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

Abstract

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 K arm an vortex street. Convective rate of change of TKE and pressure diffusion are most relevant in the vicinity of the cylinders.

The onset of sediment transport in vegetated channels predicted by turbulent kinetic energy

“…In the Widdows study, the relation for open channel flow, τ = 0.19 k t , was used to estimate the mean bed stress from the measured turbulent kinetic energy , with , , and denoting the velocity fluctuation [ Stapleton and Huntley , ]. However, as discussed in Nepf [], Ricardo et al [], and Yang et al [], this relation assumes that turbulence production is linked to bed stress, which is not true in vegetated systems, for which turbulence production is primarily associated with the vegetation. Therefore, Widdows' conclusion that the critical τ was unchanged between bare and vegetated beds [ Widdows et al , , Figure 6] was incorrect, and, in fact, their data actually show that the threshold for erosion was defined by a critical value of k t .…”

Sediment deposition within and around a finite patch of model vegetation over a range of channel velocity

“…The presence of stem turbulence depends on the stem Reynolds number Re d ( = ud/ν ), where u is the velocity within the vegetation, d is the stem diameter, and is the kinematic viscosity. Stem‐scale turbulence has been observed at Re d > 200 within natural river vegetation [ Naden et al ., ] and in many model canopies [ Liu et al ., ; Ricardo et al ., ; Zong and Nepf , ] through analysis of velocity spectra and TKE profiles. In contrast, stem‐generated turbulence is absent at low Re d [ Tanino and Nepf , ].…”

Turbulence in Rivers

“…The turbulent structure of the flow in complex geometries and the interpretation of the related fluvial processes are determined through the analysis of the spatial distribution of the mean velocity and vorticity fields and of the second-and third-order moments present in the conservation equations, provided that the data is sufficient to obtain stable statistical moments. Leite Ribeiro et al (2002), Proust et al (2013), Ricardo et al (2014) are examples of recent theoretical analyses of fluvial turbulent processes with highly complex boundary geometries performed by assuming steady-state flow conditions. When performing field studies, which are typically based on measurements of instantaneous velocities, researchers pay special attention to the steadiness of the flow to assure that measurements made in multiple spatial positions are representative and can be combined in a time-averaged description of the flow (Franca 2005a;Saggiori et al 2012).…”

“…Here, the vegetation conditions local velocities, turbulence intensities, turbulent Reynolds stresses and their vertical and horizontal distributions (e.g., Nepf 1999). Ricardo et al (2014) estimated the terms in the tke transport equation in a flow with emergent arrays of cylinders by considering velocity measurements in horizontal planes. With specific reference to the role of vegetation in turbulent flows evolving in compound channels, Koziol (2013) found, on the basis of dedicated experimental investigations, that trees placed on the floodplains do not significantly change the values of the relative turbulence intensity in the entire compound channel, but they do change the vertical distributions of the relative turbulence intensities in the three components in the floodplains and over the bottom of the main channel.…”

“…Furthermore, turbulence is responsible for physical processes in rivers such as the transport and mixing of diluted or undiluted substances, temperature transfer, sediment motion and suspension, and geomorphological evolution. Hence, the consideration of turbulence is fundamental to riverine environmental applications and requires the use of an adequate theoretical analysis [see, for instance, the amount of research dedicated to turbulence in fluvial hydraulics recently published in Schleiss et al (2014)]. …”