The turbulent/non-turbulent interface bounding a far wake

Abstract

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.

Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion

“…Note that the same threshold value (of 0.10) has been suggested by Mathew and Basu (2002) for a turbulent circular temporal shear layer. However, this threshold value is lower than that used by Bisset et al (2002) (=0.7) for a turbulent planar wake, owing to difference in the flow. Again, Table 1 shows that the RMS difference is minimum at a threshold value of 0.03 for both Velocity and VelocityVorticity criteria.…”

“…The Vorticity criterion employed here was suggested by Bisset et al (2002) and Mathew and Basu (2002). However, the threshold value to be employed in Eqs.…”

“…A thin and highly irregular interface, with a thickness of about one-two orders of magnitude smaller than the integral scale (Chevray 1982;Bisset et al 2002;Hunt et al 2006;Holzner et al 2008), is known to separate the turbulent motion from the surrounding flow. The two regions can be readily identified by adding dye to one region and using laser or some other light source for illumination (Dimotakis et al 1983;Westerweel et al 2002).…”

“…Furthermore, the flow in the non-turbulent region is practically irrotational and is rotational in the turbulent region (Corrsin 1943;Corrsin and Kistler 1954; see also Pope 2000, p 167-173). This property has been used by Bisset et al (2002), Mathew and Basu (2002) and is further tested in the present paper for interface detection. The former authors in their analysis of DNS data for a plane wake required that the magnitude of normalized vorticity at the interface be equal to a pre-determined threshold.…”

Turbulent boundary layers and channels at moderate Reynolds numbers

“…The definition can be made more precise in simulations, because the vorticity magnitude \a>\ can be computed, and irrotational flow can be characterized as where the vorticity vanishes (Bisset, Hunt & Rogers 2002). An example is figure 3(a), which shows a typical instantaneous vorticity field in a short section of the boundary-layer simulation.…”