## 2 Methodology  
The methodological approach selected for this research was derived from standardized hydrodynamic metrics found in the state-of-the-art review on fishway hydraulics with an emphasis on the results from biological studies. In the state-of-the-art research, various turbulence descriptors were considered (e.g., turbulent kinetic energy, turbulent intensity, Reynold's shear stress), out of which Reynold's shear stress has been identified as the main turbulent parameter affecting fish swimming performance and behavior [17; 50]. The Reynold's shear stress can be used as an indicator of the turbulence strength related to fish because velocity fluctuations exchange momentum between adjacent layers of fluid around fish body, acting as a force restricting fish movement. Therefore, Reynold's shear stress has been selected as the descriptive variable of turbulent flow field in this research. Flow in the fishway is three-dimensional due to the influence of the cross-walls and slots on the formation of the main flow jet and recirculation zones. [PERSON]'s shear stresses can be calculated for all three planes--streamwise (\(\tau_{uw}\)), horizontal (\(\tau_{uw}\)), and vertical (\(\tau_{vw}\)), according to the following expressions:  
u}w}, \tag{1}\] \[\tau_{uw} =\rho\overline{u\overline{\
u}\overline{\
u}},\] (2) \[\tau_{vw} =\rho\overline{\
u}\overline{\
u}\overline{\
u}\overline{\
u}, \tag{3}\]  
where: \(\rho\) = water density (1000 kg/m\({}^{3}\)), \(u^{\prime}\) = fluctuation of the streamwise velocity component \(u\) [m/s], \(v^{\prime}\) = fluctuation of the spanwise velocity component \(v\) [m/s], \(w^{\prime}\) = fluctuation of the vertical velocity component \(w\) [m/s].  
Shear stress and turbulence levels in natural rivers where fish reside for the majority of time are small in comparison to those in hydraulic structures. [PERSON] et al. [51] summarized estimates of shear stresses in natural streams available from the literature and concluded that most shear stress data were below 30 N/m\({}^{2}\), while during flash floods shear stress levels increase to 50 N/m\({}^{2}\). Their study has established two generalized biocriteria boundaries defined for 10-min exposure to an average turbulence under following [PERSON]'s shear stresses:  
1. Injury boundary--medium turbulence condition (>50 N/m\({}^{2}\)) that can induce minor injury to some species, but does not incur significant mortality over 48 h post-exposure period;
2. Disorientation boundary--low turbulence condition (>30 N/m\({}^{2}\)) that may cause a startle response that would likely put the fish at risk of predation or other hazards.  
The impact of the [PERSON]'s shear stress on the fish migration is dependent on the fish body orientation; [PERSON] et al. [52] and [PERSON] et al. [53] found that the horizontal component of Reynold's shear stress has the greatest effect on the fish, regardless of their size. In both studies it was found that fish for most of the time dwelled in the areas with Reynold's shear stress <60 N/m\({}^{2}\). [PERSON] et al. [34] concluded that the fishway configurations they investigated were very favorable for fish, because in more than 90% of the pool area, the Reynold's shear stress values were lower than 60 N/m\({}^{2}\). In this research, [PERSON] et al. biocriteria were adopted because they provide distinctive values between fish injury and the disorientation boundary.