[1] I. Nezu and H. Nakagawa, “Turbulence in openchannel flows,” 1993.
[2] V. Nikora, D. Goring, and I. McEwan, “Spatially averaged open-channel flow over rough bed,” J. Hydraul. Eng., vol. 127, pp. 123–133, 2001.
[3] J. Jimenez, “Turbulent flows over rough walls,” Annu. Rev. Fluid Mech., vol. 36, pp. 173–196, 2004.
[4] C. Manes, D. Pokrajac, and I. McEwan, “Doubleaveraged open-channel flows with small relative submergence,” J. Hydraul. Eng., vol. 133, pp. 896– 904, 2007.
[5] S. H. Mohajeri, S. Grizzi, and M. Righetti, “The structure of gravel-bed flow with intermediate submergence: A laboratory study,” Water Resour., vol. 51, no. 11, pp. 9232–9255, 2015.
[6] K. Koll, “Parameterisation of the vertical velocity profile in the wall region over rough surfaces,” River flow Conference, pp. 0–415–40815–6, 2006.
[7] J. Cooper and S. Tait, “The spatial organisation of time-averaged streamwise velocity and its correlation with the surface topography of waterworked gravel beds,” Acta Geophys., vol. 56, pp. 614–641, 2008.
[8] M. Bayazit, “Free surface flow in a channel of large relative roughness,” J. Hydraul. Res., pp. 115–126, .6791
[9] T. Buffin-Bélanger and A. Roy, “Effects of a pebble cluster on the turbulent structure of a depth-limited flow in a gravel-bed river,” Geomorphology, vol. 25, pp. 249–267, 1998.
[10] V. Nikora, “Hydrodynamics of gravel-bed rivers: Scale issues, in Gravel Bed Rivers VI: From Process Understanding to River Restoration,” 2008.
[11] S. McLean and V. Nikora, “Characteristics of turbulent unidirectional flow over rough beds: Doubleaveraging perspective with particular focus on sand dunes and gravel beds,” Water Resour. Res., vol. 42,p. W10409, 2006.
[12] J. Aberle, K. Koll, and A. Dittrich, “Form induced stresses over rough gravel-beds,” Acta Geophys., vol.55, pp. 23–32, 2008.
[13] J. Finnigan, “Turbulence in plant canopies,” Annu. Rev. Fluid Mech., vol. 32, pp. 519–571, 2000.
[14] V. Nikora and P. Rowiński, “Rough-bed flows in geophysical, environmental, and engineering systems: Double-Averaging Approach and its applications,” Acta Geophys., vol. 56,3, pp. 529– 533, 2008.
[15] S. Whitaker, The method of volume averaging. Netherland: Springer, 1999.
[16] J. Smith and S. McLean, “Spatially averaged flow over a wavy surface,” J. Geophys. Res., vol. 83, no. 12, pp. 1735–1746, 1977.
[17] T. Hoover and J. Ackerman, “Near-bed hydrodynamic measurements above boulders in shallow torrential streams: Implications for stream biota,” J. Environ., vol. 3, pp. 365–378, 2004.
[18] S. Mohajeri, M. Righetti, and G. Wharton, “On the structure of turbulent gravel bed flow: Implications for sediment transport,” Adv. Water, vol. 92, pp. 90–104, 2016.
[19] R. Hardy, J. Best, and S. Lane, “Coherent flow structures in a depth-limited flow over a gravel surface: The role of near-bed turbulence and influence of Reynolds number,” J. Geophys., 2009.
[20] H. Nepf, “Hydrodynamics of vegetated channels,” J. Hydraul. Res., vol. 50, no. 3, pp. 262–279, 2012.
[21] M. Franca, R. Ferreira, and U. Lemmin, “Parameterization of the logarithmic layer of double-averaged streamwise velocity profiles in gravel-bed river flows,” Adv. Water Resour., vol. 31, pp. 915–925, 2008.
[22] R. Gaudio, A. Miglio, and S. Dey, “Nonuniversality of von Kármán’s κ in fluvial streams,” J. Hydraul. Res., vol. 48, no. 5, pp. 658–663, Oct. 2010.
[23] V. Nikora, K. Koll, I. McEwan, and S. McLean, “Velocity distribution in the roughness layer of rough-bed flows,” J. Hydraul., vol. 30, pp. 1036– 1042, 2004.
[24] G. Katul, P. Wiberg, and J. Albertson, “A mixing layer theory for flow resistance in shallow streams,” Water Resour., vol. 38, no. 11, p. 1250, 2002.
[25] M. Hosseini, J. Abrishamai, “Open-channel hydraulics”, Imam Reza university Publication (36th Edition), 1394 (in Persian).
[26] M. Raffel, C. Willert, S. Wereley, and J. Kompenhans, Particle image velocimetry: a practical guide. A Practical Guide Springer Berlin Heidelberg, 2007.
[27] M. Detert, “Hydrodynamic processes at the watersediment interface of streambeds,” Univ. of Karlsruhe, Germany, 2008.
[28] W. Thielicke and E. Stamhuis, “PIVlab–towards userfriendly, affordable and accurate digital particle image velocimetry in MATLAB,” J. Open Res. Softw., vol. 2, no. 1, p. e30, 2014.
[29] M. Detert, V. Nikora, and G. Jirka, “Synoptic velocity and pressure fields at the water–sediment interface of streambeds,” J. Fluid Mech., vol. 660, pp. 55–86, 2010.
[30] J. Westerweel and F. Scarano, “Universal outlier detection for PIV data,” Exp. Fluids, vol. 39, pp. 1096–1100, .5002
[31] A. Prasad, R. Adrian, C. Landreth, and P. Offutt, “Effect of resolution on the speed and accuracy of particle image velocimetry interrogation,” Exp. Fluids, vol. 13, pp. 105–116, 1992.
[32] V. Nikora,, K. Koll, S. McLean, A. Dittrich, “Zeroplane displacement for rough-bed open-channel flows,” Hydraul. River Flow Conference, 2002.
[33] V. Nikora, I. McEwan, S. McLean, and S. Coleman, “Double-averaging concept for roughbed open-channel and overland flows: Theoretical background,” J. Hydraul., vol. 133, pp. 884–895, 2007.
[34] S. Bomminayuni, T. Stoesser, “Turbulence Statistics in an Open-Channel Flow over a Rough Bed“, J. Hydraul. Eng., Vol. 137, No. 11, pp. 1347-1358.
[35] R. Adrian, “Hairpin vortex organization in wall turbulence.” Physics of Fluids, Vol. 19, No. 4, 41301, .7002
[36] ل. احمدی پرگو، آموزش گام به گام اکسل 2016، انتشارات دیباگران تهران ،1395.