This paper presents a theoretical and experimental study of the long-standing fluid mechanics problem involving the temporal resolution of a large, localised initial disturbance into a sequence of solitary waves. This problem is of fundamental importance in a range of applications including tsunami and internal ocean wave modelling. This study is performed in the context of the viscous fluid conduit system-the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Due to buoyancy induced nonlinear self-steepening balanced by stress induced interfacial dispersion, the disturbance evolves into a slowly modulated wavetrain and further, into a sequence of solitary waves. An extension of Whitham modulation theory, termed the solitary wave resolution method, is used to resolve the fission of an initial disturbance into solitary waves. The developed theory predicts the relationship between the initial disturbance's profile, the number of emergent solitary waves, and their amplitude distribution, quantifying an extension of the well-known soliton resolution conjecture from integrable systems to non-integrable systems that often provide a more accurate modelling of physical systems. The theoretical predictions for the fluid conduit system are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within 1-2 waves of the prediction, and the amplitude distribution shows remarkable agreement. Universal properties of solitary wave fission in other fluid dynamics problems are identified.
This paper describes an approach for assessing the geosphere performance of nuclear waste disposal in fractured rock. In this approach, a three-dimensional heterogeneous channelnetwork model is constructed using a stochastic discrete fracture network (DFN) code. Radionuclide migration in the channel-network model is solved using the Laplace transform Galerkin finite element method, taking into account advection-dispersion in a fracture network, matrix diffusion, sorption in the rock matrix as well as radioactive chain decay. Preliminary radionuclide migration analysis was performed for fifty realizations of a synthetic block-scale DFN model. The total radionuclide release from all packages in the repository was estimated from the statistics of the results of fifty realizations under the hypothesis of ergodicity. The interpretation of the result of the three-dimensional network model by a combination of simpler one-dimensional parallel plate models is also discussed.
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