On modelling the pressure terms of the scalar flux equations

The paper is concerned with the problem of modelling the ensemble-averaged product of the pressure and scalar gradient that appears in the equations for the scalar flux. The method (for nearly-homogeneous unidirectional flow with weak gradients) is to derive nonlinear expressions for the fluctuating parts of the pressure and the scalar by formal solution (in wave-vector space) of the Navier-Stokes and the scalar equations. Substitution in the Fourier transform of the pressure correlation shows that this quantity is the sum of four terms, two of which contain the mean scalar gradient. A fourth-order cumulant-discard approximation allows this term to be expressed in terms of the single-point double products and the turbulent energy and stress spectra. A numerical calculation is made when the spectra are represented by simple functions. Finally, a tentative mode is proposed in which the remaining terms of the pressure correlation are evaluated by reference to experimental data.