A two-species continuum model for aeolian sand ripples

We formulate a continuum model for aeolian sand ripples consisting of two species of grains: a lower layer of relatively immobile clusters, with an upper layer of highly mobile grains moving on top. We predict analytically the ripple wavelength, initial ripple growth rate and threshold saltation flux for ripple formation. Numerical simulations show the evolution of realistic ripple profiles from initial surface roughness via ripple growth and merger.Comment: 9 pages, 3 figure

A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found.Comment: 7 Pages, 6 Figures; Granular Matter, 2012 (Online

Dynamics of aeolian sand ripples

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context we first review existing models. We argue on the local character of sand ripple formation. Using a hydrodynamical model we derive a nonlinear equation for the sand profile. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher order nonlinear term in the equation, leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations.Comment: 22 pages and 10 postscript figure

Avalanching on dunes and its effects: Size statistics, stratification, & seismic surveys

Geophysical research has long been interdisciplinary, with many phenomena on the Earth's surface involving multiple, linked processes that are best understood using a combination of techniques. This is particularly true in the case of grain flows on sand dunes, in which the sedimentary stratification with which geologists are concerned arises from the granular processes investigated by physicists and engineers, and the water permeation that interests hydrologists and soil scientists determines the seismic velocities of concern to exploration geophysicists. In this dissertation, I describe four projects conducted for the degree of Doctor of Philosophy, using a combination of laboratory experimentation, fieldwork, numerical simulation, and mathematical modelling to link avalanching on dunes to its effects on stratification, on the permeation of water, and on seismic surveys. Firstly, I describe experiments on erodible, unbounded, grain piles in a channel, slowly supplied with additional grains, and I demonstrate that the behaviour of the consequent, discrete avalanches alternates between two regimes, typified by their size statistics. Reconciling the `self-organised criticality' that several authors have predicted for such a system with the hysteretic behaviour that others have observed, the system exhibits quasi-periodic, system-spanning avalanches in one regime, while in the other avalanches pass at irregular intervals and have a power-law size distribution. Secondly, I link this power-law size distribution to the strata emplaced by avalanches on bounded grain piles. A low inflow rate of grains into an experimental channel develops a pile, composed of strata in which blue-dyed, coarser grains overlie finer grains. Associating stopped avalanche fronts with the `trapped kinks' described by previous authors, I show that, in sufficiently large grain piles, mean stratum width increases linearly with distance downslope. This implies the possibility of interpreting paleodune height from the strata of aeolian sandstones, and makes predictions for the structure of avalanche-associated strata within active dunes. Thirdly, I discuss investigations of these strata within active, Qatari barchan dunes, using dye-infiltration to image strata in the field and extracting samples across individual strata with sub-centimetre resolution. Downslope increases in mean stratum width are evident, while measurements of particle size distributions demonstrate preferential permeation of water along substrata composed of finer particles, explaining the strata-associated, localised regions of high water content discovered by other work on the same dunes. Finally, I consider the effect of these within-dune variations in water content on seismic surveys for oil and gas. Having used high performance computing to simulate elastic wave propagation in the vicinity of an isolated, barchan sand dune, I demonstrate that such a dune acts as a resonator, absorbing energy from Rayleigh waves and reemitting it over an extensive period of time. I derive and validate a mathematical framework that uses bulk properties of the dune to predict quantitative properties of the emitted waves, and I demonstrate the importance of internal variations in seismic velocity, resulting from variations in water content.This work was supported by a PhD studentship within the Cambridge Earth Systems Science Doctoral Training Partnership (ESS DTP), funded by the National Environmental Research Council, grant number NE/L002507/1. Additional support was provided by Schlumberger Cambridge Research (SCR), through a CASE studentship

Numerical Analysis on the Generation of Equilibrium Aeolian Sedimentary Bed-Forms From Random Surfaces

