DIASCALAR FLUX AND THE RATE OF FLUID MIXING

We define the rate at which a scalar theta mixes in a fluid flow in te rms of the flux of theta across isoscalar surfaces. This flux phi(d) i s purely diffusive and is, in principle, exactly known at all times gi ven the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to ma ke the calculation of this flux very difficult. In this paper, we deri ve an exact expression relating the instantaneous diascalar flux to th e average squared scalar gradient on an isoscalar surface which does n ot require knowledge of the spatial structure of the surface itself. T o obtain this result, a time-dependent reference state theta(t,z) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the referen ce state due to diffusion is shown to equal the divergence of the diff usive flux, i.e. (partial derivative/partial derivative z)phi(d). Thi s result provides a mathematical framework that exactly separates diff usive and advective scalar transport in incompressible fluid flows. Th e relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn-Cox model. Estimation of water mass transformation from oceanic microstructure pr ofiles and determination of the time-dependent mixing rate in numerica lly simulated flows are discussed.