Experimental verification of the gas-hydraulic analogy with reference to the dam-break problem

Bukreev, V. I.; Гусев, А. В.; Malysheva, A. A.; Malysheva, I. A.

doi:10.1007/s10697-005-0014-7

Cited by 18 publications

(38 citation statements)

References 8 publications

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“…It is evident that significant differences between the classical and modified solutions occur only in the case h * 0 < h * c ≈ 0.14, where the flow (h 1 , u 1 ) behind the discontinuous-wave front is supercritical [12]. This explains why the solutions obtained for the classical system (2.1), (2.3) adequately reproduce the experimental flow pattern in the case where the initial tailwater and headwater depths satisfy the inequality h 0 > h * c H ≈ 0.14H, because of which the constant flow (h 1 , u 1 ) formed behind the discontinuous-wave front is subcritical [1,21,23].…”

Section: Formulation Of the Problem Based On Shallow-water Theorymentioning

confidence: 93%

“…where h(x, t) is the flow depth, q(x, t) is the specific discharge (per unit width of the channel), u = q/h is the flow velocity, z(x, t) = b(x) + h(x, t) is the free-surface level, b(x) is the vertical coordinate of the bottom (bed level), g is the acceleration due to gravity and γ = γ * H is a dimensional parameter (H is the characteristic flow depth, which, for the problem considered, is set equal to the initial headwater depth; γ * is a dimensionless parameter chosen so as to agree with the results of laboratory experiments [23]). Equation (2.1) is the law of conservation of mass, and equation (2.2) is the modified conservation law for the total momentum, which is derived in [26].…”

Section: Formulation Of the Problem Based On Shallow-water Theorymentioning

confidence: 99%

“…From the results of experimental modeling [23] of the dam-break problem (2.10), it follows that, in the case of a dry channel in the tailwater region, i.e. at h 0 = 0, the characteristic Froude number behind the discontinuouswave front is given by the equality θ = θ 1 = 6.7, whence, by virtue of (2.11), we obtain γ * = γ * 1 = 0.05 ⇒ γ = γ 1 = γ * 1 H = 1.03.…”

Section: Formulation Of the Problem Based On Shallow-water Theorymentioning

confidence: 99%

“…This situation cannot be changed by accounting for bottom friction, which is a source term that makes no contribution to the Hugoniot conditions at the discontinuouswave front [19,20]. At the same time, numerous laboratory experiments have shown that these continuous solutions significantly overestimate the propagation velocity of the leading edge of the wave and distort its profile [21][22][23][24]. In experiments, the wave front propagating in a dry channel is much steeper and is subjected to breaking typical of discontinuous waves.…”

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confidence: 99%

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Open-channel waves generated by propagation of a discontinuous wave over a bottom step

Гусев

Остапенко

Malysheva

et al. 2008

J Appl Mech Tech Phys

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This paper presents the results of theoretical and experimental studies of open-channel waves generated by the propagation of a discontinuous dam-break wave over a bottom step. The cases where the initial tailwater level is higher than the step height (the step is under water) and where this value is smaller than the step height (at the initial time, water is absent on the step) are considered. Exact solutions are constructed using modified first-approximation equations of shallow-water theory, which admit the propagation of discontinuous waves in a dry channel. On the stationary hydraulic jump formed above the bottom step, the total free-stream energy is assumed to be conserved. These solutions agree with experimental data on various parameters (types of waves, wave propagation velocity, asymptotic depths behind the wave fronts).Introduction. The first-approximation equations of shallow-water theory [1-3] are widely used in modeling the propagation of discontinuous waves [4-7] (hydraulic bores [8,9]) resulting from complete or partial break of hydraulic dams or the impact of large sea tsunami-type waves [10] on shallow water. However, the classical system of the basic conservation laws of shallow-water theory (consisting of the laws of conservation of mass and total momentum [3]), while correctly describing the parameters of discontinuous waves propagating in a liquid of finite depth above an even bottom [1], is not suitable for describing wave flows above various bottom-relief features, in particular, discontinuous-wave propagation over a bottom step or a drop. This is due to the fact that the totalmomentum equation is an exact conservation law only in the case of a horizontal bottom and it cannot be used to derive Hugoniot conditions for the discontinuities arising from bed level changes.A method of deriving relations for stationary discontinuities above bed level changes using the shallowwater equations was proposed in [11] and validated in [12]. This method is based on the assumption that if two characteristics arrive at such a discontinuity, then, along with the continuity of the discharge, which follows from the mass conservation law, it is necessary to require the continuity of the Bernoulli function, which follows from the local-momentum conservation law and the conservation law for the total free-stream energy. If three characteristics arrive at a discontinuity above a bed level change, the discharge continuity is sufficient to determine all flow parameters at this discontinuity. The total energy at such a discontinuity is lost, which serves as a criterion for its stability [3]. These assumptions and a generalized method of adiabats [13] were used to study the unique solvability of dam-break problems above a bottom step [14] and a drop [15]. The obtained self-similar solutions are in fairly good agreement with experimental data [16-18] on various parameters (types of waves, wave propagation velocity, asymptotic depths behind the wave fronts).

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Section: Formulation Of the Problem Based On Shallow-water Theorymentioning

confidence: 93%

Section: Formulation Of the Problem Based On Shallow-water Theorymentioning

confidence: 99%

Section: Formulation Of the Problem Based On Shallow-water Theorymentioning

confidence: 99%

mentioning

confidence: 99%

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Open-channel waves generated by propagation of a discontinuous wave over a bottom step

Гусев

Остапенко

Malysheva

et al. 2008

J Appl Mech Tech Phys

Self Cite

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show abstract

“…1) and the acceleration due to gravity g. After conversion to dimensionless quantities, the number of geometrical parameters decreases to five, and the parameter g in the construction models remains dimensional. In the problem of a full dam break, the number of dimensionless geometrical parameters decreases to one [7]. In experiments, the wave propagation is influenced by the liquid viscosity, the hydraulic unevenness of the solid boundaries, the shape of the edges at the entrance to the breach, and the characteristics of movement of the shield.…”

mentioning

confidence: 99%