Tides in the Gulf of Kutch,India

In the Gulf of Kutch on the northwestern shelf of India the semi-diurnal constituents M₂ and S₂ get amplified approximately threefold. In contrast, amplification of the diurnal constituents K₁ and O₁ is small. From analytical and numerical solutions of linear, viscous, cross-sectionally averaged equations for tidal motion in a channel, it is seen that the observed amplification results from a combination of quarter-wavelength resonance, geometric effect due to decrease in width of the channel, and friction.     

Are artificial neural network techniques relevant for the estimation of longitudinal dispersion coefficient in rivers? / Les techniques de réseaux de neurones artificiels sont-elles pertinentes pour estimer le coefficient de dispersion longitudinale en rivières?

Abstract

Abstract Accurate application of the longitudinal dispersion model requires that specially designed experimental studies are performed in the river reach under consideration. Such studies are usually very expensive, so in order to quantify the longitudinal dispersion coefficient, as an alternative approach, various researchers have proposed numerous empirical formulae based on hydraulic and morphometric characteristics. The results are presented of the application of artificial neural networks as a parameter estimation technique. Five different cases were considered with the network trained for different arrangements of input nodes, such as channel depth, channel width, cross-sectionally averaged water velocity, shear velocity and sinuosity index. In the case where the sinuosity index is included as an input node, the results turned out to be better than those presented by other authors.     

Experimental analysis of pore-scale flow and transport in porous media

A novel, non-intrusive fluorescence imaging technique has been used to quantitatively measure the pore geometry, fluid velocity, and solute concentration within a saturated, three-dimensional porous medium. Discrete numerical averages of these quantities have been made over a representative volume of the medium and used to estimate macroscopic quantities that appear in conventional continuum models of flow and transport. The approach is meant to illustrate how microscopic information can be measured, averaged, and used to characterize medium-scale processes that are typically approximated constitutively. The experimental system consisted of a clear, cylindrical column packed with clear spherical beads and a refractive index-matched fluid seeded with fluorescent tracer particles and solute dye. By illuminating the fluid within the column with a scanning planar laser beam, details of flow and concentration within the pore spaces can be quantitatively observed, allowing for three-dimensional, dimensional, time dependent information to be obtained at good resolution. In time dependent information to be obtained at good resolution. In the current experiment, volumetrically averaged velocities and void-to-volume ratios are first compared with bulk measurements of fluid flux and medium porosity. Microscopic measurements of concentration are then used to construct cross-sectionally averaged profiles, mean breakthrough curves, and direct measurements of the dispersive flux, velocity variance, and concentration variance. In turn, the dispersive flux measurements are compared with mean concentration gradients to provide a basis for confirming the Fickian dispersion model and estimating dispersion coefficients for the medium. Coefficients determined in this manner are compared with others based upon traditional length-scale arguments, mean breakthrough analyses, and curve fits with numerical simulations.     

Comparison of longitudinal equilibrium profiles of estuaries in idealized and process-based models

The process-based morphodynamic model Delft3D-MOR and the idealized model of schuttelaars and De Swart (2000) are compared with each other. The differences between the two models in their mathematical-physical formulation as well as the boundary conditions are identified. Their effect on producing cross-sectionally averaged morphological equilibria of tidal inlets with arbitrary length and forced at the seaward boundary by a prescribed M₂ and M₄ sea- surface elevation is studied and an inventory is made of all relevant differences. The physical formulations in the source code of Delft3D-MOR are modified in various steps to resemble the formulations in the idealized model. The effect of each of the differences between the idealized and process-based model are studied by comparing the results of the idealized model to those of the adapted process-based model. The results of the idealized model can be qualitatively reproduced by the process-based model as long as the same morphological boundary condition is applied at the open sea end. This means that the simplifications concerning the mathematical formulation of the physical processes in the idealized model can be justified. Furthermore, it can be inferred that the morphological boundary condition at the open sea end is an essential element in controlling the behaviour of morphodynamic models for tidal inlets and estuaries.Responsible Editor: Jens Kappenberg     

