When you select a field to be redefined, you will see several fields listed in the resulting menu, including the coordinate components, velocity components, pressure, and temperature. Six additional quantities, local compression rate, local shear rate, local stretch rate, local vorticity, Giesekus function, and (component of the rate-of-deformation tensor along the velocity) are also available. The first three are functions of invariants of the rate of deformation tensor , while the last three are actually no longer invariant, but can be useful in some circumstances.

The three invariants are defined as follows:

(31–2)

The compression rate is defined as the trace of the rate-of-deformation tensor, , given by Equation 31–2. For an incompressible fluid, this first invariant vanishes.

The local shear rate is based on the second invariant of the rate-of-deformation tensor:

(31–3)

For a pure shear flow, this quantity provides the actual shear rate.

The local stretch rate is based on the ratio of the third invariant to the second invariant [10]:

(31–4)

For a pure uniaxial elongational flow, this quantity provides the actual stretch rate.

The magnitude of the vorticity tensor (the antisymmetric part of the velocity gradient) is given by:

(31–5)

where the absolute value is considered in order to avoid questions about the definition and the sign of . For a rigid rotation motion, this quantity provides the actual rotation velocity.

The Giesekus function is defined as:

(31–6)

and ranges between -1 (rigid rotation) and 1 (pure extension). It equals 0 for a pure shear flow.

The component of the rate of deformation tensor along the velocity field is defined as:

(31–7)

where is the unit vector along . The quantity vanishes in a pure shear flow, while it provides the stretch rate under elongation. It is interesting to note that this quantity also provides nonvanishing values for a planar flow.