## 1. Introduction

[2] Aquatic vegetation is ubiquitous in shallow fluvial systems and it often forms patchy mosaics that mutually interact with turbulent flow at various scales ranging from an individual plant scale to a scale of a river reach [*Carr et al.*, 1997; *Marba and Duarte*, 1998; *Nikora*, 2010; *Sukhodolov and Sukhodolova*, 2010]. The interactions at the scale of a finite-size patch of vegetation (intermediate scale), which are of importance for in-stream retention processes and flow resistance in vegetated channel, alter the vertical flow structure along and downstream of the patches. The models analogous to the models of canonical mixing layer [*Monin and Yaglom*, 1971; *Tennekes and Lumley*, 1972; *Pope*, 2000] were shown to describe well the vertical structure of turbulent flow with uniformly distributed submerged aquatic vegetation [*Ghisalberti and Nepf*, 2002]. The analogy between canonical hydrodynamic mixing layer and a vegetated mixing layer developing at the leading edge of a finite-size patch of vegetation was the focus of companion paper [*Sukhodolova and Sukhodolov*, 2012]. The companion paper examines the characteristics of the mean flow using a combination of theoretical and field experimental approaches which provided relationships between characteristics of vegetation and principal variables of the mixing layer. This paper introduces analysis of scaling relationships for turbulence characteristics and reports on the application of the analysis to the results of field experiments already presented in the companion paper.

[3] In turbulent flows with flexible submerged vegetation, turbulent eddies populating the mixing layer significantly affect the momentum transfer into the vegetation canopy [*Ghisalberti and Nepf*, 2002]. Propagation of turbulent eddies over the top of the canopy results in quasiperiodic fluctuations in the drag force causing swaying of the plants called *monami* motions [*Okamoto and Nezu*, 2009]. Laboratory studies show that turbulent eddies, that are also known as organized motions or coherent structures, are the reason for appearance of monami and that certain velocity thresholds have to be triggered to initiate the monami [*Ghisalberti and Nepf*, 2002]. The consequence of monami is the increased bending of individual plants in the patch and consequently an increase in the distance that fluid from the ambient layer is able to penetrate into the vegetation layer [*Okamoto and Nezu*, 2009]. Most probably that characteristics of monami can be accounted by considering the momentary balance between physical forces imposed by coherent structures and reaction forces from plants tissue. This complex task is composed of two parts: Assessment and characterization of physical forces imposed by turbulent flow, and quantitative description of reaction forces due to flexural rigidity and buoyancy of the plant's tissue. This paper examines the structure of turbulence in vegetated mixing layers and respectively contributes to the assessment of physical forces induced by turbulent flows.

[4] Although turbulence is habitually regarded as a random phenomenon, application of turbulence models in hydrodynamics implies a certain degree of determinedness in seemingly chaotic turbulent signals [*Monin and Yaglom*, 1971]. Records of fluctuating velocity and pressure are conventionally characterized by the statistical moments and correlations of their probability density functions. These moments are related in a deterministic way to the structural properties of the flow described by specific hydrodynamic models; for example, by mixing layer model [*Monin and Yaglom*, 1971; *Tennekes and Lumley*, 1972; *Pope*, 2000; *Ghisalberti and Nepf*, 2002; *Sukhodolov et al.*, 2010; *Lacy and Wyllie-Echeverria*, 2011]. Hitherto the analogy between canonical mixing layers and vegetated mixing layers was examined mainly by exploring the similarity of shape in profiles of turbulence characteristics and we hypothesize that the analogy can be further understood by investigating relations between the principal parameters of the mixing layer model and characteristics of vegetation.

[5] The concept of coherent structures introduces spatially coherent, temporally evolving vortical motions possessing distinctive correspondence between components of the velocity vector and pressure that distinguishes the structure from the surrounding incoherent liquid [*Cantwell*, 1981; *Lumley*, 1981; *Nezu and Nakagawa*, 1993; *Schoppa and Hussain*, 2000; *Jirka*, 2001; *Constantinescu et al.*, 2011]. Coherent vortices evolving in the canonical mixing layers are shown to develop through complex interactions periodically appearing along the mixing layers [*Roshko*, 1992; *Rogers and Moser*, 1992; *Winant and Browand*, 1974]. Coherent structures in canopy edge flow were recently examined for atmospheric flows with forest vegetation using large-eddy simulation (LES) technique [*Dupoint and Brunet*, 2009]. Their study revealed the strong similarities in the development of coherent structures between averaged characteristics of vegetated and canonical hydrodynamic mixing layers. Besides, as it was demonstrated by earlier laboratory investigations [*Poggi et al.*, 2004] and confirmed by recent LES studies [*Dupoint and Brunet*, 2009; *Huang et al.* 2009], vegetation properties and population density are important factors controlling the dynamics of coherent structures. Therefore the search of relationship between statistical moments of turbulence, organized motions or coherent structures, and characteristics of vegetation is an appealing task which can further clarify the dynamics of complex vegetated flows.

[6] The goals of this paper are (1) to explore semitheoretical scaling relationships for the principal hydrodynamic variables controlling the dynamics of mixing layers; (2) to introduce turbulence characteristics obtained as a result of field experimental studies and to analyze the dynamics of vegetated mixing layers by comparing field experimental data with semitheoretical scaling relations; and (3) to examine the effect of population density on the dynamics of coherent structures in a vegetated mixing layer. This study explores the hypothesis on local equilibrium between production and dissipation of turbulent kinetic energy which stabilizes vegetated mixing layer and allows for deduction of scaling relations for coherent structures.