Higher-order PDF models

In the joint velocity, composition PDF description, the user must supply an external model for the turbulence time scale r . Alternatively, one can develop a higher-order PDF model wherein the turbulence frequency > is treated as a random variable (Pope 2000). In these models, the instantaneous turbulence frequency is defined as... 

In situ adaptive tabulation Higher-order PDF models... 

In Chapter 5, we will review models referred to as moment methods, which attempt to close the chemical source term by expressing the unclosed higher-order moments in terms of lower-order moments. However, in general, such models are of limited applicability. On the other hand, transported PDF methods (discussed in Chapter 6) treat the chemical source term exactly. 

The closure problem thus reduces to finding general methods for modeling higher-order moments of the composition PDF that are valid over a wide range of chemical time scales. 

The transported PDF models discussed so far in this chapter involve the velocity and/or compositions as random variables. In order to include additional physics, other random variables such as acceleration, turbulence dissipation, scalar dissipation, etc., can be added. Examples of higher-order models developed to describe the turbulent velocity field can be found in Pope (2000), Pope (2002a), and Pope (2003). Here, we will limit our discussion to higher-order models that affect the scalar fields. 

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