Waves resulting from partial dam break with the formation of a breach in the form of a cut to the channel bottom

This paper gives experimental data on the propagation speed and height of a dam-break wave arising in the tailwater region during a partial dam break event. These data were used to confirm the Khristianovich calculation method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 97–103, May–June, 2009.     

Experimental verification of methods for calculating partial dam-break waves

This paper presents results of an experimental study of waves generated by partial break of two model dams. The previously proposed calculation methods are extended and compared with the experimental data obtained. It is shown that the wave propagation speed in the tailwater is significantly influenced by the energy losses due to flow through the breach. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 61–69, September–October, 2008     

Discharge and energy-loss coefficients in flow through a breach in a trapezoidal dam

The paper presents experimental data on the discharge and energy-loss coefficients for two weirs of polygonal profiles with lateral contraction, which are required, in particular, in simulations of partial dam-break waves. It is shown that the values of these coefficients for a trapezoidal weir with a slope ratio of 1: 3 differ insignificantly from their values for a rectangular weir. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 68–73, January–February, 2008.     

梯级溃坝洪水洪峰增强机制

我国在多条河流上修建了大量梯级水库, 梯级坝溃决诱发洪水大大超过单坝溃决洪水洪峰, 因此亟需加深对梯级坝溃决洪水洪峰增强机制的认识. 本文建立了梯级坝溃决洪水演进过程的一维浅水动力学模型, 发展了一套能捕捉激波、干湿边界和保平衡结构的数值求解方法, 通过大量算例, 系统研究了梯级坝溃决洪水演进过程的质量转化和能量转化机制. 研究结果表明, 梯级溃决中, 上游溃决诱发的洪水大大增大下游水库的质量和动量, 形成一个带动量的水塔, 同时在尾部残留一个动量较大的射流, 不断补充下游坝体溃决后水塔的质量和动量, 持续维持洪峰高度. 根据该射流-水塔机制, 建立了梯级坝溃决洪水演进过程对应的射流-水塔单坝溃决洪水过程等效模型, 该等效模型基本反映了梯级坝溃决诱发洪水的洪峰过程, 并成功预测了多个坝间距为百公里量级的梯级坝溃决洪水洪峰高程和流量, 可望为流域防洪和梯级坝设计提供理论依据.      

Force action of discontinuous waves on a vertical wall

This paper presents the results of an experimental study of the dynamic action exerted on the vertical end wall of a rectangular channel by the wave propagating in the tailwater region after total dam break. It is shown that the results of calculations using the first shallow-water approximation differ from experimental data by not more than 5%. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 129–135, March-April, 2009.     

Comparison of near- and far-fault ground motion effect on the nonlinear response of dam–reservoir–foundation systems

In this paper, it is aimed to compare the near- and far-fault ground motion effects on the nonlinear dynamic response of dams including dam–reservoir–foundation interaction. Two different types of dams, which are concrete arch and concrete faced rockfill dams, are selected to investigate the near- and far-fault ground motion effects on the dam responses. The behavior of reservoir water is taken into account using Lagrangian approach. The Drucker–Prager material model is employed in nonlinear analyses. Near and far-fault strong ground motion records, which have approximately identical peak ground accelerations, of Loma Prieta (1989) earthquake are selected for the analyses. Displacements, maximum and minimum principal stresses are determined using the finite element method. The displacements and principal stresses obtained from the analyses of dams subjected to each fault effect are compared with each other. It is clearly seen that there is more seismic demand on displacements and stresses when the dam is subjected to near-fault ground motion.     

Two‐dimensional dam break flow simulation

Numerical modelling of shallow water flow in two dimensions is presented in this work with the results obtained in dam break tests. Free surface flow in channels can be described mathematically by the shallow‐water system of equations. These equations have been discretized using an approach based on unstructured Delaunay triangles and applied to the simulation of two‐dimensional dam break flows. A cell centred finite volume method based on Roe's approximate Riemann solver across the edges of the cells is presented and the results are compared for first‐ and second‐order accuracy. Special treatment of the friction term has been adopted and will be described. The scheme is capable of handling complex flow domains as shown in the simulation corresponding to the test cases proposed, i.e. that of a dam break wave propagating into a 45° bend channel (UCL) and in a channel with a constriction (LNEC‐IST). Comparisons of experimental and numerical results are shown. Copyright © 2000 John Wiley & Sons, Ltd.     

