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Mean convected derivative second form

The expected value of the convected derivative of Q can also be written in a second independent form starting with15 [Pg.246]

Note that A, and , will, in general, depend on multi-point information from the random fields U and 0. For example, they will depend on the velocity/scalar gradients and the velocity/scalar Laplacians. Since these quantities are not contained in the one-point formulation for U(x, t) and 0(x, t), we will lump them all into an unknown random vector Z(x, f).16 Denoting the one-point joint PDF of U, 0, and Z by /u, / ,z(V, ip, z x, t), we can express it in terms of an unknown conditional joint PDF and the known joint velocity, composition PDF  [Pg.246]

15 Note that the extension to other flow quantities is formally trivial application of the chain mle would add the corresponding terms on the right-hand side of the final equality. [Pg.246]

16 Conceptually, since a random field can be represented by a Taylor expansion about the point (x, t), the random vector Z(x, t) could have as its components the infinite set of partial derivatives of U and / of all orders greater than zero with respect to x, X2, X3, and t evaluated at (x, l). [Pg.246]

The expected value of the term involving A, can then be written as [Pg.247]


See other pages where Mean convected derivative second form is mentioned: [Pg.11]    [Pg.265]    [Pg.246]    [Pg.11]    [Pg.265]    [Pg.246]    [Pg.267]    [Pg.248]    [Pg.1119]   


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