Basin Shapes Research Articles

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Generation of Basin-Induced Surface Waves Observed in the Tokachi Basin, Hokkaido, Japan.

Recent studies on basin-induced surface waves observed in deep earthquake seismograms at basin stations have shown that the excitation strength of the surface waves varies with earthquakes, as well as the basin shapes. We investigated the variation in basin-induced surface waves with earthquakes by a combination of observational and numerical studies, selecting the Tokachi Basin, Hokkaido, Japan, as the test site. A detailed comparison between the seismograms observed at the basin and rock sites for nearby and intermediate-depth earthquakes shows that the excitation strength of basin-induced surface waves with a predominant frequency of about 0.3 Hz strongly depends on the frequency content and incident angle of S-waves impinging on the basin. The observational results are complemented with two-dimensional modelings of SH and P-SV wavefields using the pseudospectral method, which successfully reproduce the effects of the frequency content and incident angle of incident S-waves. The simulation results also show that the basin edge slopes play an important role in the excitation of basin-induced surface waves.

The topography of optimal drainage basins

A model for drainage networks and their associated landscapes has been developed. This model is based on the minimum energy dissipation principle and an empirical relationship s ∼ Qα between the slope s of each link in a channel network and the mean annual discharge Q that flows through it. The model was studied using six different values for the exponent α. The surfaces of these minimum energy dissipation drainage networks appear to be more complex than simple self‐affine fractals. The drainage basins in these optimal drainage networks have power law size (area) distributions with a universal exponent, which is independent of the value of α. For the minimum energy dissipation drainage networks obtained using a particular value for α, the basin shapes are similar to each other. An empirical relationship has also been found to relate the basins' “length‐width” ratio to the value of α.

Optimal channel networks: A framework for the study of river basin morphology

Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three‐dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by‐product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiring only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature river basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures.

Influence of Anticlinal Growth on Upper Miocene Turbidite Deposits, Elk Hills Field, Kern County, California

Growth of subsea anticlines during deposition of the upper Miocene 24Z and 26R sandstones at Elk Hills caused the development of several sinuous, lenticular sand bodies. later structural growth enhanced the trap characteristics of these sandstones. Both sandstones are in the uppermost portion of the Elk Hills Shale Member of the Monterey Formation and contain channel-fill and overbank deposits of sand-rich turbidite systems. At the onset of turbidite deposition, low relief subsea anticlines separated broad basins which progressively deepened to the northeast. Channel-fill deposits of coarse-grained sand generally followed the axes of these northwest-southeast-trending basins. At several sites, channel-fill deposits also spilled north across anticlinal axes into the next lower basins. Wide bands of overbank sand and mud were deposited at sand body edges on the flat basin floors. Midway through turbidite deposition, a period of anticlinal growth substantially raised subsea relief. Channel-fill deposits continued in narrower basins but passed north into deeper basin only around well-defined sites at the anticlines' downplunge termini. Narrow basin shapes and higher anticline relief prevented significant overbank deposition. With Pliocene to Holocene uplift of the late Miocene structural trends, stratigraphic mounding of the north-directed channel-fill deposits helped create structural domes at 24Z, 2B andmore » Northwest Stevens pools. In sand bodies lacking significant overbank deposits prevented oil entrapment in sand bodies deposited at times of low anticlinal relief.« less

MATHEMATICAL ANALYSIS OF ARTIFICIAL RECHARGE FROM BASINS1

ABSTRACT: One of the most common methods of artificial recharge to the ground water is from basins. In this paper, seven analytical solutions that describe artificial recharge from basins are presented. Most of these solutions are derived by directly solving the general partial differential equation for ground water flow. The solutions differ in that they use different boundary conditions, basin shapes, and consider the nonlinearity of the artificial recharge problem differently. Use of each analytical solution is demonstrated in this paper by application to an example problem. A comparison of each analytical solution presented in this paper was made to give suggestions on their use, their ease of implementation, and their relative agreement. Although no attempt is made in the paper to conclude which analytical solution is best for all problems, some general conclusions can be stated on the applicability of the various analytical solutions. Of the analytical solutions presented in this paper, Glovers and Hantush's solutions for rectangular recharge basins are highly recommended. Baumanns solution for a circular basin also gave fairly reliable results and is very easy to evaluate numerically.

Evaluation of In-Situ Pavement Moduli from Deflection Measurements

Abstract At present, there is no direct solution that provides the pavement in-situ layer moduli from deflection measurements. Current methods evaluate the pavement layer moduli from deflection measurements using either empirical approaches or layered elastic computer programs with iterative solutions. In this study mechanistically based typical curves are developed to evaluate the moduli of the pavement layers: surface, base, subbase, and subgrade from surface deflection measurements. The curves are developed using the Chevron N-layer computer program with a large number of typical combinations of layer thicknesses and material moduli. The load is assumed to be uniformly applied on a single circular plate with a 304.8-mm (12-in.) diameter, a typical condition of the falling weight deflectometer and the road rater with a single circular plate. Twenty-four sets of curves are developed representing a wide range of layer thicknesses and deflection basin shapes. Therefore, if the layer thicknesses are known and the surface deflection measurements are determined, the four moduli of the pavement layers can be evaluated. The developed curves are simple to use without the need for previous empirical relationships or computer analysis. The curves developed here are based on static analysis.