Importance of advective zone in longitudinal mixing experiments

One-dimensional Fickian dispersion models such as the advection diffusion equation (ADE) are commonly used to analyse and predict concentration distributions downstream of contamination events in watercourses. Such models are only valid once the tracer had entered the equilibrium zone. This paper compares previous theoretical, experimental and numerical estimates of the distance to reach the equilibrium zone with new experimental values, obtained by examining the change of skewness in a tracer profile, downstream of a cross-sectionally well mixed source. Closer agreement was found with Fischers’ theoretical estimate than prior experimental and numerical studies.     

Factors affecting longitudinal dispersion in estuaries of different scale

Traditionally, the overall diluting capacity of an estuary is characterized using a coefficient of longitudinal dispersion, K_xe, which is given by the ratio of the dispersive flux of a dissolved substance to its tidally averaged longitudinal gradient. A steady-state model, which assumes a balance between the dispersive and non-dispersive fluxes and an exponential increase in estuary cross-sectional area towards the sea, has been used to derive expressions for the axial salinity distribution and the dispersive flux of salt. The model was set up assuming either a constant dispersion coefficient along the estuary or one that increased with distance towards the sea. By comparing salinity predictions with data from five UK estuaries, estimates were made of the maximum dispersive salt flux and the corresponding maximum salinity gradient for each system. The results indicated that there was an approximately linear relation between the fluxes and gradients, and the slope of a line plotted through the origin provided an estimate of a common K_xe for all five estuaries. The magnitude of K_xe was found to be about 90 m² s^–1 with a standard deviation of approximately ±32 m² s^–1. It is concluded that a representative value of 100 m² s^–1 for K_xe is a reasonable first choice when setting up a cross-sectionally averaged estuary model. The results also showed that larger systems, such as the Thames, had lower salinity gradients and lower dispersive salt fluxes, whilst smaller estuaries displayed the opposite characteristics. The model was used to predict the variation in the non-advective flux of salt along an estuary. The distribution was found to be similar to the corresponding flux distribution estimated from observations at the seaward end of the Tees estuary, despite appreciable spatial variations in the individual flux components. Allowing for a small decrease in freshwater flow, the model indicated that there was a decrease in the maximum dispersive flux between neap and spring tides. It is argued that such a reduction in flux can result in a seaward shift in the salinity distribution to a region of greater cross-section, where the freshwater transport per unit area again balances the reduced upstream dispersive flux, as found in the neap to spring response in the Tees estuary.Responsible Editor: Hans Burchard     

Double-averaging methodology and its application to turbulent flow in and above vegetation canopies

Double averaged equations for atmospheric boundary layer flows are introduced as natural extensions of single averaged Reynolds equations. We show that in circumstances where double averaged equations are needed, the two fundamental properties of Reynolds averaging are violated. First, we consider double-averaging in free air turbulence, where the aim is to separate coherent motions from background turbulence. We illustrate the different properties of the main operators that have been used and the physical meaning of the terms that result. Second, in canopy flows, the multiply connected nature of the canopy airspace leads to a different set of departures from the standard Reynolds equations. We establish the physical meaning of the extra terms that arise. Finally we briefly discuss the problems, both practical and theoretical, that arise when we use double averaged equations to interpret real data.     

Double-averaged velocity profiles over fixed dune shapes

Spatially averaged profiles of time averaged velocity, using integrals over thin horizontal slabs (Cartesian double average), are employed in characterizing the flow over fixed dune shapes. For comparison the spatial averaging method of Smith and McLean (1977) that averages along lines at constant distance from the local bed elevation is also investigated. The Cartesian double averaged profiles of the inverse of the velocity shear are nearly constant below the crest elevation, but increase rapidly above the crest level. This results in velocity profiles that increase linearly with distance from the bed below the crest. Above the crest it can be argued that the velocity increases logarithmically, but a power law profile can also be argued. Spatially averaged eddy viscosity profiles are calculated by multiplying the average Reynolds stress by the inverse shear. The resulting profile is more complex than the uniform flow counterpart.     

