Ashoor, A. and Riazi, A. (2019). Stepped spillways and energy dissipation: A non-uniform step length approach. Applied Sciences, 9(23), 5071, https://doi.org/10.3390/app9235071
Bayon, A., Toro, J.P., Bombardelli, F.A., Matos, J. and López-Jiménez, P.A. (2018). Influence of VOF technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated, skimming flow in stepped spillways. J. Hydro-Environ. Res, 19, 137–149.
Bombardelli, F.A., Inês Meireles, I. and Matos, J. (2011). Laboratory measurements and multi-block numerical simulations of the mean flow
and turbulence in the non-aerated skimming flow region of steep stepped spillways. Environ. Fluid Mech, 11, 263–288.
Celik, I.B., Ghia, U., Roache, P.J. and Freitas, C.J. (2008). Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng. Trans. ASME, 130, 078001, https://doi.org/10.1115/1.2960953
Chanson, H. and Toombes, L. (2002). Air–water flows down stepped chutes: turbulence and flow structure observations. International Journal of Multiphase Flow, 28(11), 1737-1761.
Chanson, H. (2000). Hydraulic of Roman Aqueducts: steep Chutes, Cascades and drop shafts, American journal of Archaeology, 104(1), 47-72.
Gonzalez, C.A. and Chanson, H. (2004). Scale Effects in Moderate Slope Stepped Spillways Experimental Studies in Air-Water Flows, 8th National Conference on Hydraulics in Water Engineering, Australia. 560.
Felder, S. and Chanson, H. (2011). Energy Dissipation down a Stepped Spillway with NonUniform Step Heights. Journal of Hydraulic Engineering, ASCE, 137(11), 1543- 1548.
Felder, S. and Chanson, H. (2013). Aeration, flow instabilities, and residual energy on pooled stepped spillways of embankment dams. Journal of irrigation and drainage engineering, 139(10), 880-887.
Felder, S. Chanson, H. (2014). Effects of Step Pool Porosity upon Flow Aeration and Energy Dissipation on Pooled Stepped Spillways. J. Hydraul. Eng., 140, 04014002, https://doi.org
Felder, S. and Chanson, H. (2015). Simple design criterion for residual energy on embankment dam stepped spillways, Journal of Hydraulic Engineering, 142(4), 04015062, https://doi.org /10.1061/(ASCE)HY.1943-7900.0001107
Flow Science Inc. (2016). FLOW-3D V 11.2 User’s Manual; Flow Science: Santa Fe, NM, USA.
Ghaderi, A. and Abbasi, S. (2019). Numerical investigation of labyrinth stepped spillways’ performance on energy dissipation of skimming flow. Journal of Hydraulics, 14(3), 1-16. (In Persian)
Ghaderi, A., Abbasi, S., Abraham, J. and Azamathulla, H.M. (2020). Efficiency of trapezoidal labyrinth shaped stepped spillways. Flow Measurement and Instrumentation, 72, 101711, https://doi.org/10.1016/j.flowmeasinst
Ghaderi, A., Abbasi, S. and Di Francesco, S. )2021(. Numerical Study on the Hydraulic Properties of Flow over Different Pooled Stepped Spillways. Water, 13(5), 710, https://doi.org/10
Ghaderi. A. and Abbasi. S. (2021a). Experimental and Numerical Study of the Effects of Geometric Appendance Elements on Energy Dissipation over Stepped Spillway, Water, 13(7), 957, https://doi.org
Ghaderi, A. and Abbasi, S. (2021b). Experimental Study of Energy Dissipation over Stepped Spillway with Appendance Elements on the Steps. Iranian Journal of Irrigation & Drainage, 15(3), 494-509. (In Persian)
Ghaderi, A. and Abbasi, S. (2022). The Effects of Modifying the Geometric Shapes of Steps in Stepped Spillway on Hydraulic Parameters and Energy Dissipation. Iranian Journal of Soil and Water Research, 53(5), 1035-1055. (In Persian)
Morovati, K. and Eghbalzadeh, A. (2018). Study of inception point, void fraction and pressure over pooled stepped spillways using Flow-3D. International Journal of Numerical Methods for Heat & Fluid Flow, 28(4), 982-998
Nóbrega, J.D., Matos, J., Schulz, H.E., and Canelas, R.B. (2020). Smooth and stepped spillway modeling using the SPH method. Water, 14(9), 3103, https://doi.org/10.3390/w14193103.
Rajaratnam, N. (1990). Skimming Flow in Stepped Spillways. Journal of Hydraulic Engineering, 116, 587–591.
Rice, C.E. and Kadavy, K.C. (1996). Model study of roller compacted concrete stepped spillway. Journal of Hydraulic Engineering. ASCE, 122(6), 292-297.
Roache, P.J. (1994). Perspective: A Method for Uniform Reporting of Grid Refinement Studies, J. Fluids Eng., 116(3), 405–413.
Roushangar, K. and Akhgar, S. (2019). Numerical and experimental Study of the influence of Wedge Elements on Roughness and Energy dissipation over stepped spillway. Iranian Journal of Irrigation & Drainage, 13(1), 78-88. (In Persian)
Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B. and Speziale, C.G. (1992). Development of turbulence models for shear flows by a double
expansion technique. Phys. Fluids A Fluid Dyn., 4, 1510–1520.