A geometric/kinematic interpretation of scalar mixing

Scalar mixing is interpreted in terms of the growth or decay with time of an infinitesimal spatial volume located between two neighboring iso-scalar surfaces. The divergence of the velocity of propagation of iso-scalar surfaces relative to the fluid and perpendicular to them yields a variable which may be interpreted as the inverse of a scalar characteristic mixing time. Two contributions, the planar iso-scalar surface part and the one due to its curvature, are distinguished. The former is directly linked to the diffusive and chemical mechanisms contributing to the evolution of the scalar dissipation rate. The second rank symmetric tensor, partial derivative(2)C/partial derivative x(i)partial derivative x(j), seems to play an important role in these definitions. Direct numerical simulations (DNS) help to identify possible dependences of partial derivative(2)C/partial derivative x(i)partial derivative x(j) on its invariants. (C) 1999 American Institute of Physics. [S1070-6631(99)03709-5].