## 1. Introduction

[2] The shear layer that develops along the interface of two merging flows is a prominent hydrodynamic feature of stream confluences. This shear layer is characterized by distinct vortices that rotate about vertical axes [*Biron et al.*, 1993; *Sukhodolov and Rhoads*, 2001]. Coherent turbulent vortices within confluence shear layers are similar to the predominately two-dimensional vortex structures that develop in plane mixing layers (i.e., mixing layers that develop between two parallel streams) and that emanate from the Kelvin-Helmholtz-like instability of such layers [*Rogers and Moser*, 1992]. Plane mixing layers generally increase in width downstream from the point of initial contact between the two fluids via vortex pairing [*Winant and Browand*, 1974]. The process of pairing occurs when differential rates of vortex advection and evolution between successive vortices along the mixing layer results in vortex encroachment, interaction and amalgamation. Vortex pairing is not necessarily limited to two vortices, but can be quite complex and involve multiple vortices [*Ho and Huerre*, 1984].

[3] Most confluence shear layers develop in depth-limited environments, i.e., the distance between the channel bed and water surface is small relative to the size of turbulent structures. This constraint limits fluid motion in the vertical direction [*Sukhodolov et al.*, 1998], but has little effect on velocity components in the transverse and streamwise directions. Fluid motion within depth-limited plane mixing layers can be characterized as quasi-two-dimensional [*Babarutsi and Chu*, 1998], a characterization that acknowledges fluid motion is fully three-dimensional at high frequencies, but that also recognizes the importance of strong two-dimensional effects at low frequencies corresponding to the domain of large coherent vortices [*Babarutsi and Chu*, 1998; *Uijttewaal and Tukker*, 1998]. The enhanced effects of bottom friction in depth-limited environments constrains widening of plane mixing layers via vortex pairing; rates of mixing layer growth in shallow flows are much less than in deep flows [*Chu and Babarutsi*, 1988; *Uijttewaal and Booij*, 2000].

[4] Understanding the spatial and temporal structure of shear layers at stream confluences is important for verifying assumptions underlying numerical hydrodynamical models and for attempts to derive scalar properties of turbulence structure from point measurements of velocity time series. Some numerical models assume that a single length scale is adequate to characterize turbulence at confluences [*Weerakoon et al.*, 1991; *Bradbrook et al.*, 2000a]. On the other hand, *Babarutsi and Chu* [1991, 1998] developed a plane mixing layer model with two length scales: one to account for small-scale turbulence generated by bed friction and the other to account for large-scale turbulence generated by transverse shear. One-scale and two-scale models assume that the relation among turbulence kinetic energy (TKE), turbulence dissipation rate and turbulence length scale for large-scale turbulence can be described by the relation for small-scale turbulence. This assumption implies that frequency spectra are equivalent to wave number spectra (i.e., the frozen turbulence hypothesis holds for large and small length scales) and that Kolmogorov's −5/3 power law relation defines the cascade of turbulence energy at large and small scales. The extent to which Kolmogorov's law holds at large scales has not been evaluated for shear layers at stream confluences. Laboratory experiments indicate that spectra of transverse velocity fluctuations for depth-limited mixing layers exhibit a characteristic “hump” at low frequencies [*Uijttewaal and Tukker*, 1998; *Uijttewaal and Booij*, 2000]. The high-frequency side of this hump has a slope of −3 rather than −5/3, indicating that Kolmogorov's law may not hold for large-scale turbulence in depth-limited mixing layers. A spectral slope of −3 is indicative of an inverse cascade of turbulence energy of the type that typically occurs in strongly two-dimensional turbulence, providing support for the importance of two dimensional effects at low frequencies [*Frisch*, 1995].

[5] The large-scale complexity of turbulence at confluences may also undermine the assumptions of conventional methods for deriving spatial properties of turbulence from point measurements of velocity time series. These properties commonly are obtained from spectral analysis of time series under the assumption that Taylor's frozen turbulence hypothesis (FTH) holds for the flow under consideration. This hypothesis assumes that coherent turbulent structures remain unchanged as they pass by the measurement point and that the temporal lag of the structure can be scaled to its spatial extent using the local mean velocity. Complex patterns of vortex growth, interaction and amalgamation in a shear layer may produce hydrodynamic conditions that do not conform to the FTH. Field studies at confluences indicate that streamwise turbulence intensities (*I*) can greatly exceed 10% of the mean streamwise velocity [*Sukhodolov and Rhoads*, 2001], calling into question the assumption that *I* ≪ 1, an assumption underlying the FTH [*Frisch*, 1995].

[6] This study examines the spatial-temporal structure of turbulence within the shear layer at a stream confluence. The analysis of turbulence structure is based on simultaneous two-point, high-frequency velocity measurements obtained with two three-dimensional acoustic Doppler velocimeters (ADVs). The goals are to explore (1) spatial relations among time series of velocity data collected at different locations along the shear layer, (2) the degree to which the temporal characteristics of turbulence at a single measurement location conform to the spatial characteristics of turbulence upstream from this location, (3) the extent to which the frozen turbulence hypothesis can be applied to spectra derived from time series data, and (4) the low-frequency properties of turbulence at confluences and the relation of these properties to assumptions underlying extant models of shallow mixing layers.