Water discharge over a dam

A solution is given for a problem of plane steady motion of a heavy ideal incompressible liquid which is partially bounded from below by two planes positioned at an angle of ±30° to the horizontal. The problem may be interpreted as water discharge over a dam in the form of a wedge with apex angle 120°. The so-called fixed-weir rockfill dams have a profile similar to the one considered here [1]. The flow discharge coefficient, which is very close to the experimental value, is calculated for the dam in question.     

A finite volume shock‐capturing solver of the fully coupled shallow water‐sediment equations

This paper describes a numerical solver of well‐balanced, 2D depth‐averaged shallow water‐sediment equations. The equations permit variable horizontal fluid density and are designed to model water‐sediment flow over a mobile bed. A Godunov‐type, Harten–Lax–van Leer contact (HLLC) finite volume scheme is used to solve the fully coupled system of hyperbolic conservation laws that describe flow hydrodynamics, suspended sediment transport, bedload transport and bed morphological change. Dependent variables are specially selected to handle the presence of the variable density property in the mathematical formulation. The model is verified against analytical and semi‐analytical solutions for bedload transport and suspended sediment transport, respectively. The well‐balanced property of the equations is verified for a variable‐density dam break flow over discontinuous bathymetry. Simulations of an idealised dam‐break flow over an erodible bed are in excellent agreement with previously published results, validating the ability of the model to capture the complex interaction between rapidly varying flow and an erodible bed and validating the eigenstructure of the system of variable‐density governing equations. Flow hydrodynamics and final bed topography of a laboratory‐based 2D partial dam breach over a mobile bed are satisfactorily reproduced by the numerical model. Comparison of the final bed topographies, computed for two distinct sediment transport methods, highlights the sensitivity of shallow water‐sediment models to the choice of closure relationships. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison between the theory and the numerical experiment in the problem of dam break on a jump of the cross-sectional area of a rectangular channel

Within the framework of the first approximation of the spatially one-dimensional shallow water theory the problem of flow generated by the dam break on a jump of the cross-sectional area of a rectangular channel is solved in the case in which the upper pool is wider than the lower one. The self-similar solutions constructed contain an euristic parameter related with the amount of the total flow energy lost on the cross-sectional area jump. The parameter is determined by means of comparing the one-dimensional solutions with the results of the numerical modeling of the problem on the basis of spatially two-dimensional equations of the shallow water theory.     

Experimental investigation of dynamic pressure loads during dam break

The objective of this research work has been to conduct experimental measurements on a dam break flow over a horizontal dry bed in order to provide a detailed insight, with emphasis on the pressure loads, into the dynamics of the dam break wave impacting a vertical wall downstream the dam. The experimental setup is described in detail, comprising state of the art miniaturized pressure sensors, high sampling rate data acquisition systems and high frame-rate video camera. It is a 1:2 scale of the highly cited (Lee et al., 2002, Journal of Fluids Engineering, 124) article experimental apparatus. Kinematics has been analyzed focusing on the free surface and wave front evolution. Experimental observations regarding liquid height and wave front speed have found to be in agreement with existing literature. This agreement enables the authors, assuming a similar framework, to discuss the measured pressure loads as a consequence of the dam break wave front impacting on the downstream wall. These loads show a substantial variability which has been statistically characterized. The measured quantities have been compared with the scarce available data in the literature, whose consistency is discussed. Measurements have been conducted with two filling heights. Scaling effects for such heights are also analyzed. As a direct result of the present initiative, an extensive set of data for computational tools validation is provided as Supplementary Materials, including pressure signals, wave height measurements and experimental videos.     

Spatial local solutions of the Navier-Stokes equations

This paper considers solutions of the Navier-Stokes equations polynomial in the coordinates, which. are called local solutions. For an incompressible fluid, all higher-order terms (sums of higher-order. monomials) of degree 2 are found and it is proved that nontrivial axisymmetric higher-order terms. of degree higher than 2 do not exist. Nonsolenoidal axisymmetric solutions are listed, which can be. treated as steady-state barotropic gas flows in a potential external-force field. All elliptic vortices. generalizing the well-known Kirchhoff solution are calculated. All solutions of degree 3 with the. higher-order term of partial form are found. Some of these solutions break down in a finite time. regardless of the value and sign of viscosity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 109–119, March–April, 2009.     

