Normal Drag Research Articles

A geometric model for the formation of deformation band clusters

Arrays of closely-spaced (approximately <70 mm) sub-parallel cataclastic deformation bands are common structures in deformed, high-porosity (∼10–35%) sandstones. The distribution of strain onto many small-displacement deformation bands is thought by some to result from strain-hardening of the cataclasite within individual bands. Examination of both normal and strike-slip faults with displacements ≤7 m from southeastern Utah, USA, and the North Island of New Zealand suggests, however, that clusters of deformation bands systematically develop at fault geometric irregularities (e.g., fault bends, steps, relays, intersections and zones of normal drag). The strain-hardening model does not account for clustering of deformation bands at fault geometric irregularities or the associated widespread coalescence of bands, and is not unequivocally demonstrated by post-peak macroscopic mechanical responses in laboratory rock deformation experiments. A geometric model is proposed in which individual bands within clusters develop sequentially due to migration of incremental shear strains at fault geometric irregularities as part of a slip localisation, asperity removal and strain weakening process. The geometric model, which does not require strain hardening of the fault rock, applies for the duration of faulting and a range of rock types in the brittle upper crust.

Bi-stability of a pendular disk in laminar and turbulent flows

AbstractThe simple pendulum remains one of the most fundamental systems studied in physics. It is commonly used as a model to illustrate a broad variety of mechanisms in a wide range of areas. However, in spite of this popularity, subtle behaviours still remain to be discovered and to be explored when the pendulum is strongly coupled to fluid mechanics. This is for instance illustrated in recent studies by Neill, Livelybrooks &amp; Donnelly (Am. J. Phys., vol. 75, 2007, pp. 226–229) and Bolster, Hershberger &amp; Donnelly (Phys. Rev. E, vol. 81, 2010, pp. 1–6) which highlight the impact on a simple spherical pendulum of vortex shedding and added mass effects. In the present work we show that the equilibrium of a pendular disk facing a flow exhibits bi-stability and hysteresis. We give a simple interpretation of this behaviour in terms of a two-potential-well description, only requiring to know the angular dependence of the normal drag coefficient of an inclined plate. We investigate the influence of turbulence on the equilibrium of the pendulum in general and on the observed bi-stability in particular. Our results have potentially important fundamental and practical consequences: (i) they extend the attractiveness of the pendulum as a model to investigate generic questions related to bi-stable stochastic processes, (ii) they highlight important fluid dynamic mechanisms, including turbulent drag enhancement and fluid–structure interaction issues.

Electrostatically inflated gossamer space structure voltage requirements due to orbital perturbations

This paper explores the concept of using electrostatic forces for deployment of gossamer space structures. The Electrostatically Inflated Membrane Structure (EIMS) uses two conducting membranes that are interconnected through membrane ribs. An absolute electrostatic charge is applied to the structure through active charge emission. This causes repulsion between layers of lightweight membranes that inflates the EIMS system and tensions the membranes. Assuming positive tensions, the EIMS system is modeled as a rigid system. Typical orbital perturbations are considered such as solar radiation pressure, differential gravity, and atmospheric drag which may compress the structure leading to shape destabilization. Restricting the analysis in this paper to flat membranes, the minimum potentials required to exactly compensate for the worst case scenario of differential solar radiation pressure at geostationary altitudes are estimated to be on the order of hundreds of volts. In low Earth orbit, voltage magnitudes of several kilovolts are required to reach an inflation pressure to offset the normal compressive drag pressure.

Analysis of Attitude and Dynamics Characteristic of a Kind of Submerged Buoy

In this paper, the attitude and dynamical characteristics of a kind of submerged buoy are studied. The attitude of the buoy system is calculated relatively accurately by mathematical derivations and programming, in which all the tangent and normal fluid drag forces and elastic deformation of the mooring cable are considered. Based on the ANSYS FEA software, the model of system in fluid is established, which takes the effects of fluid drag forces, pretension and additional mass into account. Then the analysis of the effect on dynamics characteristic of the system by considering the attitude or not is carried out. The results indicate that, for small-scale submerged buoy system, the completed fluid forces should not be ignored, and the vibration of mooring system of submerged buoy is most likely to be low-frequency vibration, which should be avoided in some ways.

