A k–ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows

Abstract

AbstractFlow and transport through aquatic vegetation is characterized by a wide range of length scales: water depth ($H$), plant height ($h$), stem diameter ($d$), the inverse of the plant frontal area per unit volume (${a}^{\ensuremath{-} 1} $) and the scale(s) over which $a$ varies. Turbulence is generated both at the scale(s) of the mean vertical shear, set in part by $a$, and at the scale(s) of the stem wakes, set by $d$. While turbulence from each of these sources is dissipated through the energy cascade, some shear-scale turbulence bypasses the lower wavenumbers as shear-scale eddies do work against the form drag of the plant stems, converting shear-scale turbulence into wake-scale turbulence. We have developed a $k$–$\varepsilon $ model that accounts for all of these energy pathways. The model is calibrated against laboratory data from beds of rigid cylinders under emergent and submerged conditions and validated against an independent data set from submerged rigid cylinders and a laboratory data set from a canopy of live vegetation. The new model outperforms existing $k$–$\varepsilon $ models, none of which include the $d$ scale, both in the emergent rigid cylinder case, where existing $k$–$\varepsilon $ models break down entirely, and in the submerged rigid cylinder and live plant cases, where existing $k$–$\varepsilon $ models fail to predict the strong dependence of turbulent kinetic energy on $d$. The new model is limited to canopies dense enough that dispersive fluxes are negligible.