The formation of aeolian ripples has been modeled, quite successfully, using discrete approaches like cellular automaton models. Numerical analysis of continuum models to obtain similar success in modeling ripple evolution, however, has not been studied extensively. A numerical model based on continuum theories expedites calculations, as opposed to discrete approaches which model trajectory of each and every sand grain, and are hence relatively more economical. The numerical analysis strives to contribute to the field of study of aeolian ripple migration by an extensive comparison and discussion of modeled ripple evolution results with those of a particular laboratory based wind-tunnel experiment. This research also endeavors to under- stand the physics behind ripple generation and what parameters to be modified to account for multiple grain sizes. Incorporation of multiple grain sizes would enable us to study the stratigraphy of the generated bed-forms. To obtain smoother and realistic ripple surfaces, a sixth-order compact finite difference numerical scheme is used for spatial derivates and fourth-order Runge-Kutta scheme for time derivates. The boundary conditions incorporated are periodic and the initial condition employed to generate ripple is a rough sand surface. The numerical model is applied to study the effect of varying the angle, at which the sand bed gets impacted by sand grains, on the evolution of ripples. Ripples are analyzed qualitatively and quantitatively by considering the contribution of processes involved in the evolution process. The ripple profiles and the time taken to reach equilibrium state, obtained by numerical experiments, are in close agreement with the ones obtained by the wind-tunnel experiment

Lithofacies characterization of fluvial sandstones from outcrop gamma-ray logs (Loranca Basin, Spain): the influence of provenance

Natural gamma spectral (NGS) log motifs and cluster analysis were used to characterize outcropping sandstone bodies formed in braided and highsinuosity streams of the Tertiary Tórtola fluvial system of the Loranca Basin (Spain). Five coarse-grained lithofacies comprise these deposits and determine distinct NGS log motif. Cross-plots and cluster analysis of NGS log data of the lithofacies suggest three distinct clusters. These clusters reflect distinct values for sandstones with small sets of ripple lamination, cross-stratification, and conglomerates and pebbles. Ripple-laminated sandstones show the most variability in NGS signature, whereas conglomeratic sandstones show the most uniform signature. Such cluster analysis may be used to assign NGS log data points of unknown origin to a specific fluvial lithofacies under conditions of equal rock provenance and diagenetic history. A sedimentaclastic (i.e. sedimentary parent rock) origin of sediments appears to be the main control on detrital composition that, in turn, varies with grain size

The application of terrestrial laser scanning to measure small scale changes in aeolian bedforms

Traditional methods used to measure aeolian sediment transport rely on point based sampling, such as sand traps or saltation impact sensors, which ignore the spatial heterogeneity displayed in the transport system. Obtaining an accurate transport rate is important to parameterise predictive models, which currently show large deviations between measured and predicted rates.Terrestrial laser scanning (TLS) is a tool that is rapidly emerging in the field of geomorphology. It provides the ability to capture surface elevation data of in-situ bedforms at the spatial and temporal scale necessary to link change, such as ripple migration, to the processes that drive them. Repeat scans provide digital elevation models which can be differenced to provide volumetric rates of change, in a process known as the morphologic method. However, utilising data at such high resolutions requires an accurate estimation of error in order to provide meaningful results.Typically the morphologic method documents surface change between geomorphic events. However, due to the high temporal variability displayed by the aeolian transport system, measuring topographic change during a transport event would be beneficial. Using TLS during active transport removes the ability to take multiple convergent scans. Therefore current methods of approximating error in TLS derived surfaces by using convergent scans from multiple scan locations cannot be applied.The influence of scanning geometry and survey set up is explored in order to quantify and reduce errors when scanning small scale bedforms from a single location. This is then applied to an active transport event to measure wind ripple migration, and derive a sediment transport rate using the morphologic method. The results suggest TLS is a viable tool for capturing in-situ aeolian ripples. Scan incidence angle is shown to significantly affect point density and therefore point cloud accuracy. The influence of incidence angle is different depending on the extent of the bedform studied. Ripples were measured during an active transport event in the Great Sand Dunes National Park, Colorado. Ripple morphologies and migration rates were within previously observed ranges. Applying the morphologic method highlighted ripple migration patterns, surface change and enabled an overall sediment budget to be calculated

Patterns and Collective Behavior in Granular Media: Theoretical Concepts

Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granular matter, with the focus on the onset of collective behavior and pattern formation. Their aim is two-fold: to identify general principles common for granular systems and other complex non-equilibrium systems, and to elucidate important distinctions between collective behavior in granular and continuum pattern-forming systems.Comment: Submitted to Reviews of Modern Physics. Full text with figures (2Mb pdf) avaliable at http://mti.msd.anl.gov/AransonTsimringReview/aranson_tsimring.pdf Community responce is appreciated. Comments/suggestions send to [email protected]