Study of drag reduction by gas injection for power-law fluid flow in horizontal stratified and slug flow regimes

In this work, the drag reduction by gas injection for power-law fluid flow in stratified and slug flow regimes has been studied. Experimentswere conducted to measure the pressure gradient within air/CMC solutions in a horizontal Plexiglas pipe that had a diameter of 50mm and a length of 30 m. The drag reduction ratio in stratified flow regime was predicted using the two-fluid model. The results showed that the drag reduction should occur over the large range of the liquid holdup when the flow behaviour index remained at the low value. Furthermore, for turbulent gas-laminar liquid stratified flow, the drag reduction by gas injection for Newtonian fluid was more effective than that for shear-shinning fluid, when the dimensionless liquid height remained in the area of high value. The pressure gradient model for a gas/Newtonian liquid slug flow was extended to liquids possessing the Ostwald–de Waele power law model. The proposed model was validated against 340 experimental data point over a wide range of operating conditions, fluid characteristics and pipe diameters. The dimensionless pressure drop predicted was well inside the 20% deviation region for most of the experimental data. These results substantiated the general validity of the model presented for gas/non-Newtonian two-phase slug flows.

Atomic force microscopy observations of the topography of regenerated silk fibroin aggregations

How fibroin molecules fold themselves and further self-assemble into aggregations with specific structures when the solution concentration increases is the key to understanding the natural silk-forming process of the silkworm. A regenerated Bombyx mori silk fibroin solution was prepared, and serially diluted solutions were coated on aminated coverslips. Atomic force microscopy (AFM) observations of the topography of fibroin molecules revealed a transformation from rodlike aggregations 100-200 nm long to small globules 50 mn in diameter with decreasing concentrations. When the incubation duration increased, the aggregations of fibroin molecules showed a self-assembling process, which was measured with AFM. In particular, after the molecules were incubated for more than 20 min, rodlike micelles formed and were distributed evenly on the surface of the aminated slides. Flow chamber technology was used to study the effect of the shear loading on the topography of the fibroin molecular aggregations. After a shear loading was applied, larger rodlike particles formed at a higher incubation concentration in comparison with those at a lower concentration and were obviously oriented along the direction of fluid flow.

Standing wave of finite-amplitude in an circular basin with uneven bottom

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Oscillatory Flow Induced Hydrodynamic Forces upon a Pipeline near Erosive Sandy Seabed

An experimental study of the properties of hydrodynamic forces upon a marine pipeline is presented in this paper, in the equilibrium scour conditions for various Keulegan-Carpenter numbers and various initial relative gaps between pipeline and the erosive sandy seabed. The tests are conducted in a U-shaped oscillatory water tunnel with a sand box located at the bottom of the test section. According to the experimental results, the maximum horizontal forces on the pipelines with an initial gap to seabed will decrease to some extent due to scouring process. For engineering appliances, it seems safer to estimate wave induced forces on pipelines under the assumption that seabed is plane. However, it should be noticed that great changes would be brought to the frequency properties of lift forces because of the sandy scour beneath the pipeline, which occurs for certain KC numbers.

Numerical Analysis of the Effects of Free-Stream Thermo-Chemical State on the Test Model Flow Field in High-Enthalpy Tunnel

The effects of the free-stream thermo-chemical state on the test model flow field in the high-enthalpy tunnel are studied numerically. The properties of the free-stream, which is in thermo-chemical non-equilibrium, are determined by calculating the nozzle flow field. A free-stream with total enthalpy equal to the real one in the tunnel while in thermo-chemical equilibrium is constructed artificially to simulate the natural atmosphere condition. The flow fields over the test models (blunt cone and Apollo command capsule model) under both the non-equilibrium and the virtual equilibrium free-stream conditions are calculated. By comparing the properties including pressure, temperature, species concentration and radiation distributions of these two types of flow fields, the effects of the non-equilibrium state of the free-stream in the high-enthalpy shock tunnel are analyzed.

