# What are those things?

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.

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

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