Near-Wall Coherent Structures: History, Identification and Detection - Transport and Coherent Structures in Wall Turbulence - page 179

local minimum of cannot serve as an objective criterion in
determining vortex cores. [HUN 88] proposes to use two
criteria consecutively. This approach involves identifying the
regions of low pressure , where the second invariant of the
velocity gradient tensor is positive , and attributing
these zones to the coherent vortex structures. The
combination of two different criteria helps avoid the
ambiguities that may be presented by each of the methods
taken individually.

P

P

Q > 0

3.8. Vorticity and vortices

There is no univocal relation between vorticity and a
vortex. The latter must indubitably contain intense vorticity,
but a layer of vorticity may not necessarily be associated
with a vortex, unless it rolls up. Roll-up may take place if,
among other things, the modulus

surpasses a certain
local threshold and the vorticity distribution contains
discontinuities [JIM 93]. Jeong and Hussain [JEO 95]
present a simple but relevant proof, which shows that the
maximum of

Ω

may be an inadequate criterion for
identifying vorticial structures. These authors consider a
non-viscous 18 quasi-streamwise vortex in a uniform shear
flow and a velocity field independent of . The
streamwise vorticity in the plane is supposed to be a
constant. Its distribution is of the form in polar
coordinates where . The velocity components in
directions and , therefore, remain steady. This
configuration, which will be encountered many times in

Ω

Sy

x

()

y , z

()

Ω r

x

y 2 z 2 r = +

y z

18 We will examine a similar case in Chapter 4.