Wave-like motion and secondary currents in arrays of emergent cylinders induced by large scale eddying motion

Abstract

Free-surface flows with riparian corridors are known to develop large eddies resulting from the instability associated to the inflectional profile of the longitudinal velocity in the spanwise direction. They periodically generate strong momentum exchanges inside the vegetation corridor, triggering a wave-like motion, detectable as free-surface oscillations and out-of-phase velocity components. We propose a characterization of the flow inside the vegetation corridor, focusing on the wave-like motion and its influence on secondary currents. We conditionally sample the fluid motion to highlight the structure of the phase-averaged coherent structure. Quadrant analysis shows that there is a strong variation of Reynolds stress anisotropy in the spanwise direction, which is one of the key generation mechanisms of secondary currents. Spectrograms of longitudinal and lateral velocity fluctuations reveal that the oscillatory motion is imposed on the whole of the vegetated layer, because of continuity. The analysis of the phase-averaged 2D vertical-longitudinal flow reveals that there is a complex 3D pattern of mass fluxes associated to each large eddy. In particular there is an anti-symmetric net mass imbalance which, by mass conservation, generates a mass flux directed outwards, to the main channel, near the bottom of the channel. The Eulerian expression of this motion is obtained as the spatial average of the flow over the length of the large eddy, resulting in the pattern of the secondary current in the vertical-spanwise plane. It is shown that the secondary motion is a necessary feature of free-surface turbulent flows that develop large-scale inflectional instabilities.

Tracking the Nearfield Evolution of an Initially Shallow, Neutrally Buoyant Plane Jet Over a Sloping Bottom Boundary

“…KHCS contribute to the momentum exchange and production of TKE in shear layers (Taborda et al., 2022; Truong & Uijttewaal, 2019; White & Nepf, 2008). The momentum exchange between the jet and ambient waters is mainly represented by the horizontal Reynolds stress $${-}\overline{{u}_{n}{\rhook}{v}_{n}{\rhook}}$$ at the interface ( y n = 0) (Taborda et al., 2022; Truong & Uijttewaal, 2019).…”

“…KHCS contribute to the momentum exchange and production of TKE in shear layers (Taborda et al., 2022; Truong & Uijttewaal, 2019; White & Nepf, 2008). The momentum exchange between the jet and ambient waters is mainly represented by the horizontal Reynolds stress $${-}\overline{{u}_{n}{\rhook}{v}_{n}{\rhook}}$$ at the interface ( y n = 0) (Taborda et al., 2022; Truong & Uijttewaal, 2019). The TKE production rate P n in the curvilinear coordinate system (neglecting vertical components) is given by, $$${P}_{n}=-\left(\overline{{u}_{n}^{\prime }{u}_{n}^{\prime }}\frac{\partial {\overline{u}}_{n}}{\partial {x}_{n}}+\overline{{v}_{n}^{\prime }{v}_{n}^{\prime }}\frac{\partial {\overline{v}}_{n}}{\partial {y}_{n}}+\overline{{u}_{n}^{\prime }{v}_{n}^{\prime }}\frac{\partial {\overline{u}}_{n}}{\partial {y}_{n}}+\overline{{u}_{n}^{\prime }{v}_{n}^{\prime }}\frac{\partial {\overline{v}}_{n}}{\partial {x}_{n}}\right)$$$ …”

“…In the second method, the measured flow field is reconstructed based on conditional‐averaging in order to smooth out small‐scale turbulence (Shi et al, 2023; Taborda et al., 2022; Yuan & Horner‐Devine, 2017). The conditional‐averaging approach identifies KHCS using three consecutive zero‐crossings of low‐pass filtered v n ′ (Taborda et al., 2022; White & Nepf, 2008), based, for example, on the velocity signal at P1 (Figure 12b).…”

“…In the second method, the measured flow field is reconstructed based on conditional‐averaging in order to smooth out small‐scale turbulence (Shi et al, 2023; Taborda et al., 2022; Yuan & Horner‐Devine, 2017). The conditional‐averaging approach identifies KHCS using three consecutive zero‐crossings of low‐pass filtered v n ′ (Taborda et al., 2022; White & Nepf, 2008), based, for example, on the velocity signal at P1 (Figure 12b). A typical KHCS (Figure 12b) lasts for a time period of T i and contains a sweep ( Q 4) and an ejection ( Q 2) event, as distinguished using quadrant analysis (Bagherimiyab & Lemmin, 2018; Huai et al., 2019; Nezu & Nakagawa, 1993; White & Nepf, 2008).…”

“…Examples of filtered velocity signals are shown in Figures 12a and 12b (using a low-pass filter, f filter = 4f cs following Truong and Uijttewaal ( 2019)); f cs is the dominant frequency of KHCS, that is, peak frequency in Figure 12c before nondimensionalization. In the second method, the measured flow field is reconstructed based on conditional-averaging in order to smooth out small-scale turbulence (Shi et al, 2023;Taborda et al, 2022;Yuan & Horner-Devine, 2017). The conditionalaveraging approach identifies KHCS using three consecutive zero-crossings of low-pass filtered v n ′ (Taborda et al, 2022;White & Nepf, 2008), based, for example, on the velocity signal at P1 (Figure 12b).…”