> A new geometrical feature in turbulence: A surface which contains all > extremal points of the turbulent kinetic energy
N. Peters, P. Schäfer, RWTH Aachen
Based on the profile of the absolute value u of the velocity field along streamlines, the latter are partitioned into segments at their extreme points as proposed by Wang (1). Streamline segments are then defined as parts of the streamline between the points where the gradient in streamline direction du/ds vanishes, where s is the arc length along the streamline. It is found that the boundaries of all streamline segments define a surface in space. This surface contains all local extrema of the instantaneous scalar u-field and thus also those of the turbulent kinetic energy field (k=u^2/2). Such points also include stagnation points of the flow field, which are absolute minima of the turbulent kinetic energy. As local extreme points are the ending points of dissipation elements, an approach for space filling geometries in turbulent scalar fields, such elements in the turbulent kinetic energy field also end and begin in the surface and the temporal evolution of dissipation elements and streamline segments is intimately related. It is shown that streamline segments are subject to slow as well as fast changes. This separation yields a transport equation for the probability density function (pdf) P(l) of the length l of streamline segments. Numerical solutions of the pdf equation yield a good agreement with the pdf obtained from DNS data. The interplay of viscous drift acting on small segments and linear strain acting on large segments yields, as it has already been concluded for dissipation elements that the mean length of streamline segments should scale with Taylor micro scale (2).
(1) L. Wang, 'On properties of fluid turbulence along streamlines,' J. Fluid Mech. 648, 183 – 203 (2010). (2) P. Schaefer, M. Gampert, and N. Peters, 'The length distribution of streamline segments in homogeneous isotropic decaying turbulence,' Phys. Fluids 24, 045104 (2012);
26.09.2012 at 13:30