A hierarchy of models for simulating experimental results from a 3D heterogeneous porous medium

In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of spherical, low-hydraulic-conductivity inclusions embedded in a high-hydraulic-conductivity matrix. The bi-modal medium was saturated with tracers, and then flushed with tracer-free fluid while the effluent breakthrough curves were measured. The focus for this work is to examine a hierarchy of four models (in the absence of adjustable parameters) with decreasing complexity to assess their ability to accurately represent the measured breakthrough curves. The most information-rich model was (1) a direct numerical simulation of the system in which the geometry, boundary and initial conditions, and medium properties were fully independently characterized experimentally with high fidelity. The reduced models included; (2) a simplified numerical model identical to the fully-resolved direct numerical simulation (DNS) model, but using a domain that was one-tenth the size; (3) an upscaled mobile-immobile model that allowed for a time-dependent mass-transfer coefficient; and, (4) an upscaled mobile-immobile model that assumed a space-time constant mass-transfer coefficient. The results illustrated that all four models provided accurate representations of the experimental breakthrough curves as measured by global RMS error. The primary component of error induced in the upscaled models appeared to arise from the neglect of convection within the inclusions. Interestingly, these results suggested that the conventional convection-dispersion equation, when applied in a way that resolves the heterogeneities, yields models with high fidelity without requiring the imposition of a more complex non-Fickian model.Comment: 27 pages, 9 Figure

Climatic and Topologic Controls on the Complexity of River Networks

The emergence and evolution of channel networks are controlled by the competition between the hillslopes and fluvial processes on the landscape. Investigating the geomorphic and topologic properties of these networks is important for developing predictive models describing the network dynamics under changing environment as well as for quantifying the roles of processes in creating distinct patterns of channel networks. In this dissertation, the response of landscapes to changing climatic forcing via numerical-modeling and field observations was investigated. A new framework was proposed to evaluate the complexity of catchments using two different representations of channel networks. The structural complexity was studied using the width function, which characterizes the spatial arrangement of channels. Whereas, the functional complexity was explored using the incremental area function, capturing the patterns of transport of fluxes. Our analysis reveals stronger controls of topological connectivity on the functional complexity than on structural complexity, indicating that the unchannelized surface (hillslope) contributes to the increase of heterogeneity in transport processes. Furthermore, the channel network structure was investigated using a physically-based numerical landscape evolution model for varying hillslope and fluvial processes. Different magnitudes of soil transport (D) and fluvial incision (K) coefficients represent different magnitudes of hillslope and fluvial processes. We show that different combinations of D and K result in distinct branching structure in landscapes. For example, for smaller D and K combinations (mimicking dry climate), a higher number of branching channels was observed. Whereas, for larger D and K combinations (mimicking humid climate), a higher number of side-branching channels is obtained. These results are consistent with the field observations suggesting that varying climatic conditions imprint distinct signatures on the branching structure of channel networks

A physical model for seismic noise generation by turbulent flow in rivers

Previous studies suggest that the seismic noise induced by rivers may be used to infer river transport properties, and previous theoretical work showed that bedload sediment flux can be inverted from seismic data. However, the lack of a theoretical framework relating water flow to seismic noise prevents these studies from providing accurate bedload fluxes and quantitative information on flow processes. Here we propose a forward model of seismic noise caused by turbulent flow. In agreement with previous observations, modeled turbulent flow-induced noise operates at lower frequencies than bedload-induced noise. Moreover, the differences in the spectral signatures of turbulent flow-induced and bedload-induced forces at the riverbed are significant enough that these two processes can be characterized independently using seismic records acquired at various distances from the river. In cases with isolated turbulent flow noise, we suggest that riverbed stress can be inverted. Finally, we validate our model by comparing predictions to previously reported observations. We show that our model captures the spectral peak located around 6–7 Hz and previously attributed to water flow at Hance Rapids in the Colorado River (United States); we also show that turbulent flow causes a significant part of the seismic noise recorded at the Trisuli River in Nepal, which reveals that the hysteresis curve previously reported there does not solely include bedload, but is also largely influenced by turbulent flow-induced noise. We expect the framework presented here to be useful to invert realistic bedload fluxes by enabling the removal of the turbulent flow contribution from seismic data

Modeling the dynamics and depositional patterns of sandy rivers

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2006.Includes bibliographical references.This thesis seeks to advance our understanding of the dynamic nature, spatial organization and depositional record of topography in sand-bedded rivers. I examine patterns and processes over a wide range of scales, on Earth and Mars. At the smallest scale, ripples and dunes (bedforms) arise spontaneously under most natural flow conditions, acting as the primary agents of sediment transport and flow resistance in sandy rivers. I use physical modeling in a laboratory flume to explore the feedbacks among bedform geometry, fluid flow and sediment transport. Field observations of dunes in the North Loup River, Nebraska, show that bed roughness displays a statistical steady state and robust scaling. Motivated by these data, I develop a nonlinear stochastic surface evolution model for the topography of sandy rivers which captures the essence of bedform evolution in space and time. I then use a simplified kinematic model for bedform evolution to simulate the production of stratigraphy from migrating dunes, allowing a more accurate reconstruction of river flow conditions from preserved bedform remnants in rocks. At the channel scale I examine the conditions that lead to avulsion, the rapid abandonment of a river channel in favor of a new course at lower elevation.(cont.) Simple scaling arguments and data from 30 natural systems reveal that anastomosing (multi-branch) rivers and distributary deltas are morphologies that arise when avulsion is the dominant mechanism of channel adjustment. I apply these arguments to the Niobrara River, Nebraska, which has experienced rapid in-channel deposition due to base level rise. I show that the planform pattern of the Niobrara is dominated by base-level-driven avulsions, and is decoupled from the smaller-scale sediment transport. At the largest considered scale are depositional fans, which are constructed by avulsing rivers. The evolution of a fan profile may be modeled at long time- and space-averaged scales as a diffusive process. I use such a model to invert topographic and volumetric data from a fluvial fan on Mars, producing an estimate of the time required to build the fan out of channel and overbank deposits.by Douglas J. Jerolmack.Ph.D