The role of Coherent Structures and Inhomogeneity in Near-Field Inter-Scale Turbulent Energy Transfers
arXiv:2004.10616 · doi:10.1017/jfm.2020.341
Abstract
We use DNS to study inter-scale and inter-space energy exchanges in the near-field of a turbulent wake of a square prism in terms of the KHMH equation written for a triple decomposition of the velocity field accounting for the quasi-periodic vortex shedding. Orientation-averaged terms of the KHMH are computed on the plane of the mean flow and on the geometric centreline. We consider locations between and times the width of the prism. The mean flow produces kinetic energy which feeds the vortex shedding coherent structures. In turn, these structures transfer energy to the stochastic fluctuations over all length-scales from the Taylor length to and dominate spatial turbulent transport of two-point stochastic turbulent fluctuations. The orientation-averaged non-linear inter-scale transfer rate which was found to be approximately independent of by Alves Portela et. al. (2017) in the range at a distance from the square prism requires an inter-scale transfer contribution of coherent structures for this approximate constancy. However, the near-constancy of at which was also found by Alves Portela et. al. (2017) is mostly due to stochastic fluctuations. Even so, the proximity of to the turbulence dissipation rate in the range at requires contributions of the coherent structures. Spatial inhomogeneity also makes a direct and distinct contribution to , and the constancy of close to 1 would not have been possible without it either in this near-field flow. Finally, the pressure-velocity term is also an important contributor to the KHMH, particularly at scales r larger than about , and appears to correlate with the purely stochastic non-linear inter-scale transfer rate when the orientation average is lifted.