Modelling of hydrodynamics and cohesive sediment transport in Tanshui River estuarine system,Taiwan

A laterally averaged two-dimensional numerical model is used to simulate hydrodynamics and cohesive sediment transport in the Tanshui River estuarine system. The model handles tributaries as well as the main stem of the estuarine system. Observed time series of salinity data and tidally averaged salinity distributions have been compared with model results to calibrate the turbulent diffusion coefficients. The overall model verification is achieved with comparisons of residual currents and salinity distribution. The model reproduces the prototype water surface elevation, currents and salinity distributions. Comparisons of the suspended cohesive sediment concentrations calculated by the numerical model and the field data at various stations show good agreement. The validated model is applied to investigate the tidally averaged salinity distributions, residual circulation and suspended sediment concentration under low flow conditions in the Tanshui River estuarine system. The model results show that the limit of salt intrusion in the mainstem estuary is located at Hsin-Hai bridge in Tahan Stream, 26 km from the River mouth under Q75 flow. The null point is located at the head of salt intrusion, using 1 ppt isohaline as an indicator. The tidally averaged sediment concentration distribution exhibits a local maximum around the null point.     

The effect of geometry and tidal forcing on hydrodynamics and net sediment transport in semi-enclosed tidal basins

A new depth-averaged exploratory model has been developed to investigate the hydrodynamics and the tidally averaged sediment transport in a semi-enclosed tidal basin. This model comprises the two-dimensional (2DH) dynamics in a tidal basin that consists of a channel of arbitrary length, flanked by tidal flats, in which the water motion is being driven by an asymmetric tidal forcing at the seaward side. The equations are discretized in space by means of the finite element method and solved in the frequency domain. In this study, the lateral variations of the tidal asymmetry and the tidally averaged sediment transport are analyzed, as well as their sensitivity to changes in basin geometry and external overtides. The Coriolis force is taken into account. It is found that the length of the tidal basin and, to a lesser extent, the tidal flat area and the convergence length determine the behaviour of the tidally averaged velocity and the overtides and consequently control the strength and the direction of the tidally averaged sediment transport. Furthermore, the externally prescribed overtides can have a major influence on tidal asymmetry in the basin, depending on their amplitude and phase. Finally, for sufficiently wide tidal basins, the Coriolis force generates significant lateral dynamics.     

Two-dimensional finite element modeling on the crustal shortening and the surface erosion-sedimentation process across northern piedmont of the Tianshan Mountains

The Tianshan Mountains,located in the northwestern China,are bounded by the Tarim Basin to south and the Junggar Basin to north.In the north piedmont of this mountain range,ongoing thrusting and folding forms a set of roughly parallel anticlines.Geological observations predicted that averaged over last~1 Ma time scale,the shortening rates of these anticlines are about2.1–5.5 mm/a;However by averaged over about 10±2 kyr,their shortening rates reduce to merely about 1.25±0.5 mm/a.The slow shortening of the anticlines in the last~10±2 kyr is coarsely concurrent in time with the last global deglaciation.Here,we use a two-dimensional finite element model to explore crustal deformation across north piedmont of the Tianshan Mountains under various erosion-sedimentation conditions that are assumed to represent the climate-controlled surface process.Numerical experiments show that with a relatively weak erosion-sedimentation strength,the crustal shortening is accommodated mainly by north piedmont of the Tianshan Mountains,similar to the high shortening rate of anticlines averaged over the last~1Ma.By increasing erosion-sedimentation strength,the resultant crustal shortening is transformed gradually toward the Tianshan Mountains,resulting in the shortening rate in its north piedmont being decelerated to what is observed as averaged over the last~10±2 kyr.This result suggests that erosion and sedimentation could play an important role mechanically on strain localization across an intra-continent active tectonic belt.Hence,if the climate change around the last global deglaciation could be simply representative to the enhancement of surface erosion and sedimentation across the pre-existed Tianshan Mountains and its foreland,our models indicate that the observed shortening-rate variations averaged over~1 Ma and~10±2kyr time scales around north piedmont of the Tianshan Mountains should be resulted from climate changes.     

