Disturbed periodic model for river meanders

Although river meanders are not perfectly regular their serial statistics show periodic tendencies which cannot be explained by previous stochastic models. The regular and random approaches to meander geometry can be reconciled in a disturbed periodic model with separate scale, sinuosity, and irregularity parameters. Meandering is viewed as a deterministic oscillation but irregularity is introduced by quasi-random variability in valley-floor topography and materials. For stability such a model needs either a Bagnold type limit on bend curvature or frictional damping of the oscillatory response to individual disturbances. Realistic statistical properties are derived for the second case. The differential equation for direction can be approximated by a second-order autoregression, which generates realistic simulated patterns and gives a good fit to natural direction series.     

Spatial growth of gulf stream meanders

Abstract

An attractive explanation for the observed spatial growth of the Gulf Stream meanders is that the meanders are spatially growing unstable waves. The results of a calculation based on a simple two-layer model of baroclinically unstable flow presented here support this idea. The model is a familiar one with the energy for the growth of the meander perturbations coming from the potential energy available in the geostrophic tilt of the interface between the two layers due to their velocity shear. In order to distinguish between spatial and temporal growth, it IS necessary to assume that the meanders are generated in a localized region, or equivalently, that the meanders are upstream disturbances which are amplified as they enter a region of unstable flow. This assumption is implemented mathematically through the use of a Green's function which governs the propagation of the meanders. Analysis of the spatial and temporal characteristics of the Green's function leads to a criterion which must he satisfied if the meanders arc to grow spatially. This criterion is that the mean flow velocity must be sufficiently greater than the velocity shear, U_m > √2 U_s, in order to have spatial growth. This simply means that the growing meanders must be washed downstream faster than they spread upstream, or equivalently the spatial growth is due to downstream advection of growing disturbances. The actual Gulf Stream flow is in fair agreement with this criterion.     

A universal kriging approach for spatial functional data

In a wide range of scientific fields the outputs coming from certain measurements often come in form of curves. In this paper we give a solution to the problem of spatial prediction of non-stationary functional data. We propose a new predictor by extending the classical universal kriging predictor for univariate data to the context of functional data. Using an approach similar to that used in univariate geostatistics we obtain a matrix system for estimating the weights of each functional variable on the prediction. The proposed methodology is validated by analyzing a real dataset corresponding to temperature curves obtained in several weather stations of Canada.     

A universal thermal equation-of-state

Evidence has steadily accumulated to show that at high temperatures (above the Debye temperature, θ) the thermal pressure, P_TH, of solids, is linear with T to a close approximation. This empirical finding yields a simple relationship between P, V, and T quite useful for the computation of the equation-of-state (EOS). For geophysical applications, the empirical data is, so far, limited to a few minerals, all of which are important to our geophysical models of the Earth. The same results have been found for a variety of types of solids, including alkali metals, noble gas solids, alkali halides and metals in addition to minerals. It is argued that the linearity between P_TH and T is a general high-temperature property of solids. This includes minerals. Thus it is proposed that there exists a common thermal EOS which transcends the chemical bonding type and crystallographic class.     

A universal field equation for dispersive processes in heterogeneous media

When formulated properly, most geophysical transport-type process involving passive scalars or motile particles may be described by the same space–time nonlocal field equation which consists of a classical mass balance coupled with a space–time nonlocal convective/dispersive flux. Specific examples employed here include stretched and compressed Brownian motion, diffusion in slit-nanopores, subdiffusive continuous-time random walks (CTRW), super diffusion in the turbulent atmosphere and dispersion of motile and passive particles in fractal porous media. Stretched and compressed Brownian motion, which may be thought of as Brownian motions run with nonlinear clocks, are defined as the limit processes of a special class of random walks possessing nonstationary increments. The limit process has a mean square displacement that increases as t^α+1 where α > −1 is a constant. If α = 0 the process is classical Brownian, if α < 0 we say the process is compressed Brownian while if α > 0 it is stretched. The Fokker–Planck equations for these processes are classical ade’s with dispersion coefficient proportional to t^α. The Brownian-type walks have fixed time step, but nonstationary spatial increments that are Gaussian with power law variance. With the CTRW, both the time increment and the spatial increment are random. The subdiffusive Fokker–Planck equation is fractional in time for the CTRW’s considered in this article. The second moments for a Levy spatial trajectory are infinite while the Fokker–Planck equation is an advective–dispersive equation, ade, with constant diffusion coefficient and fractional spatial derivatives. If the Lagrangian velocity is assumed Levy rather than the position, then a similar Fokker–Planck equation is obtained, but the diffusion coefficient is a power law in time. All these Fokker–Planck equations are special cases of the general non-local balance law.     

