On the basis of the two-point velocity correlation equation a new tensor length-scaleequation and in turn a dissipation rate tensor equation and the pressure–strain correlationare derived by means of asymptotic analysis and frame-invariance considerations. The newdissipation rate tensor equation can account for non-isotropy effects of the dissipationrate and streamline curvature. The entire analysis is valid for incompressible as well asfor compressible turbulence in the limit of small Mach numbers. The pressure–straincorrelation is expressed as a functional of the two-point correlation, leading to anextended 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 velocitiesand a tensor relation between the length scale and the dissipation rate tensor. Hence, aconsistent formulation of the return term in the pressure–strain correlation and thedissipation tensor equation is achieved. The model has been integrated numerically forseveral different homogeneous and inhomogeneous test cases and results are compared withDNS, LES and experimental data.