenumber cut-off. In order for lateral diffusion to effectively damp out scales immediately smaller than those with the maximum growth rate, the diffusivity K is constrained by

where k_m is the horizontal wavenumber and σ₃ the growth rate of the fastest growing mode. (The above criterion can also apply to linear convective models.) For MCC, k_m≈10^-4m^-1. Any mesoscale instability worthy of the name would need σ_m > 10^-5 s^-1. K must be at least 1000 m² s^-1 if MEI is to account for the cell-size of MCC.