Near-Wall Coherent Structures: History, Identification and Detection - Transport and Coherent Structures in Wall Turbulence - page 198

The hyperbolic trajectories are responsible for stretching and
folding. The vortices are the trajectories for which the tensor
, which is otherwise objective, is indefinite. 23 By
combining equation [3.64] and relation [3.75], for an
incompressible flow, we find the following tensor restricted
to :

A S

Z

⎡ ⎤

1

( )( )

H

2

SA −∇+∇− J ν S

⎢ ⎥

ρ

⎣ ⎦

Z

where is the Hessian [3.63] of the pressure field. The
zones where the above tensor is indefinite thus correspond to
the coherent structures according to [HAL 05]. Certain
numerical difficulties are presently there in the way of the
implementation of this strategy in DNS.

H

Figure 3.31. Comparison of a) Lagrangian detection and b) Eulerian
detection using the criterion Q in a fully developed turbulent channel flow.
This figure is taken from [GRE 07]. The plane under examination is y-z.
The boxed parts show the fine detail achievable with Lagrangian detection

23 An indefinite symmetrical matrix has eigenvalues that are both
negative and positive.