Characterization of the benthos, marine debris and bottom fish at Gray’s Reef National Marine Sanctuary

Executive Summary: Baseline characterization of resources is an essential part of marine protected area (MPA) management and is critical to inform adaptive management. Gray’s Reef National Marine Sanctuary (GRNMS) currently lacks adequate characterization of several key resources as identified in the 2006 Final Management Plan. The objectives of this characterization were to fulfill this need by characterizing the bottom fish, benthic features, marine debris, and the relationships among them for the different bottom types within the sanctuary: ledges, sparse live bottom, rippled sand, and flat sand. Particular attention was given to characterizing the different ledge types, their fish communities, and the marine debris associated with them given the importance of this bottom type to the sanctuary. The characterization has been divided into four sections. Section 1 provides a brief overview of the project, its relevance to sanctuary needs, methods of site selection, and general field procedures. Section 2 provides the survey methods, results, discussion, and recommendations for monitoring specific to the benthic characterization. Section 3 describes the characterization of marine debris. Section 4 is specific to the characterization of bottom fish. Field surveys were conducted during August 2004, May 2005, and August 2005. A total of 179 surveys were completed over ledge bottom (n=92), sparse live bottom (n=51), flat sand (n=20), and rippled sand (n=16). There were three components to each field survey: fish counting, benthic assessment, and quantification of marine debris. All components occurred within a 25 x 4 m belt transect. Two divers performed the transect at each survey site. One diver was responsible for identification of fish species, size, and abundance using a visual survey. The second diver was responsible for characterization of benthic features using five randomly placed 1 m2 quadrats, measuring ledge height and other benthic structures, and quantifying marine debris within the entire transect. GRNMS is composed of four main bottom types: flat sand, rippled sand, sparsely colonized live bottom, and densely colonized live bottom (ledges). Independent evaluation of the thematic accuracy of the GRNMS benthic map produced by Kendall et al. (2005) revealed high overall accuracy (93%). Most discrepancies between map and diver classification occurred during August 2004 and likely can be attributed to several factors, including actual map or diver errors, and changes in the bottom type due to physical forces. The four bottom types have distinct physical and biological characteristics. Flat and rippled sand bottom types were composed primarily of sand substrate and secondarily shell rubble. Flat sand and rippled sand bottom types were characterized by low percent cover (0-2%) of benthic organisms at all sites. Although the sand bottom types were largely devoid of epifauna, numerous burrows indicate the presence of infaunal organisms. Sparse live bottom and ledges were colonized by macroalgae and numerous invertebrates, including coral, gorgonians, sponges, and “other” benthic species (such as tunicates, anemones, and bryozoans). Ledges and sparse live bottom were similar in terms of diversity (H’) given the level of classification used here. However, percent cover of benthic species, with the exception of gorgonians, was significantly greater on ledge than on sparse live bottom. Percent biotic cover at sparse live bottom ranged from 0.7-26.3%, but was greater than 10% at only 7 out of 51 sites. Colonization on sparse live bottom is likely inhibited by shifting sands, as most sites were covered in a layer of sediment up to several centimeters thick. On ledge bottom type, percent cover ranged from 0.42-100%, with the highest percent cover at ledges in the central and south-central region of GRNMS. Biotic cover on ledges is influenced by local ledge characteristics. Cluster analysis of ledge dimensions (total height, undercut height, undercut width) resulted in three main categories of ledges, which were classified as short, medium, and tall. Median total percent cover was 97.6%, 75.1%, and 17.7% on tall, medium, and short ledges, respectively. Total percent cover and cover of macroalgae, sponges, and other organisms was significantly lower on short ledges compared to medium and tall ledges, but did not vary significantly between medium and tall ledges. Like sparse live bottom, short ledges may be susceptible to burial by sand, however the results indicate that ledge height may only be important to a certain threshold. There are likely other factors not considered here that also influence spatial distribution and community structure (e.g., small scale complexity, ocean currents, differential settlement patterns, and biological interactions). GRNMS is a popular site for recreational fishing and boating, and there has been increased concern about the accumulation of debris in the sanctuary and potential effects on sanctuary resources. Understanding the types, abundance, and distribution of debris is essential to improving debris removal and education efforts. Approximately two-thirds of all observed debris items found during the field surveys were fishing gear, and about half of the fishing related debris was monofilament fishing line. Other fishing related debris included leaders and spear gun parts, and