Spectral shortcut in turbulence energy transfer in open channel flow over submerged vegetation

Highlights

• There are dual ISRs in the penetration layer where KH and wake vortices coexist.

• Spectral shortcut transfers 58–71% energy from large eddies to wake-scale vortices.

• TKE transfer rate becomes fierce with λ, U_m and a decrease in H/h_v.

Abstract

This study explores the characteristics of the spectral shortcut in the turbulence kinetic energy transfer in experimental open channel flows with the presence of submerged vegetation flow. The vegetation layer was simulated by arrays of rigid vertical cylinders, distributed uniformly in the channel bed. Results indicate that there are dual inertial subranges (ISRs) in the spectral distribution of turbulence energy in the penetration layer, where the Kelvin-Helmholtz (KH) and wake vortices coexist. The lower-frequency and higher-frequency ISRs reflect the energy cascading of the KH and wake-scale vortices, respectively. Spectral shortcut narrows the ISR for the KH vortex and contributes to the ISR for the wake-scale vortices, because such an action transfers a significant amount of turbulent energy directly from the large-scale eddies to the wake-scale vortices. We study the influence of spectral shortcut on energy transfer according to the turbulence kinetic energy budget equation for shear turbulence. The transferred energy is found to account for 58–71% of the shear turbulent energy and contributes considerably to the wake-scale turbulence. The strength of the energy transfer increases with the increase in the vegetation density and the mean bulk velocity and the decrease in the relative submergence.

Introduction

Aquatic vegetation is an important component of river ecosystems that can promote biodiversity by enhancing the spatial heterogeneity in flow conditions and habitats (Kemp et al., 2000, Liu et al., 2010, Choi and Kang, 2016). Canopy flow also affects the incipient motion, transport and deposition of sediment, resulting in changes in the distribution of sediment grain size (Yang and Choi, 2010, Nepf, 2012a), bed slope (Bouteiller and Venditti, 2014) and channel morphology (Bouteiller and Venditti, 2015, Perignon et al., 2013). Research into the dynamics of the vegetated flow can help better understand the river ecology and channel geomorphology.

Generally speaking, there are two types of vortices in open channel flows through submerged vegetation. These are the low frequency Kelvin-Helmholtz (KH) vortex driven by the KH instability in the longitudinal-vertical (x-z) plane within the mixing layer (h_p < z < h_o in Fig. 1), and the high frequency wake vortex generated by individual plans in the longitudinal-lateral (x-y) plane within canopy (0 < z < h_v in Fig. 1) (Zong and Nepf, 2010, Nepf and Ghisalberti, 2008). Here h_p and h_o are the lower and upper boundaries that are characterized with turbulent kinetic energy (TKE) balance between the shear turbulence generation and dissipation terms (Wilson, 1988), and h_v is the submerged vegetation height. As part of the KH vortex penetrates the canopy, with the penetration layer located at h_p < z < h_v in Fig. 1, the vegetation breaks it into several secondary, small-scale vortices (Hout et al. 2007). This KH vortex break-up mechanism interferes the eddy cascading process, and this phenomenon is defined as the “spectral shortcut” (Finnigan, 2000).

Spectral shortcut affects the turbulent coherent structure and the flow characteristics over the whole depth. This action directly transfers the TKE from large-scale turbulence to the small-scale turbulence (Finnigan, 2000), thereby weakening the dominance of the KH vortex in the mixing layer. An analytical formula has been established to evaluate TKE transfer rate over the terrestrial canopy, where the air flow is laterally unconfined (Wilson, 1988). The influence of the spectral shortcut on the eddy distribution can be investigated by examining the turbulence spectra. According to the vertical velocity spectra in submerged vegetated flow, the spectrum peaks at a frequency corresponding to the generated secondary vortices; and the scales of the secondary vortices are same as those of the wake vortices (Poggi et al., 2004, King et al., 2012). The aggregation of the secondary vortex and the wake vortex is defined as the “wake-scale vortex”. Since the KH, secondary and wake vortices co-exist in longitudinal direction, the longitudinal velocity spectra reflect the interaction of all the turbulent structures. Meanwhile, the TKE dissipation and vertical flow subdivision can also be reflected according to the longitudinal velocity spectra (Nezu and Sanjou, 2008, Nepf and Vivoni, 2000). However, detailed studies about the longitudinal velocity spectra have been rarely conducted previously.

This study investigates various aspects of the spectral shortcut by analyzing the longitudinal velocity spectra based on the measurements in an experimental flume. The main goal is to explore the influences of the spectral shortcut on the turbulence structure and energy transfer mechanism by making use of the spectral and TKE budget analyses, respectively. The Results & Discussion Section is the main part of this article and is structured as follows. In Section 4.1, the energy cascading processes for the shear and wake vortices are separately investigated by analyzing the turbulent spectra above and below the mixing layer, i.e., in the outer zone with h_o < z < H and the lower canopy zone with 0 < z < h_p (see Fig. 1). In Section 4.2, the longitudinal velocity spectra in the penetration layer are analyzed. Section 4.3studies the flow subdivision based on TKE balance and Section 4.4 estimates the energy transfer by examining the TKE budget. The various influencing factors of the spectral shortcut are explored according to the TKE transfer rate, which can be revealed by combining the TKE budget and flow subdivision results together.