A modification of the semi-empirical theory of stratified turbulent flow, which includes an equation for the density fluctuations (the potential energy of turbulence), is applied to describe the effect of internal gravity waves (IWs) on the small-scale turbulence. After considering the periodic IWs, special attention is paid to the action of internal solitons, such as the classical Gardner solitons and a strongly nonlinear solitary wave regularly observed in the Oregon Bay of the USA. It is confirmed that the presence of potential energy allows the existence of finite turbulence at any Richardson number.

At MHD scales density fluctuations in the solar wind generally have a relative amplitude less than 0.1. The nearly incompressible MHD theory would seem then appropriate to describe a major part of the compressive turbulence at these scales. As a test of the theory, we focus on the scaling properties of density fluctuations with turbulent Mach numbers and on the level of correlation between density and temperature fluctuations. Our findings do not appear in favour of an extended applicability of the nearly incompressible theory to MHD compressive turbulence in the solar wind.