non-gear debris included cans, bottles, and rope. The spatial distribution of debris was concentrated in the center of the sanctuary and was most frequently associated with ledges rather than at other bottom types. Several factors may contribute to this observation. Ledges are often targeted by fishermen due to the association of recreationally important fish species with this bottom type. In addition, ledges are structurally complex and are often densely colonized by biota, providing numerous places for debris to become stuck or entangled. Analysis of observed boat locations indicated that higher boat activity, which is an indication of fishing, occurs in the center of the sanctuary. On ledges, the presence and abundance of debris was significantly related to observed boat density and physiographic features including ledge height, ledge area, and percent cover. While it is likely that most fishing related debris originates from boats inside the sanctuary, preliminary investigation of ocean current data indicate that currents may influence the distribution and local retention of more mobile items. Fish communities at GRNMS are closely linked to benthic habitats. A list of species encountered, probability of occurrence, abundance, and biomass by habitat is provided. Species richness, diversity, composition, abundance, and biomass of fish all showed striking differences depending on bottom type with ledges showing the highest values of nearly all metrics. Species membership was distinctly separated by bottom type as well, although very short, sparsely colonized ledges often had a similar community composition to that of sparse live bottom. Analysis of fish communities at ledges alone indicated that species richness and total abundance of fish were positively related to total percent cover of sessile invertebrates and ledge height. Either ledge attribute was sufficient to result in high abundance or species richness of fish. Fish diversity (H`) was negatively correlated with undercut height due to schools of fish species that utilize ledge undercuts such as Pareques species. Concurrent analysis of ledge types and fish communities indicated that there are five distinct combinations of ledge type and species assemblage. These include, 1) short ledges with little or no undercut that lacked many of the undercut associated species except Urophycis earlii ; 2) tall, heavily colonized, deeply undercut ledges typically with Archosargus probatocephalus, Mycteroperca sp., and Pareques sp.; 3) tall, heavily colonized but less undercut with high occurrence of Lagodon rhomboides and Balistes capriscus; 4) short, heavily colonized ledges typically with Centropristis ocyurus, Halichoeres caudalis, and Stenotomus sp.; and 5) tall, heavily colonized, less undercut typically with Archosargus probatocephalus, Caranx crysos and Seriola sp.. Higher levels of boating activity and presumably fishing pressure did not appear to influence species composition or abundance at the community level although individual species appeared affected. These results indicate that merely knowing the basic characteristics of a ledge such as total height, undercut width, and percent cover of sessile invertebrates would allow good prediction of not only species richness and abundance of fish but also which particular fish species assemblages are likely to occur there. Comparisons with prior studies indicate some major changes in the fish community at GRNMS over the last two decades although the causes of the changes are unknown. Species of interest to recreational fishermen including Centropristis striata, Mycteroperca microlepis, and Mycteroperca phenax were examined in relation to bottom features, areas of assumed high versus low fishing pressure, and spatial dispersion. Both Mycteroperca species were found more frequently when undercut height of ledges was taller. They often were found together in small mixed species groups at ledges in the north central and southwest central regions of the sanctuary. Both had lower mode size and proportion of fish above the fishery size limit in heavily fished areas of the sanctuary (i.e. high boat density) despite the presence of better habitat in that region. Black sea bass, C. striata, occurred at 98% of the ledges surveyed and appeared to be evenly distributed throughout the sanctuary. Abundance was best explained by a positive relationship with percent cover of sessile biota but was also negatively related to presence of either Mycteroperca species. This may be due to predation by the Mycteroperca species or avoidance of sites where they are present by C. striata. Suggestions for monitoring bottom features, marine debris, and bottom fish at GRNMS are provided at the end of each chapter. The present assessment has established quantitative baseline characteristics of many of the key resources and use issues at GRNMS. The methods can be used as a model for future assessments to track the trajectory of GRNMS resources. Belt transects are ideally suited to providing efficient and quantitative assessment of bottom features, debris, and fish at GRNMS. The limited visibility, sensitivity of sessile biota, and linear nature of ledge habitats greatly diminish the utility of other sampling techniques. Ledges should receive the bulk of future characterization effort due to their importance to the sanctuary and high variability in physical structure, benthic composition, and fish assemblages. (PDF contains 107 pages.)

