The turbulence cascade in the near wake of a square prism

Abstract

We present a study of the turbulence cascade on the centreline of an inhomogeneous and anisotropic near field turbulent wake generated by a square prism at Re = 3900 using the Kármán-Howarth-Monin-Hill (KHMH) equation. This is the fully generalised scale-by-scale energy balance which, unlike the Kármán-Howarth equation, does not require homogeneity or isotropy assumptions. Our data are obtained from a direct numerical simulation (DNS) and therefore enable us to access all the processes involved in this energy balance. A significant range of length-scales exists where the orientation averaged non-linear interscale transfer rate is approximately constant and negative, indicating a forward turbulence cascade on average. This average cascade consists of coexisting forward and inverse cascade behaviours in different scale space orientations. With increasing distance from the prism but within the near field of the wake, the orientationaveraged non-linear interscale transfer rate tends to be approximately equal to minus the turbulence dissipation rate even though all the inhomogeneity-related energy processes in the scale-by-scale energy balance are significant, if not equally important. We also find well-defined near −5/3 energy spectra in the streamwise direction, in particular at a centreline position where the inverse cascade behaviour occurs for streamwise oriented length-scales.

Simulation of Turbulent Emulsification in a Sonolator Mixer: Interpretation of Drop Breakage Time

“…In the strongly non-isotropic near field of the wake studied by Portela et al [35], an amplification of energy was observed in the energy-containing subrange (see model spectrum 2 in Fig. 10 a); this is associated with coherent structures (vortex shedding).…”

“…The model spectrum 2 is obtained with Eq. (3.4) in [35] and represents a 1-D energy spectrum amplified in the energy-containing subrange.…”

Interscale energy transfer in the merger of wakes of a multiscale array of rectangular cylinders

“…Note that it has been assumed that all out-of-plane gradients of the mean velocity field vanish due to the flow's symmetry (measurements are taken at the flume's mid-plane) as well as out-of-plane gradients of the coherent velocity fluctuations (this can be supported by a recent study of Portela et al [47] who performed direct numerical simulation of a flow past a rectangular prism at comparable Reynolds number).…”

Effect of blade modifications on the torque and flow field of radial impellers in stirred tanks

“…Near the impeller, turbulence intensities grow significantly, possibly explaining why the -5/3 slope is not that clear there (see fig 14). In any case, the -5/3 slope in temporal spectra has been observed even in flow cases where the Kolmogorov theory conditions for its existence are very far from being met [24][25][26] which means that its underlying cause remains fundamentally unexplained not only in our flow but also in general.…”