Thus, by analogy, the Reynolds stress is sometimes thought of as consisting of an isotropic pressure part, termed the turbulent pressure, and an off-diagonal part which may be thought of as an effective turbulent viscosity.
22.
In fact, while much effort has been expended in developing good models for the Reynolds stress in a fluid, as a practical matter, when solving the fluid equations using computational fluid dynamics, often the simplest turbulence models prove the most effective.
23.
To obtain equations containing only the mean velocity and pressure, we need to close the RANS equations by modelling the Reynolds stress term R _ { ij } as a function of the mean flow, removing any reference to the fluctuating part of the velocity.
24.
One finds that the transport equation for the Reynolds stress includes terms with higher-order correlations ( specifically, the triple correlation \ overline { v'_ i v'_ j v'_ k } ) as well as correlations with pressure fluctuations ( i . e . momentum carried by sound waves ).
25.
One class of models, closely related to the concept of turbulent viscosity, are the k-epsilon turbulence models, based upon coupled transport equations for the turbulent energy density k ( similar to the turbulent pressure, i . e . the trace of the Reynolds stress ) and the turbulent dissipation rate \ epsilon.
26.
It should also be noted that the theory of the Reynolds stress is quite analogous to the kinetic theory of gases, and indeed the stress tensor in a fluid at a point may be seen to be the ensemble average of the stress due to the thermal velocities of molecules at a given point in a fluid.
27.
This change is balanced by the mean body force, the isotropic stress owing to the mean pressure field, the viscous stresses, and apparent stress \ left (-\ rho \ overline { u _ i ^ \ prime u _ j ^ \ prime } \ right ) owing to the fluctuating velocity field, generally referred to as the Reynolds stress.