An eddifying Stommel model: fast eddy effects in a two-box ocean

ABSTRACT

A system of stochastic differential equations is formulated describing the heat and salt content of a two-box ocean. Variability in the heat and salt content and in the thermohaline circulation between the boxes is driven by fast Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability. The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian noise. The qualitative effects of this non-Gaussianity are investigated by comparing to two approximate models: one that includes only the mean eddy effects (the “averaged model”), and one that includes an additional Gaussian white-noise approximation of the eddy effects (the “Gaussian model”). Both of these approximate models are derived using the methods of fast averaging and homogenisation. In the parameter regime where the dynamics has a single stable equilibrium the averaged model has too little variability. The Gaussian model has accurate second-order statistics, but incorrect skew and rare-event probabilities. In the parameter regime where the dynamics has two stable equilibria the eddy noise is much smaller than the atmospheric noise. The averaged, Gaussian, and non-Gaussian models all have similar stationary distributions, but the jump rates between equilibria are too small for the averaged and Gaussian models.     

Metallogenic controls on the granite-related W–Sn deposits in the Hunan–Jiangxi region,China: evidence from zircon trace element geochemistry

The Nanling Range in South China is well known for its rich granite-related W–Sn deposits.To elucidate the controls of different granite-related W–Sn metallogenesis in the region,we chose five representative orerelated granites(Yanbei,Mikengshan,Tieshanlong,Qianlishan,and Yaogangxian intrusions)in the Hunan–Jiangxi region,and studied their magmatic zircon ages and trace element geochemistry.Our new zircon data showed the differences in ages,temperatures and oxygen fugacity of the ore-forming magmas.Zircon U–Pb ages of the Yanbei and Mikengshan intrusions are characterized by 142.4±2.4 and 143.0±2.3 Ma,respectively,whereas the Tieshanlong and Qianlishan intrusions are 159.5±2.3and 153.2±3.3 Ma,respectively.The Sn-related intrusions were younger than the W-related intrusions.The Tiin-zircon thermometry showed that there was no systematic difference between the Sn-related Yanbei(680–744℃)and Mikengshan(697–763℃)intrusions and the W-related Tieshanlong(730–800℃),Qianlishan(690–755℃)and Yaogangxian(686–751℃)intrusions.However,the zircon Ce^4+/Ce^3+ratios of the Yanbei(averaged at 18.3)and Mikengshan(averaged at 18.8)intrusions are lower than those of the Tieshanlong(averaged at 36.9),Qianlishan(averaged at 38.4)and Yaogangxian(averaged at 37)intrusions,indicating that the Sn-related granitic magmas might have lower oxygen fugacities than those of the W-related.This can be explained by that,in more reduced magmas,Sn is more soluble than W and thus is more enriched in the residual melt to form Sn mineralization.The difference in source materials between the Sn-related and the W-related granites seems to have contributed to the different redox conditions of the melts.     

Numerical behaviour of the downward continuation of gravity anomalies

The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the Poisson integral using point, single mean, and doubly averaged kernel are examined. Correct evaluation of the integral in its innermost zone is a challenging task. To avoid instabilities, an analytical planar approximation is used in the innermost integration zone. In addition it is shown that the single mean mode has the minimum discretization error. Downward continuation of point and mean anomalies by singly and doubly averaged kernel are the same mean anomalies on the geoid.     

Flow modelling in gravel‐bed rivers: rethinking the bottom boundary condition

A key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k ? ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k ? ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.     

