The turbulent/non-turbulent interface bounding a far wake.

*(English)*Zbl 1156.76397Summary: 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 \(Re\) [approximate] 2000.

The thickness of the continuous interface is about \(0.07b\), whereas the amplitude of fluctuations of the instantaneous interface displacement \(y_I(t)\) 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 \(y_I\) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of \(y-y_I\) the conditional mean velocity \(\langle U \rangle\) and temperature \(\langle T \rangle\) profiles show sharp jumps at the interface adjacent to a thick zone where \(\langle U \rangle\) and \(\langle T \rangle\) 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.

The thickness of the continuous interface is about \(0.07b\), whereas the amplitude of fluctuations of the instantaneous interface displacement \(y_I(t)\) 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 \(y_I\) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of \(y-y_I\) the conditional mean velocity \(\langle U \rangle\) and temperature \(\langle T \rangle\) profiles show sharp jumps at the interface adjacent to a thick zone where \(\langle U \rangle\) and \(\langle T \rangle\) 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.