Consider the discriminating scalar \(\Phi(t, \mathbf{x}) \geq 0\) governed by

\[ \frac{\partial \Phi}{\partial t}+v_{\alpha} \frac{\partial \Phi}{\partial x_{\alpha}}=\frac{\partial}{\partial x_{\alpha}} \frac{1}{\operatorname{ScRe}} \frac{\partial \Phi}{\partial x_{\alpha}}+Q(\Phi) \]

where \(S c\) is the Schmidt number associated with the molecular diffusivity and \(Q(t, \mathbf{x}, \Phi)\) the source term. Determine the source term (16.10) of the external intermittency factor \(\gamma(t, \mathbf{x})(16.2)\) for \(\mathcal{A}=\Phi(t, \mathbf{x})-e_{0}\) as function of the discriminating scalar field \(\Phi(t, \mathbf{x})\).

Eq (16.10) 

Eq (16.2) 

Transcribed Image Text:

S(t, x, eo) = (V|ve|8(e(t, x) e0)) -