J.P. Le Roux

A Hydrodynamic Classification of Grain Shapes

ABSTRACT The relationship between the fall velocity and orthogonal axis ratios of differently shaped grains with stable settling patterns is examined. Contrary to what is generally supposed, the ratio of the intermediate to the long diameter Di/Dl, which is related to the maximum projection area normal to the direction of settling, appears to have the least influence. The best correlation is shown by the ratio of the short to the long diameter Ds/Dl, with Ds/Di giving less accurate results. A modified hydrodynamic shape index given by [1 - (Ds/Dl)]x is proposed, which yields an improved, simplified settling equation applicable to spheroids, prolate and oblate spheroids, discs, cylinders, and ellipsoids. There appears to be a unique value of x for different grain shapes settling within specific ranges of Reynolds numbers. Based on the results of this study, a hydrodynamic classification of grain shapes is proposed.

Shape Entropy and Settling Velocity of Natural Grains

ABSTRACT The shape of sedimentary particles has been quantified by many different form indices, which have been utilized mainly in determining grain hydrodynamic behavior. Although the orthogonal axis dimensions required for calculating shape indices are easily measured in the case of grains larger than 2 mm, this is impractical for sand and silt. Different data sets of the settling velocity of natural quartz grains varying in size between 0.0001 and 1 cm are used in this paper to determine their mean Hofmann shape factor, which defines a polynomial curve. In the grain-size range from clay to medium-size pebbles, sand exhibits the highest sphericity, culminating with coarse to very coarse sand. The two polynomial equations describing the curve are employed to determine the settling velocity of natural grains, with a mean accuracy of 95.1 (±4.5) %. The latter is similar to that obtained for both smooth ellipsoids and angular grains, which suggests that grain roundness does not play a major role in the settling velocity of particles up to a Reynolds number of at least 4,200.

Determining the Neogene behavior of the Nazca plate by geohistory analysis

Geohistory analysis was performed on Neogene deposits south and north of La Serena, central Chile, to determine the behavior of the crust since the middle Miocene. The tectonic history of both study areas was found to be similar, but the timing of uplift and downwarp events at the two localities differs by 1.3 and 0.8 m.y., respectively, which we attribute to the approach and passing of the Juan Fernandez Ridge. From trigonometric relationships between the ridge trend, the plate vector, and the trend between the study areas, we calculated a plate-convergence rate of 6.2 cm/yr between 11.8 and 10.5 Ma and 10.1 cm/yr between 7.7 and 6.9 Ma. Rapid uplift commenced ca. 2.3 Ma, with a delay of 0.3 m.y. between the two study areas. Trigonometric constraints suggest the presence of a hitherto unsuspected oceanic plateau trending ∼014°, subducted below the present continental margin. Flat-plate subduction may thus be better developed where it is assisted by the combined buoyancy of ridge clusters instead of single subducting plateaus.

A simple method to predict the threshold of particle transport under oscillatory waves

Abstract Various methods of predicting the incipient motion of sediments under oscillatory waves have been proposed in the past, but most require that at least the wave orbital diameter d o be known. Methods based on the oscillatory Shields parameter θ ws , need the wave friction factor f w in order to calculate the critical threshold velocity, for which d o is also required. Other existing methods not requiring d o are only applicable to quartz grains and yield highly inaccurate results. In this paper, a new dimensionless threshold orbital velocity, based on all the important variables playing a role in wave transport, is plotted against the dimensionless settling velocity. This yields a relationship that allows the prediction of the threshold velocity from the wave period and grain size alone. The method has the advantages that it is valid for grains of varying size and density in laminar or turbulent fluids of different density and viscosity, does not require the wave orbital diameter, and is more accurate than previous equations.

