Hydraulic Jump Properties Over a Rough Bed

Analysis of Turbulent Hydraulic Jump over a Transitional Rough Bed of a Rectangular Channel: Universal Relations

“…The proposed theory for rough bed rectangular channels predicted universal solution depth profile, sequent depth ratio, jump length, and roller lengths in terms of effective upstream Froude number F S1 and are explicitly independent of bed roughness. The experimental data of Hughes and Flack (1984), Carollo et al (2007Carollo et al ( , 2009, and Ead and Rajaratnam (2002) support the proposed universal theory. Thus, the results for rough bed channels can be directly deduced from the classical smooth bed hydraulic jump theory, provided the upstream Froude number F 1 may be replaced by the effective upstream Froude number F S1 .…”

“…The role of the effective upstream Froude number F S1 based on bed roughness is investigated for jump length L j /h 1 . The experimental data of Hughes and Flack (1984) and Ead and Rajaratnam (2002) for jump length L j /h 1 versus F S1 are shown in Figure 7(b); which also provides strong support for the writers' universal relations, explicitly independent of bed roughness. The leading term approximations in (F S1 → 1) in Equation (43) for jump length L j /h 1 is also shown in Figure 7(b) and is in good agreement with the experimental data.…”

“…In rectangular channels the nondimensional roller length L R /h 2 and L R /h 1 against the upstream Froude number F 1 are shown in Figures 8(a) and 8(b), respectively, from the rough bed data of Hughes and Flack (1984), Ead and Rajaratnam (2002), and Carollo et al (2007). For large values of upstream Froude numbers F 1 → ∞, the roller length L R /h 2 approaches a constant universal value that depends on the bed roughness.…”

“…For a rough bed rectangular channel, Rajaratnam (1967) presented interesting data for the sequent depth and jump length in terms of parameter ke/h 1 , where ke is rough bed equivalent roughness and h1 is supercritical stream depth (Figure 1). Hughes and Flack (1984) represented the relative roughness of the bed in terms of d xx (the material size of the bed mixture for which xx of material is finer) and equivalent grain roughness height k s (assumed to be a function of d 65 ). Leutheusser and Schiller (1975) and Hughes and Flack (1984) analyzed their experimental data for a sequent depth ratio that supported Equation (2).…”

“…Hughes and Flack (1984) represented the relative roughness of the bed in terms of d xx (the material size of the bed mixture for which xx of material is finer) and equivalent grain roughness height k s (assumed to be a function of d 65 ). Leutheusser and Schiller (1975) and Hughes and Flack (1984) analyzed their experimental data for a sequent depth ratio that supported Equation (2). Recently, Pagliara et al (2008) proposed another correlation:…”