Interpretation of lunar topography : impact cratering and surface roughness

This work seeks to understand past and present surface conditions on the Moon using two different but complementary approaches: topographic analysis using high-resolution elevation data from recent spacecraft missions and forward modeling of the dominant agent of lunar surface modification, impact cratering. The first investigation focuses on global surface roughness of the Moon, using a variety of statistical parameters to explore slopes at different scales and their relation to competing geological processes. We find that highlands topography behaves as a nearly self-similar fractal system on scales of order 100 meters, and there is a distinct change in this behavior above and below approximately 1 km. Chapter 2 focuses this analysis on two localized regions: the lunar south pole, including Shackleton crater, and the large mare-filled basins on the nearside of the Moon. In particular, we find that differential slope, a statistical measure of roughness related to the curvature of a topographic profile, is extremely useful in distinguishing between geologic units. Chapter 3 introduces a numerical model that simulates a cratered terrain by emplacing features of characteristic shape geometrically, allowing for tracking of both the topography and surviving rim fragments over time. The power spectral density of cratered terrains is estimated numerically from model results and benchmarked against a 1-dimensional analytic model. The power spectral slope is observed to vary predictably with the size-frequency distribution of craters, as well as the crater shape. The final chapter employs the rim-tracking feature of the cratered terrain model to analyze the evolving size-frequency distribution of craters under different criteria for identifying "visible" craters from surviving rim fragments. A geometric bias exists that systematically over counts large or small craters, depending on the rim fraction required to count a given feature as either visible or erased.

Large-eddy simulations of fully developed turbulent channel and pipe flows with smooth and rough walls

Studies in turbulence often focus on two flow conditions, both of which occur frequently in real-world flows and are sought-after for their value in advancing turbulence theory. These are the high Reynolds number regime and the effect of wall surface roughness. In this dissertation, a Large-Eddy Simulation (LES) recreates both conditions over a wide range of Reynolds numbers Re_τ = O(10²)-O(10⁸) and accounts for roughness by locally modeling the statistical effects of near-wall anisotropic fine scales in a thin layer immediately above the rough surface. A subgrid, roughness-corrected wall model is introduced to dynamically transmit this modeled information from the wall to the outer LES, which uses a stretched-vortex subgrid-scale model operating in the bulk of the flow. Of primary interest is the Reynolds number and roughness dependence of these flows in terms of first and second order statistics. The LES is first applied to a fully turbulent uniformly-smooth/rough channel flow to capture the flow dynamics over smooth, transitionally rough and fully rough regimes. Results include a Moody-like diagram for the wall averaged friction factor, believed to be the first of its kind obtained from LES. Confirmation is found for experimentally observed logarithmic behavior in the normalized stream-wise turbulent intensities. Tight logarithmic collapse, scaled on the wall friction velocity, is found for smooth-wall flows when Re_τ ≥ O(10⁶) and in fully rough cases. Since the wall model operates locally and dynamically, the framework is used to investigate non-uniform roughness distribution cases in a channel, where the flow adjustments to sudden surface changes are investigated. Recovery of mean quantities and turbulent statistics after transitions are discussed qualitatively and quantitatively at various roughness and Reynolds number levels. The internal boundary layer, which is defined as the border between the flow affected by the new surface condition and the unaffected part, is computed, and a collapse of the profiles on a length scale containing the logarithm of friction Reynolds number is presented. Finally, we turn to the possibility of expanding the present framework to accommodate more general geometries. As a first step, the whole LES framework is modified for use in the curvilinear geometry of a fully-developed turbulent pipe flow, with implementation carried out in a spectral element solver capable of handling complex wall profiles. The friction factors have shown favorable agreement with the superpipe data, and the LES estimates of the Karman constant and additive constant of the log-law closely match values obtained from experiment.