The ecological basis of fishery yield of the Puerto Rico-Virgin Islands Insular Shelf: 1987 Assessment

A literature review was conducted to locate information on the flow of energy from primary producers to the fishery stocks of the Puerto Rican-Virgin Islands insular shelf. This report uses site-specific information to describe the major ecological subsystems, or habitats, of the region, to identify the more common species and the subsystems in which they occur, to quantify productivity and biomass, and to outline trophic relationships. Discussions on each topic and subsystem vary in substance and detail, being limited by the availability and accessibility of information. (PDF contains 189 pages) Seven distinct subsystems are described: mangrove estuary, seagrass bed, coral reef, algal plain, sand/mud bottom, shelf break, and overlying pelagic. Over 50 tables provide lists of species found in each habitat on various surveys dating back to 1956. Estimates of density, relative abundance, and productivity are provided when possible. We evaluated whether sufficient information exists to support an analysis of the energy basis of fishery production in the area, beginning with the design and development of an ecosystem model. Data needs in three categories - species lists, biomass, and trophic relations - were examined for each subsystem and for each of three species groups - primary producers, invertebrates, and fish. We concluded that adequate data, sufficient for modeling purposes, are available in 16 (25%) of 64 categories; limited data, those requiring greater extrapolation, are available in 35 (55%) categories; and no data are available in 13 (20%) categories. The best-studied subsystems are seagrass beds and coral reefs, with at least limited data in all categories. Invertebrates, the intermediate link in the food web between primary producers and fishes, are the least quantified group in the region. Primary production and fishes, however, are relatively well-studied, providing sufficient data to support an ecosystem-level analysis and to initiate a modeling effort.

Aspects of quality control of wind profiler measurements in complex topography

It is well known in the scientific community that some remote sensing instruments assume that sample volumes present homogeneous conditions within a defined meteorological profile. At complex topographic sites and under extreme meteorological conditions, this assumption may be fallible depending on the site, and it is more likely to fail in the lower layers of the atmosphere. This piece of work tests the homogeneity of the wind field over a boundary layer wind profiler radar located in complex terrain on the coast under different meteorological conditions. The results reveal the qualitative importance of being aware of deviations in this homogeneity assumption and evaluate its effect on the final product. Patterns of behavior in data have been identified in order to simplify the analysis of the complex signal registered. The quality information obtained from the homogeneity study under different meteorological conditions provides useful indicators for the best alternatives the system can offer to build wind profiles. Finally, the results are also to be considered in order to integrate them in a quality algorithm implemented at the product level.

An Atomistic-Continuum Hybrid Simulation Of Fluid Flows Over Superhydrophobic Surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper, an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces, in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths, which cannot be obtained by molecular dynamics simulation alone.

Vortex dislocations in wake-type flow induced by spanwise disturbances

Vortex dislocations in wake-type flow induced by three types of spanwise disturbances superimposed on an upstream velocity profile are investigated by direct numerical simulations. Three distinct modes of vortex dislocations and flow transitions have been found. A local spanwise exponential decay disturbance leads to the appearance of a twisted chainlike mode of vortex dislocation. A stepped spanwise disturbance causes a streamwise periodic spotlike mode of vortex dislocation. A spanwise sinusoidal wavy disturbance with a moderate waviness causes a strong unsteadiness of wake behavior. This unsteadiness starts with a systematic periodic mode of vortex dislocation in the spanwise direction followed by the spanwise vortex shedding suppressed completely with increased time and the near wake becoming a steady shear flow. Characteristics of these modes of vortex dislocation and complex vortex linkages over the dislocation, as well as the corresponding dynamic processes related to the appearance of dislocations, are described by examining the variations of vortex lines and vorticity distribution. The nature of the vortex dislocation is demonstrated by the substantial vorticity modification of the spanwise vortex from the original spanwise direction to streamwise and vertical directions, accompanied by the appearance of noticeable vortex branching and complex vortex linking, all of which are produced at the locations with the biggest phase difference or with a frequency discontinuity between shedding cells. The effect of vortex dislocation on flow transition, either to an unsteady irregular vortex flow or suppression of the Kaacutermaacuten vortex shedding making the wake flow steady state, is analyzed. Distinct similarities are found in the mechanism and main flow phenomena between the present numerical results obtained in wake-type flows and the experimental-numerical results of cylinder wakes reported in previous studies.

An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths which cannot be obtained by molecular dynamics simulation alone.

