Research papersSpectral shortcut in turbulence energy transfer in open channel flow over submerged vegetation
Graphical abstract
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 (hp < z < ho in Fig. 1), and the high frequency wake vortex generated by individual plans in the longitudinal-lateral (x-y) plane within canopy (0 < z < hv in Fig. 1) (Zong and Nepf, 2010, Nepf and Ghisalberti, 2008). Here hp and ho 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 hv is the submerged vegetation height. As part of the KH vortex penetrates the canopy, with the penetration layer located at hp < z < hv 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 ho < z < H and the lower canopy zone with 0 < z < hp (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.
Section snippets
Turbulent kinetic energy budget equation
The turbulent kinetic energy (TKE) budget equation is introduced here as the fundamental backdrop, because both flow subdivision and energy transfer are studied by making use of this equation. A horizontal plane-averaging procedure has been commonly conducted to study the submerged vegetation flow in an open channel (Nepf, 2012b, Nezu and Sanjou, 2008, Nepf and Vivoni, 2000). The temporal and horizontal averaged TKE conservation equation is presented below, with some less important terms being
Experimental set-up and measurement
Experiments were conducted in a glass-walled recirculating flume of 12 m in length, 0.6 m in width (B = 0.6 m) and 0.6 m in depth in the Sediment Research Laboratory at Hohai University (Fig. 2). The flow discharge Q was controlled by the variable frequency pump and flow meter system at the flume inlet with an accuracy of 0.001 L s−1, and the flow depth H was controlled by the tailgate at the outlet with an accuracy of 0.5 mm. The flume bed slope S was adjustable to maintain a constant water
Spectra of the shear and wake turbulence
The turbulence spectrum presents the occurrence possibility F(f) (i.e., the spectral density) of eddies with varying frequencies f at a fixed point in the turbulent flow. Fig. 3 presents spectral distributions in the upper mixing layer (Fig. 3a & c) and lower canopy zone (Fig. 3b & d) at locations 1 & 2 in Case B-3-30. For turbulence in the upper mixing layer, the spectral density in Fig. 3a is larger than that in Fig. 3c, because the KH instability is much fiercer at location 1. The
Conclusions
The turbulent velocity measurement and spectrum analysis were conducted based on the experiments in an open channel with submerged rigid vegetation. The purpose of this investigation was to understand the spectral shortcut characteristics between the KH and wake-scale vortices. The results have been discussed in terms of the spectral distribution, flow subdivision and energy transfer. The main findings of this investigation are summarized as follows.
- 1.
The spectral distribution may exhibit one of
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was partly supported by the National Natural Science Foundation of China [grant numbers 51579079, 51979084, 51239003]; the 111 Project [grant number B17015]; and China Scholarship Council project [grant number 201806715026]. We also thank Professor Bidya Sagar Pani and Professor Saiyu Yuan for their help in revising this work.
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