A universal nutrient application strategy for the bioremediation of oil-polluted beaches

Biostimulation by nutrient application is a viable technology for restoring oil-contaminated beaches. Maximizing the nutrient residence time is key for achieving a rapid cost-effective cleanup. We considered the nutrient injection strategy through a perforated pipe at the high tide line and we simulated numerically beach hydraulics, which allowed us to estimate the optimal injection flow rate of nutrient solution. Our results indicate that the optimal application is one that starts following the falling high tide and lasts for half tidal cycle. The saturated wet-front of the nutrient solution on the beach surface would move seaward with the same speed of the falling tide keeping a constant distance with the tide line. The numerical results were generalized to beaches of wide ranges of hydraulic and tidal properties using a novel dimensionless formulation for water flow and solute transport in porous media. Nomographs were presented to provide the flow rate based on four parameters: The beach slope and hydraulic conductivity, and tidal amplitude and period.     

A fluid model for the shape of accretionary wedges

In this paper the accretionary wedges landward of most oceanic trenches are modelled assuming a Newtonian fluid rheology.It is shown that lubrication theory is applicable and that the addition of material to the wedges can be neglected in determining the shape of the wedges. The predicted shape of the wedges is in good agreement with bathymetric profiles across the Kurile, Ryukyu and Aleutian wedges. From the shape of the above wedges, it is deduced that accretionary sediments have viscosities between 10¹⁸ and 10¹⁹ poise.     

A cross-shore suspended sediment transport shape function parameterisation for natural beaches

A new field-based parameterisation (‘shape function’) describing the distribution of cross-shore suspended sediment transport across a beach profile is presented. Time-averaged and depth-integrated suspended sediment fluxes were measured over 39 tides at Sennen Cove, Cornwall, UK, for a range of wave conditions (offshore significant wave heights 0.1–2.5 m). The suspended sediment flux data were heuristically separated into four transport components: (1) mean flux in the surf/shoaling zone; (2) oscillatory flux in the surf/shoaling zone; (3) onshore flux in the swash/inner surf zone and (4) offshore flux in the swash/inner surf zone. Each of these transport components was related to the local water depth (h) normalised by the breakpoint depth (h_b) and the four resulting suspended transport shape functions were combined to form a total suspended load shape function. Each shape function component is scaled independently by the wave energy level through h_b. The total suspended load shape function predicts onshore sediment transport under low-energy conditions, with peaks at the breakpoint and in the swash zone, in agreement with the field observations. Under high-energy conditions the total suspended load shape function predicts onshore transport in the shoaling zone, offshore transport in the surf zone and onshore transport in the inner swash zone.     

A landscape shape index-based sampling approach for land cover accuracy assessment

Spatial sampling design is one of the key steps in land cover accuracy assessment, and many traditional sampling approaches may not achieve credible spatial sampling due to the high spatial heterogeneity of land cover. This paper characterizes the spatial heterogeneity with three-level LSIs and determines the subsequent sample sizes and their spatial distributions. The three-level LSIs are rLSI in a region, cLSI for each land cover class and uLSI in each geographic sampling unit in the region. The rLSIs are used to derive appropriate sample sizes in the target regions. The cLSIs are used to assure that larger sample numbers are allocated to land cover classes with higher spatial heterogeneity. The uLSIs provide useful measures for selecting optimal geographic units in which sample sites will be located. This LSI-based sampling approach can derive the sample sizes and determine their distributions in an adaptive way according to the spatial heterogeneity. An experimental case study further demonstrates that the LSI-based sampling approach obtains more appropriate sample sizes for each region, sufficient sample numbers for rare classes, and optimal sample distributions in the geographical space.     

A simple formula for shape and depth determination from residual gravity anomalies

This paper presents a simple method for shape and depth determination of a buried structure from residual gravity anomalies along profile. The method utilizes the anomaly values of the origin and characteristic points of the profile to construct a relationship between the shape factor and depth of the causative source. For fixed points, the depth is determined for each shape factor. The computed depths are then plotted against the shape factor representing a continuous monotonically increasing curve. The solution for the shape and depth of the buried structure is then read at the common intersection point of the depth curves. This method is applied to synthetic data with and without random errors. Finally, the validity of the method is tested on two field examples from the USA.     

