## 1. Introduction

[2] Aquatic vegetation plays a key role in many ecosystems [e.g., *Bunn and Arthington*, 2002]. It alters mean and turbulent flow, which in turn can influence the transport of sediment [e.g., *López and García*, 1998, 2001, *Nepf*, 2012]. The modified hydrodynamics can also impact nutrient uptake [*Morris et al*., 2008], light availability [*Madsen et al*., 2001], and metabolic function [*Nikora*, 2010]. The magnitude of flow through a canopy impacts the growth of organisms within the canopy. For example, reduced flow affects the food availability and growth of bivalves in a seagrass canopy [*Boström et al*., 2006].

[3] Most previous research has focused on fully developed flow over long canopies of vegetation (see review in *Nepf* [2012]). However, vegetation often grows in a mosaic of short patches [*Sand-Jensen and Madsen*, 1992], with individual patches too short to reach fully developed conditions. For typical river macrophytes, the distance to reach fully developed flow over a long canopy is 1–10 m [*Sukhodolov and Sukhodolova*, 2006; *Ghisalberti and Nepf*, 2009]. A few researchers have made observations of the transition in the mean and turbulent velocity at the leading edge of a canopy [*Gambi et al*., 1990; *Fonseca and Koehl*, 2006; *Kregting et al*., 2011; *Sukhodolova and Sukhodolov*, 2012], and these transition regions have been associated with higher nutrient uptake rates [*Morris et al*., 2008] and distinctive sediment deposition patterns [*Zong and Nepf*, 2010].

[4] Terrestrial vegetation has been studied more extensively than aquatic vegetation, with experimental and numerical methods describing flow adjustment at a forest edge [e.g., *Brunet et al*., 1994; *Irvine et al*., 1997; *Morse et al*., 2002; *Yang et al*., 2006; *Dupont et al*., 2011]. These studies introduce the following basic features of flow adjustment near a canopy leading edge (Figure 1). Let *x* and *z* be the streamwise and vertical directions, with velocity *u* and *w*, respectively. Overbar will denote time averages and prime will denote deviations from the time average, i.e., turbulent fluctuations.

[5] First, velocity begins to decelerate some distance upstream of the canopy, due to the high-pressure region generated at the canopy leading edge, and continues to decelerate within the canopy (*x* > 0), due to the canopy drag. From continuity, the deceleration of velocity within the canopy (*U _{c}*) is associated with a vertical velocity out from the canopy . The initial adjustment extends from the leading edge over length

*X*(subscript

_{D}*D*denotes deflection and deceleration). In this region, the mean vertical advection is significant relative to vertical turbulent transport at the top of the canopy [

*Yang et al*., 2006], and turbulence development is restricted by the upward flow [

*Irvine et al*., 1997;

*Morse et al*., 2002]. Most terrestrial studies scale

*X*with canopy height,

_{D}*h*(typically 8–12

*h*), but acknowledge that

*X*is dependent on the canopy density [e.g.,

_{D}*Yang et al*., 2006;

*Dupont and Brunet*, 2009].

*Belcher et al*. [2003] suggest that

*X*scales with the canopy drag length scale,

_{D}*L*, which is a function of the frontal area per canopy volume (

_{c}*a*), the canopy drag coefficient

*C*, and the canopy solid volume fraction

_{D}*ϕ*. Specifically, . Since most aquatic canopies have high porosity (

*ϕ*< 0.1), this may be approximated .

[6] Second, a mixing layer with coherent vortex structures grows with distance from the leading edge, eventually reaching a fixed vertical size. As the layer grows, the turbulent stress at the top of the canopy ( , Figure 1b) increases and eventually reaches a constant value at distance *X _{*}* from the leading edge. The subscript * connects this length scale to the maximum friction velocity at the top of the canopy, which we denote

*u*= max . Considering a forest canopy edge,

_{*}*Irvine et al*. [1997] noted that all turbulence statistics eventually reach constant values in equilibrium with the canopy interface. This results in an equilibrium layer of finite height embedded within a boundary layer that continues to grow with distance from the leading edge. Unlike terrestrial flows, which are unbounded, aquatic flows are bounded by the water surface (Figure 1), so that the boundary layer can also reach a fully developed stage. In addition, small ratios of water depth (

*H*) to canopy height (

*h*) may impact flow adjustment. The objective of this paper is to describe the adjustment of flow from open channel conditions to vegetated flow, focusing on aquatic systems and the influence of water depth ratio (

*H*/

*h*). The following three questions will be addressed. What length scales describe the initial deceleration and mixing-layer growth? Does the initial flow adjustment depend on the canopy length? How much flow remains within the canopy layer?