Wave friction factor as related to the Shields parameter for steady currents

Abstract The wave friction factor fw is an important dimensionless parameter used to estimate wave-induced bed shear stress which, together with current-induced bed shear stress, controls sediment transport in the marine and lacustrine environment. However, fw is either overestimated or underestimated by existing equations. The matter is complicated by the fact that different equations must be used for hydrodynamically smooth or rough flows, but the limit between these two boundary conditions is still poorly defined. Some equations also require estimated values for the Nikuradse roughness length and the wave boundary layer thickness, neither of which can be derived accurately. It is, therefore, not surprising that fw values as calculated by existing equations differ by as much as a factor of 3. In the present paper, fw is related to the Shields parameter β for unidirectional currents, which not only facilitates the direct comparison and summation of bed shear stresses, but also yields a more accurate equation valid for grains of different density in any fluid irrespective of the boundary condition.

Application of the Hofmann shape entropy to determine the settling velocity of irregular, semi-ellipsoidal grains

Abstract In earlier studies on the settling velocity of irregular particles, it was observed that some of these grains settle faster than regular, symmetrical grains of the same weight and shape (as defined by the Janke shape factor). This was attributed to the smaller projection areas of irregular grains perpendicular to the fall direction. The effect of roundness was considered to be undetectable at Reynolds numbers less than 2. In this study, the original data are re-examined using the more accurate settling equations for smooth particles currently available. It is concluded that the higher settling rates of irregular particles reported by previous investigators should not necessarily be attributed to a reduction in their projection area, but may be partly related to their departure from typical spheroidal shapes. Roundness has a small, but nevertheless positive influence on the settling velocity. A new settling equation for irregular, semi-ellipsoidal grains is proposed, which has a mean error of only 5.15% for the particular data set, compared to 9.89% of the best equation based on the Janke shape factor. This equation can be used for pipette analysis of very fine sediments settling at Reynolds numbers less than 2.

Geotectonic evolution of the Bransfield Basin, Antarctic Peninsula: Insights from analogue models

Abstract The Bransfield Strait, located between the South Shetland Islands and the north-western end of the Antarctic Peninsula, is a back-arc basin transitional between rifting and spreading. We compiled a geomorphological structural map of the Bransfield Basin combining published data and the interpretation of bathymetric images. Several analogue experiments reproducing the interaction between the Scotia, Antarctic, and Phoenix plates were carried out. The fault configuration observed in the geomorphological structural map was well reproduced by one of these analogue models. The results suggest the establishment of a transpressional regime to the west of the southern segment of the Shackleton Fracture Zone and a transtensional regime to the south-west of the South Scotia Ridge by at least c. 7 Ma. A probable mechanism for the opening of the Bransfield Basin requires two processes: 1) Significant transtensional effects in the Bransfield Basin caused by the configuration and drift vector of the Scotia Plate after the activity of the West Scotia Ridge ceased at c. 7 Ma. 2) Roll-back of the Phoenix Plate under the South Shetland Islands after cessation of spreading activity of the Phoenix Ridge at 3.3 ± 0.2 Ma, causing the north-westward migration of the South Shetland Trench.

Estimation of Channel Sinuosity from Paleocurrent Data: A Method Using Fractal Geometry: DISCUSSION

The use of fractals to solve geological problems is an exciting new development in the Earth Sciences, and Ghosh (2000) is to be congratulated for his application of fractal geometry to estimate channel sinuosities from paleocurrent data. In spite of the skepticism voiced by Miall (1996) as to the validity of methods based on paleocurrent dispersal patterns, any progress in this field is to be welcomed. In fact, although the technique proposed by Ghosh (2000) represents an entirely new angle to solving the problem, the results closely approximate those produced by the method of Le Roux (1992) as modified in 1994 (Fig. 1). Surely, the good correlation between two independent techniques that are based purely on theoretical principles, must indicate that there is some merit in the paleocurrent approach. Figure 1 Comparison of sinuosity values for different consistency ratios using the methods of Le Roux (1994) and Ghosh (2000). Ghosh used a theoretical model considering the shape of a single meander, but the method …