Tomographic PIV experiments were performed in the near-fiel
d of the turbulent flow past
a square cylinder. A classical Reynolds decomposition was p
erformed on the resulting
velocity fields into a time invariant mean flow and a fluctuatin
g velocity field. This fluc-
tuating velocity field was then further decomposed into cohe
rent and residual/stochastic
fluctuations. The statistical distributions of the second a
nd third invariants of the ve-
locity gradient tensor were then computed at various stream
wise locations, along the
centre line of the flow and within the shear layers. These inva
riants were calculated from
both the Reynolds-decomposed fluctuating velocity fields an
d the coherent and stochas-
tic fluctuating velocity fields. The range of spatial locatio
ns probed incorporates regions
of contrasting flow physics, including a mean recirculation
region and separated shear
layers, both upstream and downstream of the location of peak
turbulence intensity along
the centre line. These different flow physics are also reflecte
d in the velocity gradients
themselves with different topologies, as characterised by t
he statistical distributions of
the constituent enstrophy and strain-rate invariants, for
the three different fluctuating
velocity fields. Despite these differing flow physics the ubiq
uitous self-similar “tear drop”-
shaped joint probability density function between the seco
nd and third invariants of the
velocity gradient tensor is observed along the centre line a
nd shear layer when calcu-
lated from both the Reynolds decomposed and the stochastic v
elocity fluctuations. These
“tear drop”-shaped joint probability density functions ar
e not, however, observed when
calculated from the coherent velocity fluctuations. This “t
ear drop” shape is classically
associated to the statistical distribution of the velocity
gradient tensor invariants in fully
developed turbulent flows in which there are no coherent dyna
mics present, and hence
spectral peaks at low wavenumbers. The results presented in
this manuscript, however,
show that such “tear drops” also exist in spatially developi
ng inhomogeneous turbulent
flows. This suggests that the “tear drop” shape may not just be
a universal feature of
fully developed turbulence but of turbulent flows in general.