Wind-induced response and excitation characteristics of an inclined cable model in the critical Reynolds number range

This paper focuses on wind-induced vibrations of dry inclined bridge cables in the critical Reynolds number range. The cable response and the associated wind load characteristics are studied experimentally, in the third phase of a major wind tunnel investigation on cable aerodynamics at the National Research Council Canada. The displacement (and acceleration) response of a 6.7m long section cable model, 160mm in diameter, was monitored simultaneously with 162 surface pressure taps, for inclinations of 60°, 77° and 90°. The data corroborate the susceptibility of dry cables to respond, primarily in the across-flow direction, to load variations associated with transitions between flow regimes throughout the drag crisis region. The most vigorous vibrations (stopped at approximately 60% diameter response amplitude) were observed at 60°, with damping ratios below 0.2%. Significant “lock-in” between the lift force and the violent sway cable response was identified in terms of the transfer function between the two during the large vibration events. The large responses were confined to a narrow Reynolds number range, often at flow conditions giving the minimum normal (drag) coefficient and a significant derivative of the lift coefficient with respect to Reynolds number. Throughout the drag crisis region, significant variation in flow characteristics along the cable aligned at 60° has been observed, in terms of both mean pressure distributions and pressure fluctuations.

Undulatory Locomotion of Caenorhabditis elegans on Wet Surfaces

The physical and biomechanical principles that govern undulatory movement on wet surfaces have important applications in physiology, physics, and engineering. The nematode Caenorhabditis elegans, with its highly stereotypical and functionally distinct sinusoidal locomotory gaits, is an excellent system in which to dissect these properties. Measurements of the main forces governing the C. elegans crawling gait on lubricated surfaces have been scarce, primarily due to difficulties in estimating the physical features at the nematode-gel interface. Using kinematic data and a hydrodynamic model based on lubrication theory, we calculate both the surface drag forces and the nematode's bending force while crawling on the surface of agar gels within a preexisting groove. We find that the normal and tangential surface drag coefficients during crawling are ∼222 and 22, respectively, and the drag coefficient ratio is ∼10. During crawling, the calculated internal bending force is time-periodic and spatially complex, exhibiting a phase lag with respect to the nematode's body bending curvature. This phase lag is largely due to viscous drag forces, which are higher during crawling as compared to swimming in an aqueous buffer solution. The spatial patterns of bending force generated during either swimming or crawling correlate well with previously described gait-specific features of calcium signals in muscle. Further, our analysis indicates that one may be able to control the motility gait of C. elegans by judiciously adjusting the magnitude of the surface drag coefficients.

Comparative Analysis of Movement Characteristics of Lancelet and Fish Spermatozoa Having Different Morphologies

The movement characteristics of the sperm and their flagella obtained from a lancelet and 35 species from almost all orders of fishes were examined using high-speed video microscopy. The aim was to clarify the relationship between the motility parameters of the spermatozoa having different morphologies and how these motility parameters affect the swimming speed of the spermatozoa. The motility parameters representing the flagellar waveform, the wavelength, and the amplitude were neither very different between the spermatozoa of the different species nor related to the swimming speed. In contrast, the beat frequency was remarkably changed in the different spermatozoa and was proportional to the swimming speed. The maximum shear angle of the flagellar wave, which is directly related to the maximum sliding displacement between the doublet microtubules, remained nearly constant while the beat frequency varied widely; therefore, the spermatozoa beat in the constant sliding displacement mode. An analysis of the relationship between swimming speed and flagellar length revealed that short flagella were at a disadvantage in developing swimming speed; however, so were extra-long flagella. The ratio of the swimming speed to the wave velocity calculated from the wavelength and the beat frequency depended on the distance from the glass surface. The swimming speeds calculated using the original resistive-force theory were greater than the measured values. To rationalize the measured values, the ratio between the normal and tangential drag coefficient in the resistive-force theory was corrected; namely, 1.99 at 1 μm and 1.63 at 3 μm from the glass surface.

Characterization of geometry and normal drag coefficients of copper nets

Application of copper alloy netting in marine aquaculture has potential benefits associated with reduced biofouling, improved cage volume stability, structural strength and protection from predators. In this paper, experimental studies of drag forces on copper alloy net panels are reported. Based on these studies, empirical values for normal drag coefficients are proposed for various types of copper netting. These findings are compared to the previously published data on standard nylon nets. It is shown that copper nets exhibit significantly lower resistance to currents, which corresponds to lower values of drag coefficient.

Modeling of dynamic behavior of a single-point moored submersible fish cage under currents

The submergence behavior of a small volume fish cage in a single-point mooring system under currents is investigated using a numerical model. Results are validated by comparing to a scaled physical model tow test. The current induced submergence depth, as a function of net chamber solidity for various water velocities is examined. The system remains at the surface at low water velocities until the solidity dependent threshold is reached. At higher currents, the system enters an unstable submergence regime where a small change in the system design could significantly impact the predicted submergence depth. The distribution of current throughout the water column also plays an important role in the steady state response of the structure.Analytical formulas to approximate the dependence of normal drag coefficient for cylinders and spheres on Reynolds number (Re) are proposed. The formulas for cylinders expand the expressions of Choo and Casarella (1971) to account for the decrease in drag forces experimentally observed for 2×105<Re<106. Modeling of this effect is important for proper interpretation of Froude scale physical modeling data.

