Planar isotropy of passive scalar turbulent mixing with a mean perpendicular gradient

A recently proposed evolution equation [Vaienti et at, Physics D 85, 405 (1 994)] for the probability density functions (PDF's) of turbulent passive sc alar increments obtained under the assumptions of fully three-dimensional h omogeneity and isotropy is submitted to validation using direct numerical s imulation (DNS) results of the mixing of a passive scalar with a nonzero me an gradient by a homogeneous and isotropic turbulent velocity field. It is shown that this approach leads to a quantitatively correct balance between the different terms of the equation, in a plane perpendicular to the mean g radient, at small scales and at large Peclet number. A weaker assumption of homogeneity and isotropy restricted to the plane normal to the mean gradie nt is then considered to derive an equation describing the evolution of the PDF's as a function of the spatial scale and the scalar increments. A very good agreement between the theory and the DNS data is obtained at all scal es. As a particular case of the theory, we derive a generalized form for th e well-known Yaglom equation (the isotropic relation between the second-ord er moments for temperature increments and the third-order velocity-temperat ure mixed moments). This approach allows us to determine quantitatively how the integral scale properties influence the properties of mixing throughou t the whole range of scales. In the simple configuration considered here, t he PDF's of the scalar increments perpendicular to the mean gradient can be theoretically described once the sources of inhomogeneity and anisotropy a t large scales are correctly taken into account. [S1063-651X(99)02108-X].