Supersaturation of vertically propagating internal gravity waves

The usual assumption that vertically propagating internal gravity waves will cease growing with height once their amplitudes are such as to permit convective instability anywhere within the wave is reexamined. Two factors lead to amplitude limitation: (1) wave clipping associated with convective mixing, and (2) energetic constraints associated with the rate at which the wave can supply energy to the convection. It is found that these two factors limit supersaturation to about 50 percent for waves with short horizontal wavelengths and high relative phase speeds. Usually the degree of supersaturation will be much less. These factors also lead to a gradual, rather than sudden, cessation of wave growth with height.