## 1. Introduction

[2] Woody debris jams substantially influence river geomorphology and ecology, and rivers with debris jams are often distinct from those without [*Bilby and Likens*, 1980; *Keller and Swanson*, 1979; *Montgomery et al.*, 1996]. The natural formation of wood into debris jams, defined as the buildup of woody material of variable sizes and quantities into a distinctive unit, has been imitated by the river restoration industry [*Abbe et al.*, 2003; *Bernhardt et al.*, 2005]. Debris jams are often used in restoration channel design to alter channel hydraulics and morphology for specific goals such as bank protection or habitat formation. Successful restoration projects require an understanding of the relationship between the structure of debris jams, resultant hydraulic processes, and eventual geomorphic forms. This relationship is based on the hydraulics of jams beginning with an alteration of local flow.

[3] Shifting flow patterns due to a single log, multiple logs or an entire debris jam alter the spatial distribution of shear stress [*Manga and Kirchner*, 2000; *Daniels and Rhoads*, 2004b]. At the reach scale, woody debris repartitions boundary shear stress, resulting in overall finer bed material [*Buffington and Montgomery*, 1999a]. Woody debris also decreases the spacing between pools [*Gurnell and Sweet*, 1998], increases pool area [*Lisle*, 1995], and increases channel width [*Smith et al.*, 1993]. At the patch scale, the addition of woody debris alters the spatial distribution of shear stress, creating patches of scour and deposition and sediment sorting [*Smith et al.*, 1993]. Scour around woody debris is caused by flow convergence where diverted flow intersects the main unaffected flow, forming coarse-bedded pools at the outer tip of the wood piece or jam [*Cherry and Beschta*, 1989]. Flow separation upstream of woody debris causes backwater effects, and blockage of flow causes reduced velocities downstream, resulting in reduced shear stress on the bed and deposition of fines [*Wallerstein et al.*, 1997].

[4] The specific effects of a debris jam first depend on the magnitude of flow. Despite our current understanding that little geomorphic change occurs during base flows [*Wolman and Miller*, 1960], past research is limited to data collected at such low flows. The closest study to flood discharges was *Daniels and Rhoads* [2004a], who studied the three-dimensional flow structures around large woody debris for two flow stages. However, the higher discharge was below bankfull, and so we still lack empirical documentation of how debris jams affect flow at bankfull or flood stages.

[5] Second, debris jams alter channel morphology and hydraulics on the basis of the distinctive geometry of the wood piece or pieces [*Lisle*, 1986]. For many years, the majority of studies of the localized hydraulics of wood in rivers have been limited to those of single solid objects (for a review, see *Gippel* [1995]). Recently, our understanding of woody debris' local hydraulics have expanded to include the three-dimensional flow fields around entire jams within a meander bend [*Daniels and Rhoads*, 2004a] and the flow fields within and around engineered log structures [*Shields et al.*, 2001]. Yet, the single log model still dominates the literature, providing the predictive relationships between woody debris geometry and flow. This single log model, defined as the representation of woody debris by cylinders, has been used in multiple flume-based studies to derive the predictive relationship between flow and the geometry and orientation of a single wood piece [*Young*, 1991; *Gippel et al.*, 1992; *Wilcox et al.*, 2006].

[6] However, woody debris often accumulates into jams, which can be combinations of wood pieces from the nearby bank and those transported fluvially from upstream sources [*Abbe and Montgomery*, 2003]. Beginning with a single key member, these “combination jams” evolve into intricate matrices of wood pieces of widely variable sizes. Therefore, to define the relationship between jam structure and composition and hydraulic changes associated with debris jams, it is necessary to treat them as complex and dynamic accumulations of material ranging in size from leaves and twigs to entire tree trunks. Here, jam composition is defined by the number and size of wood pieces, the volume and surface area of these pieces, and the open space between wood pieces, also referred to as the jam porosity.

### 1.1. Hydraulics of Debris Jams

[7] The relationship between jam structure and hydraulic function is quantified through drag force (*F*_{D}), which is the difference in pressure the water exerts on the jam from upstream to downstream [*Abbe and Montgomery*, 1996]. Empirically, *F*_{D} is given by

where *U* is the density of water, *A*_{F(emp)} is the empirical (i.e., measurable) submerged frontal area of the obstruction normal to flow, *U*_{Ap} is the approach velocity measured as the mean free-stream velocity, and *C*_{D} is the drag coefficient of the obstruction. When woody debris is modeled as a cylinder, *A*_{F(emp)} is simply the diameter of the object multiplied by its length. The approach velocity is independent of the object, and may be manipulated in a controlled setting or measured in a natural one. Therefore the contribution of *C*_{D} to *F*_{D} can be directly quantified [*Young*, 1991].

[8] Natural debris jams are poorly described as cylinders; instead they are irregular, porous, and three dimensional. Therefore *A*_{F(emp)} loses its meaning in that the frontal area of a jam is a poor representation of the geometry of the jam relative to the flow. Similarly, *C*_{D} previously has been solved for a two-dimensional nonporous object (e.g., cylindrical rods) [*Gippel et al.*, 1992], which likely misrepresents the drag properties of a debris jam. Isolating the influences of *A*_{F(emp)} and *C*_{D} cannot easily be done because they are interrelated, thus separating the terms may misrepresent their contributions to the drag force.

[9] Instead, we use the combined term (*C*_{D}*A*_{F})_{calc} in order to bridge the hydraulic and the structural realities of debris jams. This term describes the drag form of a jam, defined as the shape and size of a jam as it dictates its drag force. This combined term has the potential to account for the entire depth of accumulated material including total roughness within the jam (i.e., surface area of woody pieces) and the open space, or porosity.

### 1.2. Goals and Structure

[10] The goal of this study is to define the relationship between jam composition and the hydraulics of debris jams, document the hydraulic drag on natural debris jams at a high channel-forming flow, and illustrate the utility of the combined term (*C*_{D}*A*_{F})_{calc} in analyzing the hydraulics of natural debris jams. We work at the scale of a single jam in order to expand upon the single-log model used in previous studies. By using naturally formed and manipulated debris jams, we investigated the local hydraulics associated with these complex structures. We systematically altered debris jam porosity via targeted removal of specified size classes of wood, isolating the effects of differing structure and composition.

[11] In this paper, we first examine the composition of three natural jams in a high-gradient mountain river in the Northeast United States, as such detailed quantitative descriptions of jams are rare and broad qualitative measurements of jams was thought to be misleading for our intended hydraulic analysis. Second, we report local velocity and shear stress distributions, focusing on their adjustments as jam structure and composition change. Third, we predict the potential shifts in areas of scour and deposition. Fourth, we quantify at various stages of jam manipulation the drag force (*F*_{D}), the drag coefficient (*C*_{D}) and the combined term (*C*_{D}*A*_{F})_{calc}. Fifth, we explore the influence of total volume, surface area and porosity on *F*_{D} and (*C*_{D}*A*_{F})_{calc}, thus providing a quantitative and predictive link between natural debris jam characteristics and drag force. Finally, we compare our results to those reported for single-log models, and the potential error in using such models when analyzing natural debris jams.