Abstract. Flow visualization experiments were conducted on a transparent replica of a natural, rough-walled rock fracture from the Stripa Mine, Sweden, for inlet conditions of constant pressure and flow rate over a range of angles of inclination. The experiments demonstrated that infiltrating water proceeds through unsaturated rock fractures along nonuniform, localized preferential flow paths. Even though constant inlet conditions were maintained, pervasive unsteady or intermittent flow was also observed in these experiments, where portions of the flow channel underwent cycles of snapping and reforming. Experiments conducted on parallel plates with a sequence of apertures progressing from small to large to small reproduced intermittent flow. Measurements of the frequency of intermittent flow events and the volume of water metered between events were obtained from the fracture replica and parallel plate experiments and related to the Bond and capillary numbers to generalize the results. The frequency data from the fracture replica experiments did not follow the same trend as the data from the parallel plate experiments for similar Bond and capillary numbers, but the volume of water metered data was consistent in these experiments. IntroductionFractures in the unsaturated zone play an important role in water infiltration and contaminant transport. Field studies have provided considerable evidence that water proceeds along fast flow paths through partially saturated fractures. Bomb-pulse Chlorine 36 at Yucca Mountain, Nevada, was found at elevated concentrations several hundred meters deep, indicating that water had migrated from the land surface to these depths in a time period of only several decades [Liu et al., 1995]. Seeps collected in tunnels at Rainier Mesa, Nevada, were chemically distinct from matrix water, and their isotopic ratios indicated recent meteoric origin [Wang et al., 1993]. Recharge water was observed to flow quickly through a thick unsaturated fractured chalk zone in the Negev Desert in Israel [Nativ et al., 1995]. These observations were explained by water migrating rapidly along localized preferential flow paths through unsaturated rock fractures. Preferential flow channels reduce rock matrix-fracture interaction compared to models that predict spatially uniform flow, thereby accelerating groundwater travel in unsaturated fractured porous media [Glass et al., 1995]. Understanding the mechanisms controlling fast flow is important for developing conceptual models describing seepage of liquids through unsaturated, fractured porous media.Liquids in unsaturated porous media migrate under the combined action of gravity, pressure, capillary, and viscous forces. The relative magnitude of these forces can be quantified using the Bond and capillary numbers. The ratio between where A 9 is the density difference between the infiltrating liquid and the air, !7 is the gravitational acceleration constant, /3 is the angle of inclination of the fracture measured from the horizontal, b is the aperture, cr is ...

Experimental and numerical results concerning solid particle motion in a plane wake are presented that demonstrate the importance of large-scale vortex structures in self-organizing dispersion processes. Previous studies have demonstrated that a time scale ratio involving the aerodynamic response time of the particles and a characteristic time of the vortex structures is an important parameter for indicating the qualitative and quantitative nature of the dispersion process. A stretching and folding mechanism associated with vortex development and merging interactions has been suggested as a description for characterizing particle dispersion in plane mixing layers at intermediate time scale ratios. For plane wakes where large-scale vortex mergers rarely occur, a highly organized particle dispersion process focuses intermediate time scale ratio particles along the boundaries of the large-scale vortices. The fractal correlation dimension associated with chaotic systems is found to be a useful parameter for quantifying the relative organization of the dispersion patterns as a function of the particle time scale ratio.

The dispersion of particles in a plane mixing layer between two air streams is investigated using experimental and numerical techniques. The results show that large-scale spanwise vortices strongly influence the particle dispersion process. Particles with aerodynamic response times on the order of the large scale vortex time scales are found to concentrate near the outer edges of the vortex structures. Time average velocity measurements also demonstrate that these particles tend to move away from the center of the mixing layer. Substantial changes in the lateral particle dispersion are producible by controlled forcing of the vortex structures. Comparisons between the experimental particle dispersion patterns and numerical simulations show striking similarities. A two-part model involving stretching and folding is suggested as a particle dispersion mechanism.

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In chemical manufacturing processes, equipment degradation can have a significant impact on process performance or cause unit failures that result in considerable downtime. Hence, maintenance planning is an important consideration, and there have been increased efforts in scheduling production and maintenance operations jointly. In this context, one major challenge is the inherent uncertainty in predictive equipment health models. In particular, the probability distribution associated with the stochasticity in such models is often difficult to estimate and hence not known exactly. In this work, we apply a distributionally robust optimization (DRO) approach to address this problem. Specifically, the proposed formulation optimizes the worst‐case expected outcome with respect to a Wasserstein ambiguity set, and we apply a decision rule approach that allows multistage mixed‐integer recourse. Computational experiments, including a real‐world industrial case study, are conducted, where the results demonstrate the significant benefits from binary recourse and DRO in terms of solution quality.

The nonlinear response of an initially flat sea bed to a monochromatic surface progressive wave was studied using the multiple scale perturbation method. Two opposite-traveling subliminal internal ‘‘mud’’ waves are selectively excited and form a resonant triad with the surface wave. The amplitudes of the internal waves grow on a time scale much longer than the period of the surface wave. It was found that the sea bed response is critically dependent on the density ratio of water and soil, depth of water, and depth and viscosity of the saturated soil. The result of instability analysis is in qualitative agreement with the result of a wave flume experiment.

We consider standing wave solutions of various dispersive models with non-standard form of the dispersion terms. Using index count calculations, together with the information from a variational construction, we develop sharp conditions for spectral stability of these waves.

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