Those objects are wall-attached coherent structures reaching the logarithmic layer and extracted from a direct numerical simulation (DNS) of a turbulent channel at a Reynolds Number of 4000 based on the channel half-height and the wall friction velocity.

**Clusters** are defined in terms of the discriminant
of the velocity gradient. Briefly, a vortex clusters is a connected
region satisfying

$$D>a D^\prime(y)$$

where D is the discriminant of the velocity gradient tensor, \(D'(y)\) is its standard deviation as a function of the wall-normal direction and \(a=0.02\) a thresholding parameter obtained from a percolation analysis. Connectivity is defined in terms of the six orthogonal neighbors in the Cartesian mesh of the DNS. Geometrically, they are `sponges of worms' with a thickness of the order of 7 Kolmogorov unit lengths, but without a clearly defined shape. Each object is circumscribed within a box aligned to the Cartesian axes. Full details can be found here.

**UVsters** are the structures contributing most to
the tangential Reynolds stress, which are obtained by extending the
clasical one-dimensional quadrant analysis to three dimensions. The
quadrant events are defined as connected regions satisfying

$$-uv > H u^\prime(y)v^\prime(y)$$

where \(u\) and \(v\) are the instantaneous streamwise and wall-normal velocity fluctuations respectively, \(u'(y)\) and \(v'(y)\) their root-mean-square values and \(H\) the hyperbolic-hole size, taken to be \(H=1.75\) from a percolation analysis. Geometrically, they are `sponges of flakes' with a thickness of the order of 12 Kolmogorov unit lengths. Full details can be found here.

© 2013. Adrián Lozano and Guillem Borrell

Images by Adrián Lozano, webapp by Guillem Borrell. Thanks to our boss, Javier Jiménez, that sometimes lets us go nuts.

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