Near-Wall Coherent Structures: History, Identification and Detection - Transport and Coherent Structures in Wall Turbulence - page 154

y + Figure 3.17. a) Outlines of the wall-normal velocity at in the plane

in a channel flow at . b) Linear stochastic estimation of the
wall-normal velocity simultaneously conditioned by an event in quadrant
II at position

= 30

− Re

τ =

180 x z

x and in quadrant IV at

x

3.6. Critical points and topology

3.6.1. Critical points

Critical points 6 are an important concept in dynamical
systems theory [OTT 93, STR 00]. Consider the dynamical
system governed by the temporal differential equations

dX

( )

1

== Xf XX ,

1 1 1 2

dt
dX

[3.18]

( )

2

== X fXX ,

2 2 1 2

dt

6 These are also known as “fixed points”.