Scalar variance conditional

In the statistical theory of fluid mixing presented in Chapter 3, well macromixed corresponds to the condition that the scalar means () are independent of position, and well micromixed corresponds to the condition that the scalar variances are null. An equivalent definition can be developed from the residence time distribution discussed below. 

In Section 3.2, we show that under the same conditions the right-hand side of (1.24) is equal to the negative scalar dissipation rate ((3.45), p. 70). Thus, the micromixing time is related to the scalar dissipation rate e and the scalar variance by... 

For a homogeneous scalar field with an isotropic filter, the conditional expected value of the scalar will have the property (+U,

transport equation can be derived for the residual scalar variance defined by11... 

Figure 6.2. Sketch of conditional scalar Laplacian for (p) =0.90 and three values of the variance.

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