Horizontal mixing of quasi-uniform straight compound channel flows

Abstract

The generation and evolution of large-scale vortices with vertical axis (macro-vortices) in a straight compound channel under quasi-uniform flow conditions is investigated. We discuss possible similarities and clear differences with free shear layer flows induced by the meeting of shallow streams of different speeds. An experimental investigation based on particle image velocimetry (PIV) measurements of free-surface velocities forms the basis for an analysis of both the specific features of macro-vortices and of the related mean flow characteristics. Dynamical properties strongly depend on the ratio r h between the main channel flow depth (h * mc ) and the floodplain depth (h * fp ), and three flow classes can be identified. 'Shallow flows' (r h > 3) are dominated by strong shearing and large macro-vortices populating the transition region between the main channel and the floodplains. The mean streamwise velocity induced in 'intermediate flows'(2 6 r h 6 3) is characterized by a dip in the transition region, while it closely resembles that occurring in a rectangular channel in the case of 'deep flows' (r h < 2). For both the latter cases the shear in the transition region decreases and the macro-vortices are also generated in the wall boundary layer of the floodplains. The typical size of the quasi-two-dimensional macro-vortices, generated at the transition region, is found to be independent of the streamwise coordinate. This and the non-monotonic behaviour of the mean streamwise velocity suggest that in straight compound channels the topographic forcing is so dominant that conceptual models interpreting these flows as free shear layers may largely fail to describe the physics of compound channels flows.

Transversal and longitudinal mixing in compound channels

“…The main agents controlling these phenomena are the quasi‐two‐dimensional (2‐D) macrovortical structures, which arise at the main‐channel/floodplains transition region, owing to the strong generation of vorticity at the flow‐depth jump. As suggested by Nezu et al [1999] and verified by Stocchino and Brocchini [2010], the dynamics of the flow field and, hence, of the vorticity, strongly depends on the flow characteristics in terms of the flow‐depth ratio r h , between the depth in the main channel ( ) and the depth in the floodplains ( ) as first introduced by Shiono and Knight [1991] and later modified by Nezu et al [1999]. In a more recent contribution, Stocchino et al [2011] investigated the different dispersion regimes occurring in compound channel flows and highlighting the dependence of mixing both on the depth ratio r h and on the subcritical/supercritical character of the flow, i.e., on the Froude number ( Fr ).…”

“…The present paper follows and extends the studies of the previous contribution by Stocchino and Brocchini [2010] and Stocchino et al [2011]. In particular, Stocchino and Brocchini [2010] was dedicated to the study of the characteristics of the Eulerian turbulent flow, also in relation to the still open question: Can compound channels flows be described as free mixing layers?…”

“…However, this aspect was not investigated by Stocchino et al [2011]. In the present contribution, which can be thought as a natural extension of Stocchino and Brocchini [2010] and Stocchino et al [2011], the scope is the evaluation of the longitudinal and transversal mixing coefficients and their dependence on the main physical parameters (the Froude number Fr and the flow‐depth ratio r h ). To this end, the experimental data set has been significantly extended covering a wider range of the controlling parameters.…”

“…In particular, Stocchino and Brocchini [2010] was dedicated to the study of the characteristics of the Eulerian turbulent flow, also in relation to the still open question: Can compound channels flows be described as free mixing layers? Stocchino and Brocchini [2010]demonstrated that the specific geometry of the compound channels, in particular the flow‐depth jump between the main channel and the floodplains, is a source of vorticity that induces the formation of quasi‐2‐D macrovortices that, once generated, preserve their size while being convected downstream. At that stage, the Lagrangian properties of the flow were completely ignored Stocchino et al [2011]…”

Turbulence in Rivers

“…2.4, which shows macrovortices in the transition regions and a mean flow velocity distribution along the transversal direction (see Stocchino et al 2011). Recent experimental investigations (Stocchino and Brocchini 2010), which were based on use of the PIV technique, revealed that the population and properties of macrovortices largely depend on the typical depth gradients, i.e., on the ratio r h between the largest and smallest flow depths. Shallow flows (r h [ 3) are dominated by strong shearing and large macrovortices populate the transition region between the main channel and the floodplains.…”