On the basis of the two-point velocity correlation equation a new tensor length-scale equation and in turn a dissipation rate tensor equation and the pressure–strain correlation are derived by means of asymptotic analysis and frame-invariance considerations. The new dissipation rate tensor equation can account for non-isotropy effects of the dissipation rate and streamline curvature. The entire analysis is valid for incompressible as well as for compressible turbulence in the limit of small Mach numbers. The pressure–strain correlation is expressed as a functional of the two-point correlation, leading to an extended compressible version of the linear formulation of the pressure–strain correlation. In this turbulence modelling approach the only terms which still need ad hoc closure assumptions are the triple correlation of the fluctuating velocities and a tensor relation between the length scale and the dissipation rate tensor. Hence, a consistent formulation of the return term in the pressure–strain correlation and the dissipation tensor equation is achieved. The model has been integrated numerically for several different homogeneous and inhomogeneous test cases and results are compared with DNS, LES and experimental data.