Subgrid PDF
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\bar{P}(\underline{\psi}) | \bar{P}(\underline{\psi}) | ||
\equiv \int_V | \equiv \int_V | ||
| - | \ | + | \prod_i^N \delta \left( \Phi_j(\mathbf{x'},t) - \psi_j \right) |
G \left( \mathbf{x} -\mathbf{x'}, \Delta \right) dV' | G \left( \mathbf{x} -\mathbf{x'}, \Delta \right) dV' | ||
</math> | </math> | ||
Revision as of 12:17, 10 November 2005
A subgrid probability density function 
is the distribution function of scalar 
at subrid scales.
The probability of observing values between 
within the filter volume is 
where 
is the Dirac delta function,
is a positive defined filter function
with filter width 
.
The joint subgrid PDF of 
scalars is
where 
is the phase space for the scalar variables
