Critical Richardson number in a viscous fluid for different Mach numbers, M, in both plots. The corresponding wave numbers k_max of the most unstable mode at the onset of instability are plotted, and the wave number is normalised by the inverse of the characteristic length 1 /L_u. The horizontal line in both plots corresponds to Ri = 0.25. In a) the atmosphere is weakly stratified with θ = 2, whereas in b)θ = 10, which corresponds to a strongly stratified atmosphere.