Coupling a Boundary Layer Wall Shear-stress Model with Field Experiments in a Shallow Tidal River

Recently, Mathis et al. (2011) developed a conceptual approach that is able to predict instantaneous wall-shear stress fluctuations in turbulent boundary layers. This approach embeds the scale interaction mechanisms, namely superposition and modulation, into a wall-model capable of predicting the fluctuating component of the streamwise wall-shear stress. The present study investigates the potential benefits of this new approach for research on environmental flows, where near-wall information is often missing. The database considered here comes from field measurements using acoustic Doppler velocimeters carried out in a shallow tidal river (Suisun Slough in North San Francisco Bay). Amongst the data, only the sets having defined boundary layer properties are retained. The model, applied to these selected cases, shows promising results. Despite significant uncertainties in the field measurements, statistical analysis and comparisons of energy content demonstrate that predictions using these data agree relatively well with laboratory predictions and DNS results. INTRODUCTION In wall-bounded turbulent flows the wall shear-stress τw constitutes a key parameter for accurate prediction of the flow behaviour. Over the years, many studies have been devoted toward understanding and modelling the Reynolds number dependency of the mean, time-averaged, value τ̄w, which is used in boundary layer inner-scaling via the friction velocityUτ = √ τ̄w/ρ , where ρ is the fluid density (see for example Schlichting & Gersten, 2000; Monkewitz et al., 2007, amongst others). However, little is known about the fluctuating component, τ ′ w, which can be responsible for extreme and destructive events, such as wind gusts in atmospheric flows or scouring and mechanical damage on an aircraft (see figure 3 of Örlü & Schlatter, 2011). In environmental flows, the wall shear-stress is of great ecological importance where it is linked to erosion, bed formation, sediment and nutrient transportation, etc (Grant & Madsen, 1986; Rowiński et al., 2005; Grant & Marusic, 2012). Unfortunately, the wall shear-stress is largely inaccessible in field measurements, which prompts the need for predictive models to reconstruct the missing information. Here, the fluctuating component is defined as τ ′ w(x, t) = τw(x, t)− τ̄w(x), where τw(x, t) and τ̄w(x) are the total and mean values of the wall shear-stress, respectively. The coordinates x, y and z refer to the streamwise, spanwise and wall-normal directions. The respective fluctuating velocity components are denoted by u, v and w. Over-bars indicate time-averaged values, and the superscript “+” is used to denote viscous scaling of length z+ = zUτ/ν and velocities u+ = u/Uτ , where ν is the kinematic viscosity of the fluid. Recently, Mathis et al. (2013) proposed a novel conceptual approach to build up a predictive model able to reconstruct the fluctuating wall shear-stress based on a single point measurement taken in the log-layer away from the wall. The model is based on many years of empirical observations, both experimental and numerical, that have clearly established that strong interactions exist between the near-wall region and motions in the outer region. Namely, the Reynolds number effects are closely related to the increasingly energetic content of the large-scale structures associated with the log-layer (Kim & Adrian, 1999; del Álamo & Jiménez, 2003; Hutchins & Marusic, 2007a, amongst others), through superposition and modulation effects (Bandyopadhyay & Hussain, 1984; Grinvald & Nikora, 1988; Hutchins & Marusic, 2007b; Mathis et al., 2009, 2011). The wall-shear stress model was originally derived from the streamwise velocity model developed by Marusic et al. (2010) and Mathis et al. (2011), where an algebraic relationship between the streamwise velocity component and the wall shear stress is know, and is of the form: τ ′+ wp(t ) = τ ′∗ w (t ) { 1+α u′+ OL(t ) } +α u′+ OL(t ), (1) where τ ′+ wp is the predicted time-series normalised by wall variables, τ ′+ wp = τ ′ wp/(ρU 2 τ ) and t + = tU τ /ν . The timeseries τ ′∗ w , which is normalised in wall units, represents the