Numerical simulation study of flow characteristics through staggered emergent square cylinders in an idealized fishway

This study reveals the combined effects of flow rate (Q) and square-cylinder side length (D) on flow characteristics through staggered emergent square cylinders. For a bed slope of S = 2.0%, a channel width of B = 2.2 m and a square-cylinder area proportion of λ = 0.167, 16 cases are devised by combining four square-cylinder sizes (D = 0.733, 0.440, 0.314 and 0.244 m) with four flow rates (Q = 400, 600, 900 and 1200 l s−1). The permutational multivariate analysis of variance (PERMANOVA) indicates that both Q and D are significantly correlated with seven important hydraulic parameters (p-value = 0.010 and 0.047, respectively; coefficient of determination = 0.948 and 0.891, respectively). Furthermore, on the basis of the traditional single-variable power-function fitting formulas, this study proposes more accurate double-variable power-function fitting formulas for seven hydraulic parameters and four flow separation/reattachment parameters. Additionally, this study quantitatively compares the newly-obtained fitting formulas and flow variables with those in the previous studies.