Near-Wall Coherent Structures: History, Identification and Detection - Transport and Coherent Structures in Wall Turbulence - page 175

domain 13 , , then the maximum value is
reached on the boundary , unless is constant in .
Consequently, the pressure should reach a minimum in
the domain delimited by the condition

2 P

Δ ∇ = 2 ρ Q ≥ 0 P

Σ Δ Δ P

P

. However, Q ≥ 0

Δ
′

must inevitably be surrounded by a connected domain ,
where 14 , at the boundary of which the pressure
reaches another minimum, because of the same Hopf
principle mentioned above (see Figure 3.26). Therefore, the
zones do not necessarily denote the local minima, as is
correctly pointed out by Jeong and Hussain [JEO 95].
Furthermore, the results found by Chacin and Cantwell
[CHA 00] indicate that there is a non-negligible proportion of
the structures that engender high Reynolds stresses in the
zones and . These active regions cannot be
revealed by the minimum pressure criterion, which is,
therefore, not an entirely adequate method for detecting
coherent wall structures. We will return to this point in the
next section.

Δ

Q < 0

Σ ′ ′

Δ

Q > 0

Δ> 0

Q < 0

Figure 3.26. Diagrammatic representation of the zones and of the
variation in pressure in accordance with the Hopf principle. The pressure
reaches a maximum on the boundary of the domain and a minimum
in the domain at point A. It also reaches another minimum at points B and
C on the boundary of

Q

Q ≥ 0

by the same principle

Q ≤ 0

13 Which must necessarily be three-dimensional in this case.
14 For reasons of simple continuity of the invariant Q .