## 1. Introduction

[2] During recent years, three-dimensional (3-D) computational fluid dynamics (CFD) modeling has emerged as a powerful tool for studying complex turbulent flows in man-made and natural waterways. Such models have been applied to simulate flows in simple curved open channels [*Wilson et al.*, 2003; *Van Balen et al.*, 2009, 2010a, 2010b; *Stoesser et al.*, 2010; *Constantinescu et al.*, 2011] and real-life meandering streams or rivers [*Ferguson et al.*, 2003; *Rodriguez et al.*, 2004; *Kang et al.*, 2011; *Kang and Sotiropoulos*, 2011]. Available CFD models for open channel and river flows do not solve directly the unsteady, three-dimensional Navier-Stokes equations because carrying out direct numerical simulation (DNS) for real-life waterways at high Reynolds number is not feasible because of the excessive computational cost. For that, all existing CFD models solve either temporally averaged or spatially filtered forms of the Navier-Stokes equations, which give rise to Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulation (LES) models, respectively. As a result of the averaging or filtering operations, additional terms, such as the Reynolds stress tensor (for RANS models) or the subgrid stress (SGS) tensor (for LES), appear in the resulting equations, which need to be closed by an appropriate turbulence closure model. In RANS models the eddy viscosity concept is widely employed to model the Reynolds stress tensor, which assumes that the anisotropic part of the Reynolds stress tensor is linearly proportional to the time-averaged strain rate tensor [*Pope*, 2000; *Durbin and Pettersson Reif*, 2001]. This is the so-called Boussinesq approximation, which is inherently based on the assumption that turbulence is locally isotropic. Consequently, RANS models based on the Boussinesq approximation are often referred to as isotropic RANS models. Examples of such models include, among others, the *k*- model [*Launder and Sharma*, 1974], the *k*- model [*Wilcox*, 1993], the shear stress transport (SST) model [*Menter et al.*, 2003], etc. In LES models (see, e.g., *Sagaut* [1988]), on the other hand, the Smagorinsky model [*Smagorinsky*, 1963] has been widely employed to model the SGS tensor. The Smagorinsky model is also based on the eddy viscosity model, which assumes that the SGS tensor is linearly proportional to the instantaneous, resolved strain rate tensor.

[3] In spite of the fact that in both isotropic RANS and LES models an isotropic eddy viscosity model is employed, the role of the eddy viscosity is fundamentally different in the two approaches. Namely, in RANS models the eddy viscosity accounts for all scales of turbulent eddies, except perhaps very large scale periodic unsteadiness which can be captured by unsteady RANS models. In LES models, on the other hand, scales of motion larger than the grid spacing are directly resolved by the simulation and only subgrid-scale eddies are modeled. As a result in flows in which large-scale organized coherent structures are responsible for producing most of the Reynolds stresses, as is often the case in natural waterways, LES with sufficient resolution can resolve directly most turbulence in the flow and only a relatively small portion of the energy needs to be handled by the SGS model. A direct consequence of this fundamental difference between LES and RANS simulation is that as the grid is refined the former converges to a DNS while the latter converges to a grid-independent time-averaged RANS solution [*Sagaut*, 1988; *Pope*, 2000].

[4] Isotropic RANS models have been popular engineering simulation tools for resolving complex flow and sediment transport in rivers mainly because of their computational expedience. For instance, such models have been employed to predict flows in large rivers [*Sinha et al.*, 1998; *Ferguson et al.*, 2003; *Rodriguez et al.*, 2004; *Ge and Sotiropoulos*, 2005], flows in curved open channels [*Wilson et al.*, 2003; *Stoesser et al.*, 2010; *Kang et al.*, 2011], sediment transport in curved open channels [*Wu et al.*, 2000; *Olsen*, 2003; *Khosronejad et al.*, 2011] and to model delta morphodynamics [*Edmonds and Slingerland*, 2010]. In spite of these numerous applications, the limitation of the RANS models in predictions of turbulent flows in real-life waterways has yet to be extensively investigated.

[5] There exist few previous studies which attempted to compare the performance of isotropic RANS models and LES for predicting flows in simple curved channels. *Stoesser et al.* [2010], for instance, simulated flow in a flat-bed circular bend using LES and isotropic RANS models. Their RANS simulation results were in good agreement with the LES results and were able to predict the curvature-driven secondary flow cell as well as the outer bank secondary cell, which has been linked to turbulence anisotropy effects [*Blanckaert and Vriend*, 2004; *Van Balen et al.*, 2009; *Kang and Sotiropoulos*, 2011]. However, *Stoesser et al.* [2010] reported that the RANS model fails to predict the persistence of the outer bank cell (OBC) until the exit of the bend. *Van Balen et al.* [2010a] simulated flow in a circular bend using the isotropic RANS model and LES. They showed very good agreement between the mean velocity profiles predicted by the RANS and LES models. They further argued that the good agreement is because in the flow they considered there is a strong tendency toward isotropy of the turbulence stresses in the bend and turbulence related momentum transport does not play a major role in the transport of mean momentum. They also concluded that assumptions made within either the filtering (LES) or the statistical (RANS) framework are of marginal influence and a simple modeling of the turbulence effects suffices. *Van Balen et al.* [2010b], on the other hand, compared the RANS simulation and the LES for flow in a different circular bend and showed that the RANS computation cannot predict the OBC and the internal shear layer near the inner bank. However, they did not provide clear explanations on why the RANS results are poorer than the LES results.

[6] It is evident from the above literature review that only few studies have been reported thus far aimed at systematically investigating the predictive capabilities or RANS and LES and that the results of these studies are often inconclusive and/or contradictory to each other. Furthermore, no study has been reported in the literature seeking to compare RANS and LES models for a natural meandering channel. In this study, we seek to contribute to clarifying the predictive capabilities of isotropic RANS models in simulations of turbulent flow in a natural-like meandering channel. We employ the SST model of *Menter et al.* [2003] to close the RANS equations [see *Kang et al.*, [2011] and apply it in unsteady RANS mode to simulate bankfull flow in the field-scale meandering stream at the St. Anthony Falls Laboratory (SAFL) Outdoor StreamLab (OSL) [*Kang and Sotiropoulos*, 2011]. The RANS simulations are compared with the LES and experimental measurements of the same flow previously reported by *Kang and Sotiropoulos* [2011]. To eliminate numerical uncertainties and enable a meaningful comparison of the two turbulence modeling strategies, both simulations were carried out under exactly the same conditions with same number of grid nodes and time step. The LES reported by *Kang and Sotiropoulos* [2011] revealed a series of complex flow phenomena occurring in the meander bend, which include the curvature-driven secondary flow, the anisotropy driven outer bank secondary flow, horizontal recirculation (or dead) zones along the inner bank, and the outer and inner bank shear layers. In this paper we will scrutinize the ability of the RANS model to capture these phenomena and also identify the physical reasons for any modeling shortcomings. We will also discuss the implications of our findings in the context of applying isotropic RANS models to hydrodynamic and morphodynamic simulations of natural waterways. We first briefly describe the computational models we employ in section 2 and subsequently describe the experimental facility (OSL) we use as the test case and the computational parameters in section 3. This is followed by comparisons of the numerical solutions of the LES and RANS simulation in section 4, and the discussion of the flow visualization experiments in section 5. In section 6 we discuss the physical reasons for the discrepancies between the results of the two models, and finally in section 7 we summarize the key conclusions of this work.