Lagrangian Coherent Structure Analysis on the Vegetated Compound Channel with Numerical Simulation

Jin Hwan Hwang,Seongeun Choi

doi:10.3390/w14030406

Abstract

Natural channels often consist of a mainstream near their thalwegs and shallow vegetated areas near shores. The compounded and partially vegetated cross-sections play a significantly role in determining the hydrodynamic characteristics of a channel. By employing the Lagrangian Coherent Structure (LCS) analysis, the present work unravels the effect of vegetation and geometry on the hydrodynamic interactions between mainstreams with the various depths and vegetated shallow areas. The LCS method is the concept of dynamical system analyses, which is determined by the finite-time Lyapunov exponents (FTLE) field of fluid particles. It enables to overcome the limitations of using the particle tracking method in cost and time for simulations. Since the LCSs represent material surfaces or asymptotic lines which particles approach, but do not pass through, they match well with the trajectories of particles or materials obtained by solving particle motion equations. Therefore, the temporal and spatial developments of the interfacial layers could be investigated by using the FTLE. As the difference of depth becomes appreciable, the values of FTLE are relatively larger farther from the vegetated area. It implies that the interfacial layer becomes wider with the larger size of vortex produced by the differences of velocities between the mainstreams and the vegetated areas. In other words, as depth differences become large, materials and momentum can be spread from the vegetated area to or collected from a wider area of the mainstream.

Highlights

The shallow and vegetated area in a channel is a place of sinking energy due to its enhanced resistance by drags, which differentiates momentums in this place from that in the mainstream near the thalwegs
When the Stokes number increases to 0.1 (Figure 3b), the particles still flow along the Lagrangian Coherent Structure (LCS) lines very similar to Figure 3a, even though the particle concentration near the core of the vortex becomes lower than the case of Stokes Number (St) = 0.005
The instantaneous finite-time Lyapunov exponents (FTLE) field of case 1 is constructed with the velocity fields and this FTLE presents the structures of the vortex and its downstream migration, which could be a crucial component in determining interfacial boundaries between main and vegetation affecting areas

Summary

Introduction

The shallow and vegetated area in a channel is a place of sinking energy due to its enhanced resistance by drags, which differentiates momentums in this place from that in the mainstream near the thalwegs. Turbulence and low-dimensional flow characteristics, in other words, wakes, may be an efficient natural apparatus for delivering momentum from the mainstream to the vegetated area, which has momentum deficiencies. For controlling water quality and managing ecology, it is quite substantial to understand how turbulence and wakes are distributed and developed around the interface between mainstreams and vegetated areas. Vegetation (e.g., Posidonia oceanica, mangrove forests, Spartina saltmarshes) can largely modify the wave-induced flow field, increasing energy dissipation and improving resilience of coastal areas against beach erosion and tsunami. Research in this topic has produced plenty of papers, among which the most relevant are [1,2,3]

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