  A new model for the "rapid" part of the velocity/pressure-gradient
correlation in the Reynolds averaged Navier-Stokes equations is suggested. It
is shown that in an inhomogeneous incompressible turbulent flow, the model that
is linear in the Reynolds stresses should include two model coefficients. A
functional form of the coefficients is analyzed in some extreme turbulence
states. As demonstrated, the proposed model reduces to the standard linear
pressure-strain model in homogeneous turbulence and can satisfy realizability
conditions provided the coefficients are functions of the mean velocity
gradients and the Reynolds stresses. In an inhomogeneous turbulent flow,
coefficients should depend on parameters directly related to inhomogeneous
effects. The model is validated using direct numerical simulation data from two
flows: the plane wake and the plane mixing layer.
