Abstract The paper discusses the basic physical phenomena involved in pressure-density interactions, and presents models of pressure-velocity, pressure-scalar, baroclinic and dilatation effects for variable density low Mach-number turbulence. Their implementation in the κ- ε framework is then described and their performance evaluated. The models assume that both scalar transport and turbulence generation arising from pressure-density interactions in flames are caused by the motion of large scale turbulent thermals superposed on the normal turbulence mechanism. The velocity of the thermals is related directly to the mean pressure gradient and local density differences in the flames. It is furthermore assumed that the correction for dilatation effects in the φ- ε system can be determined from the constraint of conservation of the angular momentum of turbulence per unit mass. Simple corrections of the κ- ε system are proposed for fast chemistry diffusion and premixed flames subject to variable pressure gradients, which offer substantial improvements in the predictions of the flames. Some problems remain, particularly in predictions of turbulence in premixed flames, owing to large scale instabilities of the flames observed in the experiments.