Sedimentation in Pull-Apart Basins: Active Examples in Eastern Turkey

The Erzincan, Susehri, Niksar, and Lake Hazar basins are actively evolving pull-apart basins in eastern Turkey. Their structural, drainage, and depositional systems generally support a pull-apart basin sedimentation model based on ancient pull-apart basin deposits. This model involves marginal coarse-grained sedimentation adjacent to master faults, axial fine-grained sedimentation away from master faults, and high sedimentation rates. However, studies of the Turkish pull-apart basins suggest the following refinements in the model. (1) Detailed sedimentary facies patterns and the dominant facies of a pull-apart basin vary according to basin shape, climate, drainage character, and volcanic activity. Depositional environments near fault-bounded margins include alluvial fan, fan delta, and alluvial apron. Depositional environments in central areas away from fault-bounded margins include active braid plain, inactive braid plain, meander plain, salt playa, marsh, lacustrine, mouth-bar delta, and volcanic. (2) If internally drained, a pull-apart basin is likely to contain axial and transverse drainages. If externally drained, the drainage pattern varies and may exit the basin axially or transversely. (3) Pull-apart basin shapes are not necessarily rhomboidal. Comparison of data from the Turkish pull-aparts with other modern and ancient pull-apart basins suggests that sediment thickness (y) is related to length of a pull-apart basin parallel to master fault overlap (x) by the equation y = .08x + .26. This relationship predicts sediment thickness in the Erzincan, Susehri, Niksar, and Lake Hazar pull-apart basins is 2.9, 2.1, 1.5, and 0.68 km, respectively.

The classification of Mixed-Layer Dynamics of Lakes of Small to Medium Size

Abstract An analysis of the time scales of processes relevant to wind mixing in lakes indicates that the response of a lake to wind may be classified into four regimes with respect to thermocline deepening behavior, depending on the relative sizes of the parameters describing wind strength, basin size and stratification. The dependence is described in terms of a mixed layer Richardson number and the aspect ratio of the mixed layer thickness to length. The classification is used to explain the diversity of phenomena reported in the literature for wind events in a number of different lakes and laboratory tanks which are either short enough or narrow enough for rotational effects to be unimportant. The classification is derived with reference to a two-layer, rectangular basin in the absence of Coriolis forces and surface heating. The classification is exended in a simple way to more realistic stratifications and basin shapes to predict the overall mixing features of a wind event. Response to wind varies from...

Classification of nested tributary basins in analysis of drainage basin shape

Tributary basins in Strahler‐ordered drainage systems may be classified as order w formative or order w excess according to whether the order w mouth stream outflows into a stream of order equal to or greater than w. This classification distinguishes spatial nesting among tributary basins, formative tributaries locating farther from the main basin mouth than excess tributaries. Basin shape is analyzed by using standard indices and applying the method of unrolling perimeter radials for Fourier series analysis. The empirical results from 336 drainage basin shapes demonstrate differentiation of basin shapes between gemorphologic environments, between basin order levels 3 and 4, and between formative and excess tributary basin types at the order 3 level. The order level contrasts indicate scale dependency in drainage basin shapes, and the tributary order type contrasts suggest spatial nesting controls such that basins sampled solely by Strahler order level are not homogeneous with regard to shape properties.

The relation between mainstream length and area in drainage basins

Hack and Gray have both found that data on mainstream lengths and basin areas can be represented by the equation L′ = CAn′, where C is about 1.4 (measurements in miles), and n′ is about 0.6. Hack has suggested that the deviation of n′ from ½ can be explained by an elongation of drainage basin shapes with increasing area. We point out that variations of stream sinuosity with area can also affect the value of n′. A simple approximate formula is deduced that relates mainstream length, sinuosity, basin shape, and area, and shows how the contributions of sinuosity and shape variation to the quantity (n′ − ½) may be separated and evaluated. Data that illustrate these points are presented for both real and simulated stream systems. Our conclusions are: (1) Variation in mainstream sinuosity with area can be responsible for a significant part of the deviation of n′ from ½. (2) The generally accepted statement that drainage basins become more elongated as their area increases needs further investigation.

The Foundations of Atolls: A Discussion

The problem of the origin of barrier reefs and atolls is biological as well as geological. By failing to determine the organic composition and the age of elevated limestones, some workers have given much undeserved support to the theory of subsidence. Uncon-formable contacts between elevated limestones and older volcanics on tropical islands have little bearing on the subsidence theory unless the limestones are coralliferous. Recent studies show that many elevated coral reefs have a foundation of non-coralliferous limestone, and in some cases this limestone is geologically considerably older. The basin-shaped limestone islands in Fiji which certain writers have interpreted as elevated atolls are not usually to be so considered. Under proper conditions the basins are formed by subaërial solution regardless of the structure, age, or organic composition of the limestone. Even tiny remnants of so-called much dissected, elevated atolls show individually well-developed basin shapes.