Experimental study of spectral energy fluxes in turbulence generated by a fractal, tree-like object

Abstract

We report on an experimental study of the kinetic energy fluxes between scales in the turbulent near-wake flow downstream of a fractal, tree-like object. Experiments are performed in a liquid channel and data are acquired using planar Particle Image Velocimetry (PIV). The data are analyzed based on the filtering framework of relevance to Large Eddy Simulations. The flow and energy fluxes differ from the case of a canonical flow such as the cylinder wake, where typically kinetic energy is injected into turbulence by an object characterized by a single, well-defined, length-scale. For a fractal tree-like object, we find that the measured energy flux is strongly dependent on scale. In the present flow, scale-dependent injection of kinetic energy into the cascade arises from production as well as spatial transport terms. The injection rate spectrum is evaluated directly from the data by quantifying the rate of change of spectral energy flux as a function of wavenumber. The net injection rate spectrum is observed to scale approximately as ∼k−7/3, in accordance with heuristic and dimensional arguments previously used for the kinetic energy production rate spectrum in shear flows. In order to scale the results, we consider an equivalent mixing length-scale that can be obtained from the tree geometry by adding over the relevant scales of successive branch clusters. In prior work, this equivalent length scale has been found to collapse the eddy-viscosity well. Here we find that this scale also collapses the energy flux and the net injection rate spectrum successfully.