Ultrahigh‐resolution seismic reflection imaging of the Alpine Fault, New Zealand

High‐resolution seismic reflection surveys across active fault zones are capable of supplying key structural information required for assessments of seismic hazard and risk. We have recorded a 360 m long ultrahigh‐resolution seismic reflection profile across the Alpine Fault in New Zealand. The Alpine Fault, a continental transform that juxtaposes major tectonic plates, is capable of generating large (M &gt; 7.8) damaging earthquakes. Our seismic profile across a northern section of the fault targets fault zone structures in Holocene to late Pleistocene sediments and underlying Triassic and Paleozoic basement units from 3.5 to 150 m depth. Since ultrashallow seismic data are strongly influenced by near‐surface heterogeneity and source‐generated noise, an innovative processing sequence and nonstandard processing parameters are required to produce detailed information on the complex alluvial, glaciofluvial and glaciolacustrine sediments and shallow to steep dipping fault‐related features. We present high‐quality images of structures and deformation within the fault zone that extend and complement interpretations based on shallow paleoseismic and ground‐penetrating radar studies. Our images demonstrate that the Alpine Fault dips 75°–80° to the southeast through the Quaternary sediments, and there is evidence that it continues to dip steeply between the shallow basement units. We interpret characteristic curved basement surfaces on either side of the Alpine Fault and deformation in the footwall as consequences of normal drag generated by the reverse‐slip components of displacement on the fault. The fault dip and apparent ∼35 m vertical offset of the late Pleistocene erosional basement surface across the Alpine Fault yield a provisional dip‐slip rate of 2.0 ± 0.6 mm/yr. The more significant dextral‐slip rate cannot be determined from our seismic profile.

Submarine debris flow impact on suspended (free-span) pipelines: Normal and longitudinal drag forces

Computational fluid dynamics (CFD) analysis was employed to numerically simulate impact of clay-rich submarine debris flows on a suspended (free-span) pipeline at various angles of attack. The resultant horizontal drag force can be decomposed into two components: normal and parallel to the pipe axis. A method is presented for estimating the normal and longitudinal drag forces on a suspended pipeline and is applicable to a wide of impact situations. The work presented here complements the results of an earlier investigation into the drag forces on suspended and laid-on-seafloor pipelines. The previous investigation consisted of both physical laboratory experiments and CFD numerical analyses, for an impact situation normal to the pipe axis. The impact Reynolds numbers presented in this paper range between about 2 and 320. This range is considered appropriate for practical design purposes.

Stresses in planar normal faulting: shallow compression caused by fault-plane mismatch

Shallow horizontal compressive stress often occurs near the top of the hangingwall plate in numerical modelling of planar normal faulting, extending horizontally for up to 14 km from the fault plane. This compression is attributed to a potential downward mismatch between the dips of the opposing fault planes which would rotate differentially if unconstrained to remain in contact. The mismatch is suppressed by downward increasing lithostatic pressure which applies equal but opposite couples to the fault planes forcing them to remain in contact. This gives rise to shallow compression and deep tension on both sides of the fault. The potential mismatch originates partly from differential loading on opposite sides of the fault, but also from the anti-symmetrical shapes of the footwall and hangingwall plates. These two contributions oppose each other in normal faulting but reinforce in reverse faulting. The modelling also reveals large fault-parallel compressive stress adjacent to the footwall. This compression acts as a seal inhibiting fluid flow across the fault and preventing upflow adjacent to the footwall. In contrast, smaller fault-parallel tension adjacent to the hangingwall provides a low pressure channel for upward fluid flow adjacent to the fault, giving rise to a zone of weakness. Strain relief in this weak zone, in response to shallow mismatch compression, may explain the so-called normal fault drag near the top of the hangingwall.