Fluctuation characteristics of arc voltage and jet flow in a non-transferred dc plasma generated at reduced pressure

A torch with a set of inter-electrode inserts between the cathode and the anode/nozzle with a wide nozzle exit was designed to generate plasma jets at chamber pressures of 500–10 000 Pa. The variation of the arc voltage was examined with the change in working parameters such as gas flow rate and chamber pressure. The fluctuation in the arc voltage was recorded with an oscilloscope, and the plasma jet fluctuation near the torch exit was observed with a high-speed video camera and detected with a double-electrostatic probe. Results show that the 300 Hz wave originated from the tri-phase rectified power supply was always detected under all generating conditions. Helmholtz oscillations over 3000 Hz was detected superposed on the 300 Hz wave at gas flow rates higher than 8.8 slm with a peak to valley amplitude lower than 5% of the average voltage value. No appreciable voltage fluctuation caused by the irregular arc root movement is detected, and mechanisms for the arc voltage and jet flow fluctuations are discussed.

Electron flow through cytochrome P450

The cytochromes P450 (P450s) are a remarkable class of heme enzymes that catalyze the metabolism of xenobiotics and the biosynthesis of signaling molecules. Controlled electron flow into the thiolate-ligated heme active site allows P450s to activate molecular oxygen and hydroxylate aliphatic C–H bonds via the formation of high-valent metal-oxo intermediates (compounds I and II). Due to the reactive nature and short lifetimes of these intermediates, many of the fundamental steps in catalysis have not been observed directly. The Gray group and others have developed photochemical methods, known as “flash-quench,” for triggering electron transfer (ET) and generating redox intermediates in proteins in the absence of native ET partners. Photo-triggering affords a high degree of temporal precision for the gating of an ET event; the initial ET and subsequent reactions can be monitored on the nanosecond-to-second timescale using transient absorption (TA) spectroscopies. Chapter 1 catalogues critical aspects of P450 structure and mechanism, including the native pathway for formation of compound I, and outlines the development of photochemical processes that can be used to artificially trigger ET in proteins. Chapters 2 and 3 describe the development of these photochemical methods to establish electronic communication between a photosensitizer and the buried P450 heme. Chapter 2 describes the design and characterization of a Ru-P450-BM3 conjugate containing a ruthenium photosensitizer covalently tethered to the P450 surface, and nanosecond-to-second kinetics of the photo-triggered ET event are presented. By analyzing data at multiple wavelengths, we have identified the formation of multiple ET intermediates, including the catalytically relevant compound II; this intermediate is generated by oxidation of a bound water molecule in the ferric resting state enzyme. The work in Chapter 3 probes the role of a tryptophan residue situated between the photosensitizer and heme in the aforementioned Ru-P450 BM3 conjugate. Replacement of this tryptophan with histidine does not perturb the P450 structure, yet it completely eliminates the ET reactivity described in Chapter 2. The presence of an analogous tryptophan in Ru-P450 CYP119 conjugates also is necessary for observing oxidative ET, but the yield of heme oxidation is lower. Chapter 4 offers a basic description of the theoretical underpinnings required to analyze ET. Single-step ET theory is first presented, followed by extensions to multistep ET: electron “hopping.” The generation of “hopping maps” and use of a hopping map program to analyze the rate advantage of hopping over single-step ET is described, beginning with an established rhenium-tryptophan-azurin hopping system. This ET analysis is then applied to the Ru-tryptophan-P450 systems described in Chapter 2; this strongly supports the presence of hopping in Ru-P450 conjugates. Chapter 5 explores the implementation of flash-quench and other phototriggered methods to examine the native reductive ET and gas binding events that activate molecular oxygen. In particular, TA kinetics that demonstrate heme reduction on the microsecond timescale for four Ru-P450 conjugates are presented. In addition, we implement laser flash-photolysis of P450 ferrous–CO to study the rates of CO rebinding in the thermophilic P450 CYP119 at variable temperature. Chapter 6 describes the development and implementation of air-sensitive potentiometric redox titrations to determine the solution reduction potentials of a series of P450 BM3 mutants, which were designed for non-native cyclopropanation of styrene in vivo. An important conclusion from this work is that substitution of the axial cysteine for serine shifts the wild type reduction potential positive by 130 mV, facilitating reduction by biological redox cofactors in the presence of poorly-bound substrates. While this mutation abolishes oxygenation activity, these mutants are capable of catalyzing the cyclopropanation of styrene, even within the confines of an E. coli cell. Four appendices are also provided, including photochemical heme oxidation in ruthenium-modified nitric oxide synthase (Appendix A), general protocols (Appendix B), Chapter-specific notes (Appendix C) and Matlab scripts used for data analysis (Appendix D).

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.