General Points - Transport and Coherent Structures in Wall Turbulence - page 5

1.3. Notations

The complexity of certain equations means that we have
to use the mixed forms of notation in this topic. Figure 1.1
shows the notations that will be used. The position along the
primary direction of the flow will be indicated by x or x .
The instantaneous local velocity in this direction will be
denoted either by U or by U depending on the context. We
will denote the component in the wall-normal direction y (or
x ) by V or U . The spanwise direction will be indicated by
z (or x ) with the corresponding velocity component written
as W or

U .

Figure 1.1. Notations

1.4. Reynolds equations

Consider the equation of instantaneous momentum along,
say, the direction x for an incompressible fluid:

∂ U ∂ U

2

∂ UV ∂ UW 1 ∂ P

2

[1.10] + + + = − + ν ∇ U

∂ t ∂ x ∂ y ∂ z ρ∂ x