Concentration C is defined by the spatial arrangement of obstacles regularly spaced in both longitudinal ax and transverse ay directions. These parameters (ax, ay) were selected to systematically span a range of obstacle densities (9 % to 64 %) to simulate varying degrees of hydraulic resistance encountered in natural floodplains. The concentration is given by: 1C=D2ax⋅ay This concentration C represents the obstacles density within the flow and plays a crucial role in determining these obstacles impact on the flow dynamics.

Reynolds decomposition separates flow into mean and fluctuating components (Aksel, 2023). The Reynolds decomposition of the velocity field u is expressed as: 2u=u‾+u′ Reynolds decomposition separates mean u‾ and turbulent u′ components, enabling RANS derivation.

The global Reynolds number for this study, defined as: 3Re=URHυ Where U is the bulk velocity and RH is the Hydraulic radius, and υ is water viscosity. This dimensionless parameter serves as a standardized indicator of the inertial dominance within the channel, ensuring the study remains consistent with high-energy floodplain dynamics.

Turbulent kinetic energy (TKE) represents the energy contained in the flow of turbulent fluctuations (Kosari et al., 2018). It is calculated as the sum of the velocity fluctuations variances: 4κT=12(u′2‾+v′2‾+w′2‾) Where u′,v′ and w′ are the fluctuating velocity components, and u′2‾,v′2‾ and w′2‾ represent the time-averaged variances of these fluctuations.

Water surface tension arises from cohesive forces between surface molecules. For simulations, the value of 0.072 N m⁻¹ (25 °C) is adopted. It is modeled via the Continuum Surface Force approach. 5FCSF=σκδ(r)n The surface tension coefficient σ is a fluid property, while κ represents interface curvature. The Dirac delta function δ localizes the tension force at the interface.

Wall shear stress τw, critical for near-boundary flow analysis, quantifies frictional forces at fluid-solid interfaces. Computed from near-wall velocity gradients in ANSYS Fluent, it follows: 6τw=μ⋅∂u∂zz=0 where μ is the fluid dynamic viscosity and ∂u/∂z represents the velocity gradient normal to the wall. Accurate wall shear stress governs sediment transport, erosion, and hydraulic structure stability predictions.

The Strouhal number (St) is a dimensionless parameter that characterizes the oscillatory behavior of fluid flow (Jiang and Cheng, 2017; Blevins, 1977; Williamson and Govardhan, 2004), particularly in vortex shedding phenomena. It is defined as: 7St=fDU where f= vortex shedding frequency, D = characteristic length (cylinder diameter/obstacle width), U = free-stream velocity.

This framework analyzes cylindrical obstacle dynamics via: Reynolds decomposition (turbulence), TKE (intensity quantification), and biphasic flow (air-water interactions) and forms the foundation of the numerical methodology.

The study employs the incompressible RANS equations solved via the VOF method. While Large Eddy Simulation (LES) is recognized for resolving instantaneous sub-grid scales, the RANS framework was strategically selected here as the optimal tool for interpreting macroscopic hydraulic variables (Mahjoub et al., 2024b; Kosari et al., 2018; Roulund et al., 2005; Senturk et al., 2023), specifically bulk energy dissipation and mean resistance coefficients. Given that the engineering objective is to quantify global flow behavior rather than transient fine-scale fluctuations, the RANS approach provides a degree of fidelity that is precisely calibrated to the scale of the outputs required, ensuring a robust balance between computational efficiency and the precision needed for floodplain modeling, consistent with prior hydraulic applications (Aksel, 2023; Roulund et al., 2005b; Senturk et al., 2023).

The mass continuity equation ensures the conservation of mass and it is expressed as: 8∂ρ∂t+∇⋅(ρu)=0 where ρ is the fluid density, and u is the mean velocity vector.

The momentum conservation equation describes the balance of forces acting on a fluid and it is expressed as follows: 9ρ∂u∂t+u⋅∇u=-∇p+∇⋅[μ(∇u+∇uT)]+fs+fg Fluid density is denoted by ρ, velocity vector by u, and time by t. Pressure is p, dynamic viscosity μ characterizes shear resistance, fs accounts for interfacial surface tension, and fg represents gravitational acceleration. This framework comprehensively models fluid motion.

Biphasic flow involves coexisting distinct phases (Kosari et al., 2018). The Volume of Fluid (VOF) method (Hirt and Nichols, 1981) tracks interfaces using volume fraction α per computational cell. The equation governing biphasic flow in the VOF method is: 10∂α∂t+u⋅∇α=0 The dimensionless parameter α (0≤α≤1) indicates phase distribution. Mass conservation for the tracked phase is maintained by solving the volume fraction equation alongside the Navier-Stokes equations.

The TKE transport equation governs convection-diffusion, shear/buoyancy production, and viscous dissipation (Schiestel, 2006). Turbulence closure challenges in hydraulic engineering demand rigorous calibration and validation for reliable approximations.

This laboratory-scale model employs a 10 m × 0.8 m × 0.6 m canal. Initial conditions (0.1 m depth, 1 m s⁻¹ velocity) ensure dynamic similarity (Mahjoub et al., 2024a; Chanson, 2006). To provide essential context for the turbulence modeling, the global Reynolds number of the flow was calculated as Re=105 confirming a fully turbulent regime consistent with standard floodplain dynamics. Furthermore, the Froude number was determined to be Fr=1.01 indicating that the simulations were conducted under critical flow conditions, which is a key threshold for assessing energy dissipation and wave stability in open channels. The VOF method models air-water flow with no-slip walls. Pressure-velocity coupling applies first-order upwind (dissipation/stability) and second-order upwind (momentum/TKE/accuracy) schemes, with global time stepping for convergence.

All configurations used 2 cm elements, 0.4 max skewness, enhanced smoothing. Curvature: 0.02 cm min, 10° angle. Inflation: 0.272 ratio, 5 layers, 1.2 growth. Mesh independence confirmed. Figure 2 shows mesh refinement near obstacles (50 % concentration), capturing complex phenomena for accurate local interaction simulation.

Three closure models were validated: k-ε, K-ω and SST. All demonstrated comparable accuracy near obstacles. However, based on literature demonstrating the K-ω model's efficacy in flows with adverse pressure gradients and separation (Aksel, 2023; Roulund et al., 2005; Senturk et al., 2023; Cassan and Laurens, 2016), it was selected to ensure reliable fluid behavior representation.