Near-Wall Coherent Structures: History, Identification and Detection - Transport and Coherent Structures in Wall Turbulence - page 174

Figure 3.25. Spatial correspondence of the isosurfaces and the
active zones, in which the Reynolds stresses are engendered. This figure is
adapted from [CHA 00]. For a color version of this figure, see
www.iste.co.uk/tardu/wallturbulence.zip

Δ= 0

One of the simple criteria for detecting vortex structures
is the determination of low-pressure zones ([ROB 91a and b]
and Figure 3.5). Indeed, the pressure reaches a minimum
value at the center of a 2D vortex. Remember Poisson's
equation, governing the pressure field, established in
Chapter 2:

2

∂
ρ∂ ∂

1 P 1

[3.48]

2

aa =− =− ∇ P

ik ki

xx ρ

i i

In light of equation [3.28], we can see that the invariant
is directly linked to

Q

1 2

[3.49]

2 Q

=∇

P

for an incompressible flow. The operator lends itself well
to the application of the Hopf maximum principle: if, in a

Δ