A universal approach to alpha-cellulose extraction for radiocarbon analysis of 14C-free to post-bomb ages

In order to expand our in-house capabilities for tree-ring ¹⁴C measurements in support of atmospheric ¹⁴C reconstruction research, we designed a very versatile and inclusive procedure to produce high-quality α-cellulose homogenized extracts. The procedure can be easily scaled up or down (≤10 to 40 samples) and/or modified on demand (chemical steps can be easily adjusted to sample requirements as well, e.g., increased or diminished, according to the amount of available material and/or contaminants to be removed). Procedure setups are straightforward, and all products and instruments required are off-the-shelf. One to three days may be used to extract chipped wood to α-cellulose homogenized fibers that can be further used by high-precision ¹⁴C accelerator mass spectrometry (AMS) analysis. The full procedure, which includes recommendations for wood reduction to chips, chemical treatment, and ¹⁴C-AMS sample processing, measurements and data handling was tested on over 110 wood samples from post-bomb 1950AD to ¹⁴C limit. Radiocarbon results were in the order of 0.29% or better, based on replication and regardless of the age group studied. Best background was in the order of 54 kyrs BP, without any type of background correction. Fourier transform infrared (FTIR) analysis was used as a characterizing tool to confirm the removal of unwanted carbon compounds during the production of α-cellulose extracts. For those analysis, we chose woods that are normally rich in resinous and parenchymatous structures. Results confirmed that our protocol produces pure α-cellulose extracts for ¹⁴C analysis, and therefore this procedure can be safely applied to atmospheric ¹⁴C reconstructions at pantropical regions.     

A statistical approach to the earth's shape

Oneapproach to the study of the distribution of the Earth's surface elevation is to look for the log normal curves that best fit the hypsographic curve.A new calculation of the parameters of the log normal curves, obtained using elevation data provided by the National Geophysical Data Center Boulder Co., is presented here.A anomalous flattening is observed for the ellipsoid which best fits the oceanic abyssal plain. The global shape of the oceanic floors seems to be less flattened than the geoid, with a marked asymmetry between the two hemispheres. There is a close correlation between the distribution of continents and the elevation of oceanic floors as a function of latitude.     

Effect of different meander curvatures on spatial variation of coherent turbulent flow structure inside ingoing multi-bend river meanders

In this paper, the effect of different curvatures on the spatial variation of coherent flow structure inside two physical models with both strongly curved and mild multi-bend meanders is investigated. Three dimensional flow velocities at three sequential meanders were measured using an Acoustic Doppler Velocity meter (Micro-ADV). Three dimensions of flow velocity are classified into two major classes and eight different bursting events. The contribution probability and transition probability of each zone is calculated from experimental data. The results indicated that the effect of curvature in sequential bends was important particularly for strongly curved bends. The contribution probability of the events for strongly curved meanders with relative curvature (R_c/B) of 2.6 were found to be higher than for mild curved meanders with relative curvature (R_c/B) of 4.43. The minimum contribution probability was found in external inward interaction event. In addition, analysis of bursting events showed that the highest values of transition probabilities occurred in the stable organizations for both models. The influences of different curvatures on distributions of the Reynolds shear stress, the turbulent kinetic energy, the streamwise velocity and the vertical velocity were also shown to be in good agreement with eroded bed. The above results can be useful for finding meandering patterns inside rivers and also in river training works.     

A new isolation device using shape memory alloy and its application for long-span structures

The key points to consider in determining the effectiveness of using structural isolation with shape memory alloys (SMA) are the constitutive model, the SMA isolation device and the analysis method. In this paper, a simplifi ed constitutive model based on the classic theory of plasticity is proposed to simulate the behavior of the superelasticity of the SMA, in which the martensite volume fraction is considered as one of the state variables. Comparisons between simulation results and experimental results ar...     

Overbank deposition along the concave side of the Red River meanders,Manitoba, and its geomorphic significance

Slow earth sliding is pervasive along the concave side of Red River meanders that impinge on Lake Agassiz glaciolacustrine deposits. These failures form elongated, low‐angled (c. 6 to 10°) landslide zones along the valleysides. Silty overbank deposits that accumulated during the 1999 spring freshet extend continuously along the landslide zones over hundreds of metres and aggraded the lower slopes over a distance 50 to 80 m from the channel margin. The aggradation is not obviously related to meander curvature or location within a meander. Along seven slope profiles surveyed in 1999 near Letellier, Manitoba, the deposits locally are up to 21 cm thick and generally thin with increasing distance from, and height above, the river. Local deposit thickness relates to distance from the channel, duration of inundation of the landslide surface, mesotopography, and variations in vegetation cover. Immediately adjacent to the river, accumulated overbank deposits are up to 4 m thick. The 1999 overbank deposits also were present along the moderately sloped (c. 23 to 27°) concave banks eroding into the floodplain, but the deposits are thinner (locally up to c. 7 cm thick) and cover a narrower area (10 to 30 m wide) than the deposits within the landslide zones. Concave overbank deposition is part of a sediment reworking process that consists of overbank aggradation on the landslide zones, subsequent gradual downslope displacement from earth sliding, and eventually reworking by the river at the toe of the landslide. The presence of the deposits dampens the outward migration of the meanders and contributes to a low rate of contemporary lateral channel migration. Concave overbank sedimentation occurs along most Red River meanders between at least Emerson and St. Adolphe, Manitoba. © Her Majesty the Queen in right of Canada.     

