A vorticity stretching diagnostic for turbulent and transitional flows

Abstract

Vorticity stretching in wall-bounded turbulent and transitional flows has been investigated by means
of a new diagnostic measure, denoted by ?, designed to pick up regions with large amounts of vorticity
stretching. It is based on the maximum vorticity stretching component in every spatial point, thus yielding a
three-dimensional scalar field. The measure was applied in four different flows with increasing complexity: (a)
the near-wall cycle in an asymptotic suction boundary layer (ASBL), (b) K-type transition in a plane channel
flow, (c) fully turbulent channel flow at Re? = 180 and (d) a complex turbulent three-dimensional separated
flow. Instantaneous data show that the coherent structures associated with intense vorticity stretching in all four
cases have the shape of flat ‘pancake’ structures in the vicinity of high-speed streaks, here denoted ‘h-type’
events. The other event found is of ‘l-type’, present on top of an unstable low-speed streak. These events (l-type)
are further thought to be associated with the exponential growth of streamwise vorticity in the turbulent nearwall
cycle. It was found that the largest occurrence of vorticity stretching in the fully turbulent wall-bounded
flows is present at a wall-normal distance of y+ = 6.5, i.e. in the transition between the viscous sublayer and
buffer layer. The associated structures have a streamwise length of ?200–300 wall units. In K-type transition,
the ?-measure accurately locates the regions of interest, in particular the formation of high-speed streaks near
thewall (h-type) and the appearance of the hairpin vortex (l-type). In the turbulent separated flow, the structures
containing large amounts of vorticity stretching increase in size and magnitude in the shear layer upstream
of the separation bubble but vanish in the backflow region itself. Overall, the measure proved to be useful in
showing growing instabilities before they develop into structures, highlighting the mechanisms creating high
shear region on a wall and showing turbulence creation associated with instantaneous separations.

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Identifiers

ORCID for Neil D. Sandham: orcid.org/0000-0002-5107-0944

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