The velocity fields of a turbulent wake behind a flat plate obtained from the direct
numerical simulations of Moser et al. (1998) are used to study the structure of the
flow in the intermittent zone where there are, alternately, regions of fully turbulent
flow and non-turbulent velocity fluctuations on either side of a thin randomly moving
interface. Comparisons are made with a wake that is ‘forced’ by amplifying initial
velocity fluctuations. A temperature field T, with constant values of 1.0 and 0 above
and below the wake, is transported across the wake as a passive scalar. The value of
the Reynolds number based on the centreplane mean velocity defect and half-width
b of the wake is Re ≈ 2000.
The thickness of the continuous interface is about 0.07b, whereas the amplitude of
fluctuations of the instantaneous interface displacement yI(t) is an order of magnitude
larger, being about 0.5b. This explains why the mean statistics of vorticity in the
intermittent zone can be calculated in terms of the probability distribution of yI
and the instantaneous discontinuity in vorticity across the interface. When plotted as
functions of y−yI the conditional mean velocity 〈U〉 and temperature 〈T〉 profiles
show sharp jumps at the interface adjacent to a thick zone where 〈U〉 and 〈T〉 vary
much more slowly.
Statistics for the conditional vorticity and velocity variances, available in such detail
only from DNS data, show how streamwise and spanwise components of vorticity are
generated by vortex stretching in the bulges of the interface. While mean Reynolds
stresses (in the fixed reference frame) decrease gradually in the intermittent zone,
conditional stresses are roughly constant and then decrease sharply towards zero
at the interface. Flow fields around the interface, analysed in terms of the local
streamline pattern, confirm and explain previous results that the advancement of the
vortical interface into the irrotational flow is driven by large-scale eddy motion.
Terms used in one-point turbulence models are evaluated both conventionally and
conditionally in the interface region, and the current practice in statistical models of
approximating entrainment by a diffusion process is assessed.