Distribution and structural characteristics of the Xi’an Section of the Weihe Fault

The results of seismic deep reflection, high resolution refraction and shallow artificial seismic exploration indicate that the fault on the northern bank of the Weihe river is composed of two faults, one is the Yaodian-Zhangjiawan fault and the other is the Chuanzhang-Zuitou fault. The 22 km long Yaodian-Zhangjiawan fault of EW-striking starts from Chenjiagou via Yaodian town, Qianpai village, Bili village, Wujia town and Zhangjiawan to Jiajiatan. The 15 km long Chuanzhang-Zuitou fault striking near EW starts from Chuanzhang via Mabei to Zuitou. The Weihe fault offset the basement and upper crust, the reflecting layers of TQ, TN, TE and Tg are ruptured at depth of about 15 km. In the deep part, the Weihe fault and the secondary fault form a Y-shaped structure or a synthetic low angle intersection. The Weihe fault is a listric normal fault. The fault has obvious structural characteristics of a reversed-drag normal fault and a normal drag normal fault with the depth of 1 000 m, and also has the characteristics of syngenetic sediment. The Weihe fault is one of the faults which control the basin sediment, and it is the boundary fault of Xi’an depression and Xianyang salient. The depth of the fault decreases from the west to east gradually, the deep part intersects with the Lintong-Chang’an fault at the intersection part of Weihe River, Jinghe River and Bahe River and the shallow part connects with the Weinan-Jingyang fault. The seismic exploration results indicate that no fault exists on southern bank of the Weihe River.

Multidisciplinary approach to an extensional syncline model for the Mesozoic Cameros Basin (N Spain)

In this paper we explore the possibility of reconstructing the initial geometry of inverted basins using combined geophysical and geological methods: seismic reflection profiles, paleomagnetism, analogue modelling and 3D geometrical analysis. These techniques allow for some unknowns in the geometry and evolution of extensional sedimentary basins (mainly the normal drag–reverse drag geometrical problem) to be solved. The example chosen for checking these techniques is the Cameros Basin (northern Iberian Chain), formed during the Late Jurassic–Early Cretaceous, and inverted during the Tertiary compressional stage. According to the reconstruction proposed, the Cameros Basin can be characterised as a lens-shaped, syncline basin with maximum thickness of deposits of about 8000 m in its depocenter, gradually diminishing toward the North and South. The extensional geometry of the Cameros Basin is defined by: 1) a large-scale growth syncline over the major basement fault, with southward-dipping beds in the northern basin margin, forming a southward-opening sedimentary wedge, with upward-decreasing dip values (large-scale normal drag geometry); 2) roll-over anticlines at the contact between the pre-rift series against the normal fault limiting the basin (smaller-scale reverse drag geometry). The combined syncline–anticline syn-extensional structures were characterised by means of paleomagnetic analysis of a remagnetization acquired at the time of extension. Analogue models indicate that the development of syncline basin geometries in extensional settings, as the one interpreted for the Cameros Basin, is closely related to the presence of a detachment level in the pre-rift sequence above the main basement faults.

Faults in conventional flow simulation models: a consideration of representational assumptions and geological uncertainties

Even when geologically based methods are used to determine fault rock permeabilities and thicknesses for input into flow simulators, a wide range of simplifying assumptions regarding fault structure and content are still present. Many of these assumptions are addressed by defining quantitative and flexible methods for realistic parameterization of fault-related uncertainties, and by defining automated methods for including these effects routinely in full-field flow simulation modelling. The fault effects considered include: the two-phase properties of fault rocks; the spatial distributions of naturally variable or uncertain single-phase fault rock properties and fault throws; and the frequencies and properties of sub-resolution fault system or fault zone complexities, including sub-seismic faults, normal drag and damage zones, paired slip surfaces and fault relay zones. Innovative two-phase or geometrical upscaling approaches implemented in a reservoir simulator pre-processor provide transmissibility solutions incorporating the effect, but represented within the geometrical framework of the full-field flow simulation model. The solutions and flexible workflows are applied and discussed within the context of a sensitivity study carried out on two faulted versions of the same full-field flow simulation model. Significant influence of some of these generally neglected fault-related assumptions and uncertainties is revealed.

Two‐dimensional distinct element modeling of the structure and growth of normal faults in multilayer sequences: 1. Model calibration, boundary conditions, and selected results

The distinct element method is used for modeling the growth of normal faults in layered sequences. The models consist of circular particles that can be bonded together with breakable cement. Size effects of the model mechanical properties were studied for a constant average particle size and various sample widths. The study revealed that the bulk strength of the model material decreases with increasing sample size. Consequently, numerical lab tests and the associated construction of failure envelopes were performed for the specific layer width to particle diameter ratios used in the multilayer models. The normal faulting models are composed of strong layers (bonded particles) and weak layers (nonbonded particles) that are deformed in response to movement on a predefined fault at the base of the sequence. The modeling reproduces many of the geometries observed in natural faults, including (1) changes in fault dip due to different modes of failure in the strong and weak layers, (2) fault bifurcation (splaying), (3) the flexure of strong layers and the rotation of associated blocks to form normal drag, and (4) the progressive linkage of fault segments. The model fault zone geometries and their growth are compared to natural faults from Kilve foreshore (Somerset, United Kingdom). Both the model and natural faults provide support for the well‐known general trend that fault zone width increases with increasing displacement.