Density and total pressure behavior in the process of forced and spontaneous reconnection

The specific features of the density and total pressure (the sum of magnetic and gas-kinetic pressures) behavior in the process of forced (by the example of propagation of a magnetic acoustic wave in the vicinity of the X-point) and spontaneous (by the example of development of a helical Thirring mode) reconnection are considered. It is shown that the total pressure distribution depends weakly on the initial value of the gas-kinetic pressure, the strength of the z-component of the magnetic field, and the thermal conductivity in a wide range of parameters. The character of density distribution is determined only by the thermal conductivity. It is also shown that the behavior of the total pressure and density in the case of spontaneous reconnection weakly depends on the thermal conductivity, in contrast to the forced case. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 11–15, July–August, 1999.     

On the structure of characteristic surfaces related to partial differential equations of first and higher orders. II

The generalized method of characteristics is developed within the framework of the geometric Monge picture. Hopf-Lax-type extremality solutions are obtained for a broad class of Cauchy problems for nonlinear partial differential equations of the first and higher orders. A special Hamilton-Jacobi-type case is analyzed separately. An exact extremality Hopf-Lax-type solution of the Cauchy problem for the nonlinear Burgers equation is obtained, and its linearization to the Hopf-Cole expression and to the corresponding Airy-type linear partial differential equation is found and discussed. Published in Neliniini Kolyvannya, Vol. 8, No. 4, pp. 529–543, October–December, 2005.     

A Complete Solution of the Wave Equations for Transversely Isotropic Media

A transversely isotropic material in the sense of Green is considered. A complete solution in terms of retarded potential functions for the wave equations in transversely isotropic media is presented. In this paper we reduce the number of potential functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastostatics is cited, where the solution is reduced to the Lekhnitskii–Hu–Nowacki solution. The solution is simplified for the special case of isotropy. In this way, a new series of potential functions (to the best knowledge of the author) for the elastodynamics problem of isotropic materials is presented This solution is reduced to a special case of the Cauchy–Kovalevski–Somigliana solution, if the displacements satisfy specific conditions. Finally, Boggio's Theorem is generalized for transversely isotropic media which may be of interest to the reader beyond the present application. Dedicated to Morton E. Gurtin     

Addendum to: Symmetry classification of quasi-linear PDE’s. II: an exceptional case

This short note completes the symmetry analysis of a class of quasi-linear partial differential equations considered in the previous paper (Nonlinear Dynamics 51: 309–316, 2008): it deals with an “exceptional” Lie point symmetry which is admitted only if the involved parameters are fixed by precise relationships. The peculiarity of this symmetry is enhanced by the fact that, combined with the presence of a conditional symmetry of “weak” type, it leads to a family of solutions which include, as a particular case, a relevant solution of the Grad–Schlüter–Shafranov equation, well known in plasma physics.     

Some types of kinetic equations reducible to partial differential equations

The possibility of passing from the kinetic equation to a partial differential equations is rigorously mathematically proved for the case of nearly elastic scattering processes. Some examples are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 12–16, September–October, 2007.     

Investigation of the velocity fluctuation spectrum of a vortex flow of vibrationally excited molecular gas in a glow discharge

The flow velocity fluctuations in a gas laser are measured under non-self-maintained glow discharge conditions. Spectra of the pulsating velocity signal on the frequency interval up to 2 kHz and the time dependence of the signal under glow and neutral flow conditions for pure nitrogen, a mixture of nitrogen and helium, and a trial CO₂-N₂-He mixture are obtained. Deformation (due to the action of the discharge) of the spectra of the transverse velocity component in the wake of a right circular cylinder is observed. In order to analyze the data obtained a model of the dynamic response of the pulsating velocity is constructed and a model of the Kármán vortex street behind a body is generalized with allowance for variations of the oscillation phase in the street. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 81–91, March–April, 2000. The work was carried out with partial financial support from the Russian Foundation for Basic Research (projects Nos. 96-01-00372 and 99-01-01199).     

On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions

In this article, we study the large time behavior of solutions of first-order Hamilton–Jacobi Equations set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy–Neumann problems by using two fairly different methods: the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the “weak KAM approach”, which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry–Mather sets.