The terms of turbulent kinetic energy budget within random arrays of emergent cylinders

This article is aimed at quantifying and discussing the relative magnitude of key terms of the equation of conservation of turbulent kinetic energy (TKE) in the inter-stem space of a flow within arrays of vertical cylinders simulating plant stems of emergent and rigid vegetation. The spatial distribution of turbulent quantities and mean flow variables are influenced by two fundamental space scales, the diameter of the stems and the local stem areal number-density. Both may vary considerably since the areal distribution of plant stems in natural systems is generally not homogeneous; they are often arranged in alternating sparse and dense patches. The magnitude of the terms of the budget of TKE in the inter-stem space has seldom been quantified experimentally and is currently not well known. This work addresses this research need. New databases, consisting of three-component LDA velocity series and two-component PIV velocity maps, obtained in carefully controlled laboratory conditions, were used to calculate the terms of the TKE budget. The physical system comprises random arrays of rigid and emergent cylinders with longitudinally varying areal number-density. It is verified that the main source of TKE is vortex shedding from individual cylinders. The rates of production and dissipation are not in equilibrium. Regions with negative production, a previously unreported feature, are identified. Turbulent transport is particularly important along the von Karman vortex street. Convective rate of change of TKE and pressure diffusion are most relevant in the vicinity of the cylinders.