A theoretical model for change of shape of spring-water radon anomalies with epicentral distance

A model for radon anomalies before earthquakes, with a relatively fast increase in radon concentration at the beginning of the anomaly, is postulated. A calculation based on this model shows that a parameter can be deduced from the form of the radon anomalies, which depends on the epicentral distance of the measurement point. After adjustment of some parameters the model calculation is in good agreement with observed earthquake precursor anomalies.     

基于韦伯-费希纳定律的营养状态普适韦伯指数公式

在适当设定各营养状态指标参照值Cj0的基础上,用相应于参照值Cj0的指标规范值xj作为基于韦伯-费希纳定律的营养状态指数公式中的刺激量.由于各项指标的同级营养状态标准的规范值xjl差异不大,从而可认为各指标的营养状态韦伯指数公式都具有一个共同适用的韦伯常数α,并采用智能解域搜索算法优化α,得出对所有14项营养指标皆适用的营养状态普适韦伯指数公式.将营养状态韦伯指数公式应用于数十个湖泊的富营养化评价,并与其它多种方法的评价结果进行比较,结果表明该公式不但理论依据充分,而且具有简单、适用的特点.     

泛协克里金的对偶形式

针对最一般的泛协克里金,借助矩阵分析方法表述出了它的对偶形式,并用空间自伴算子和空间共轭空间的观点给对偶克里金的实质作出了解释．借助对偶克金的结果,把泛协克里金的估计结果表成线性插值形式,从而请楚地显示出泛协克里格估计的插值和外推性质．     

A new indicator of elastic spectral shape for the reliable selection of ground motion records

How to select a limited number of ground motion records (GMRs) is an important challenge for the non‐linear analysis of structures. Since epsilon (ε_Sa) is an indicator of spectral shape, which has a significant correlation with the non‐linear response of a structure, the selection of GMRs based on the hazard‐related target ε_Sa is a reasonable approach. In this paper, an alternative indicator of spectral shape is proposed, which results in a more reliable prediction of the non‐linear response for the structures with the natural period of 0.25 to 3.0 s. This new parameter, named eta (η), is a linear combination of ε_Sa and the peak ground velocity epsilon (ε_PGV). It is shown that η, as a non‐linear response predictor, is remarkably more efficient than the well‐known and convenient parameter ε_Sa. The influence of η‐filtration in the collapse analysis of an eight‐story reinforced concrete structure with special moment‐resisting frames was studied. Statistical analysis of the results confirmed that the difference between ε‐filtration and η‐filtration can be very significant at some hazard levels. In the case of this structure, the resulting annual frequency of collapse was found to be lower in the case of η‐based record selection, in comparison with the ε‐based record‐selection approach. Copyright © 2011 John Wiley & Sons, Ltd.     

A method of estimating the stress exponent in the flow law for rocks using fold shape

On the basis of experiment and theory, we expect rocks to deform in a linear fashion when diffusive processes control deformation, and nonlinearly in most other situations. The geometric characteristics of buckle folds in layered materials are dependent on rheological parameters, and in particular depend strongly on the stress exponent,n _L , of the stiff layers involved. Thus, information about the deformation rocks have undergone and their rheological state during deformation can be obtained by studying fold shapes and strain distributions. This is important because there is uncertainty in extrapolating laboratory-derived flow laws to the very slow natural strain rates and large strains found in nature.We have studied the development of buckle folds in linear and nonlinear materials using finite-element modeling, and interpolated the numerical results to construct plots relating several geometric parameters to variations in power-law exponent,n _L , and viscosity ratio,m, of layer to matrix. Such plots allow for a comparison of the results of numerical models with data for many natural and experimentally-produced folds, and there is consistency among the data for folds produced in physical models, using both linear and nonlinear materials and the numerical simulations. data for folds from the Appalachian Mountains, the Alps and elsewhere, however, suggest high values ofn _L in the flow laws for a number of rock types. The unexpectedly high estimates ofn _L suggest that other factors, such as strain softening or anisotropy, may influence fold shape, and thus complicate the estimation of the rheological properties of rocks.