Geometry of half‐grabens containing a mid‐level viscous décollement

ABSTRACTIn this work, we explore by means of analogue models how different basin‐bounding fault geometries and thickness of a viscous layer within the otherwise brittle pre‐rift sequence influence the deformation and sedimentary patterns of basins related to extension. The experimental device consists of a rigid wooden basement in the footwall to simulate a listric fault. The hangingwall consists of a sequence of pre‐rift deposits, including the shallow interlayered viscous layer, and a syn‐rift sequence deposited at constant intervals during extension. Two different geometries exist of listric normal faults, dip at 30 and 60° at surface. This imposes different geometries in the hangingwall anticlines and their associated sedimentary basins. A strong contrast exists between models with and without a viscous layer. With a viscous décollement, areas near the main basement fault show a wide normal drag and the hangingwall basin is gently synclinal, with dips in the fault side progressively shallowing upwards. A secondary roll‐over structure appears in some of the models. Other structures are: (1) reverse faults dipping steeply towards the main fault, (2) antithetic faults in the footwall, appearing only in models with the 30° dipping fault and silicone‐level thicknesses of 1 and 1.5 cm and (3) listric normal faults linked to the termination of the detachment level opposite to the main fault, with significant thickness changes in the syn‐tectonic units. The experiments demonstrate the importance of detachment level in conditioning the geometry of extensional sedimentary basins and the possibility of syncline basin geometries associated with a main basement fault. Comparison with several basins with half‐graben geometries containing a mid‐level décollement supports the experimental results and constrains their interpretation.

Development of a Simulation Method for Body Behavior in Skydiving and Analysis of the Most Stable Position

The objective of this study was to develop a simulation method for analysis of body behavior in skydiving freefall and to clarify the most stable body position during the freefall. The details of the developed simulation method were firstly described. Using the simulation method, we conducted an optimizing calculation to maximize an objective function with respect to the stability in the freefall. It was found that the most stable position became arched one. In order to clarify the reason why the most stable position became arched, optimization with respect to a simple shaped object which consists of 20 cylinders was conducted. Then the angle to maximize the restoring moment for each cylinder element was analytically calculated and compared with the optimized angle. From the results, we conclude that the most stable position becomes arched mainly since the restoring moment at each part itself becomes maximum at that angle. We also conclude that the magnitude of the arch in the most stable position is determined by the ratio of the normal and tangential drag coefficients.

Mechanical Study of Standard Six Beat Front Crawl Swimming by Using Swimming Human Simulation Model

There are many dynamical problems in front crawl swimming which have not been fully investigated by analytical approaches. Therefore, in this paper, standard six beat front crawl swimming is analyzed by the swimming human simulation model SWUM, which has been developed by the authors. First, the outline of the simulation model, the joint motion for one stroke cycle, and the specifications of calculation are described respectively. Next, contribution of each fluid force component and of each body part to the thrust, effect of the flutter kick, estimation of the active drag, roll motion, and the propulsive efficiency are discussed respectively. The following results were theoretically obtained: The thrust is produced at the upper limb by the normal drag force component. The flutter kick plays a role in raising the lower half of the body. The active drag coefficient in the simulation becomes 0.082. Buoyancy determines the primal wave of the roll motion fluctuation. The propulsive efficiency in the simulation becomes 0.2.

Development of Swimming Human Simulation Model Considering Rigid Body Dynamics and Unsteady Fluid Force for Whole Body

The purpose of this study is to develop a swimming human simulation model considering rigid body dynamics and unsteady fluid force for the whole body, which will be utilized to analyze various dynamical problems in human swimming. First, the modeling methods and their formulations for the human body and the fluid force are respectively described. Second, experiments to identify the coefficients of the normal drag and the added mass are conducted by use of an experimental setup, in which a limb model rotates in the water, and its rotating angle and the bending moment at the root are measured. As the result of the identification, the present model for the fluid force was found to have satisfactory performance in order to represent the unsteady fluctuations of the experimental data, although it has 10% error. Third, a simulation for the gliding position is conducted in order to identify the tangential drag coefficient. Finally, a simulation example of standard six beat front crawl swimming is shown. The swimming speed of the simulation became a reasonable value, indicating the validity of the present simulation model, although it is 7.5% lower than the actual swimming.