Streamflow simulations for continental-scale river basins in a global atmospheric general circulation model

Streamflow simulations for 23 major river basins from the third-generation general circulation model (GCM) of the Canadian Centre for Climate Modelling and Analysis are assessed. Precipitation and runoff data are used from the AMIP II simulation in which the GCM is integrated for a 17-yr period with specific sea surface temperatures and sea-ice concentrations. Compared to the observations, the components of the global hydrological cycle and, the globally averaged precipitation and runoff over land, are well simulated. There remain, however, discrepancies in the simulation of regional precipitation and consequently runoff amounts, which lead to differences in basin-wide averaged quantities. Mean annual model precipitation is within 20% of the observed estimates for 13 out of 23 river basins considered. Model mean annual runoff is within 20% of the observed estimates for only 4 out of these 13 river basins. Analysis of basin-wide averaged monthly precipitation and streamflow data, and the errors associated with the mean, and amplitude and phase of the annual cycles, indicate that model streamflow simulations improve with improvement in GCM precipitation.     

On the aquifer's integrated balance equations

A general methodology is presented for describing transport phenomena in porous media at a macroscopic level. Then, these macroscopic balance equations are integrated (or averaged) along the vertical for confined, leaky and phreatic aquifers.The results are employed to derive (averaged) aquifer equations for the flow of water and of a solute (hydrodynamic dispersion). It is shown that in all cases, the resulting equation is identical to that derived on the basis of an assumption of horizontal flow (the Dupuit assumption).Macrodispersion, occurring at the aquifer level, is discussed and appropriate coefficients are proposed.     

太阳黑子磁场极性指数时间序列

本文根据苏黎世天文台太阳黑子11年周期资料和太阳黑子磁场磁性变化周期特征,构建了太阳黑子磁场磁性指数IM(Magnetic Index)时间序列,用IM(i)表示.为了便于采用数学方法研究太阳黑子磁场磁性指数变化与诸多地球物理现象之间的联系,本文给出了1749～2007年月平均太阳黑子磁场磁性指数时间序列数据.     

Incorporating topographic variability into a simple regional snowmelt model

General circulation models (GCMs), or stand‐alone models that are forced by the output from GCMs, are increasingly being used to simulate the interactions between snow cover, snowmelt, climate and water resources. The variation in snowpack extent, and hence albedo, through time in a cell is likely to be substantial, especially in mid‐latitude mountainous regions. As a consequence, the energy budget simulation by a GCM relies on a realistic representation of snowpack extent. Similarly, from a water resource perspective, the spatial extent of the pack is key in predicting meltwater discharges into rivers. In this paper a simple computationally efficient regional snow model has been developed, which is based on a degree‐day approach and simulates the fraction of the model domain covered by snow, the spatially averaged melt rate and the mean snowpack depth. Computational efficiency is achieved through a novel spatial averaging procedure, which relies on the assumptions that precipitation and temperature scale linearly with elevation and that the distribution of elevations in the domain can be modelled by a continuous function. The resulting spatially averaged model is compared with both observations of the duration of snow cover throughout Austria and with results from a distributed model based on the same underlying assumptions but applied at a fine spatial resolution. The new spatially averaged model successfully simulated the seasonal snow duration observations and reproduced the daily dynamics of snow cover extent, the spatially averaged melt rate and mean pack depth simulated by the distributed model. It, therefore, offers a computationally efficient and easily applied alternative to the current crop of regional snow models. Copyright © 2004 John Wiley & Sons, Ltd.     

Particle simulations of dispersion using observed meandering and turbulence

A Lagrangian stochastic particle model driven by observed winds from a network of 13 sonic anemometers is used to simulate the transport of contaminates due to meandering of the mean wind vector and diffusion by turbulence. The turbulence and the meandering motions are extracted from the observed velocity variances using a variable averaging window width. Such partitioning enables determination of the separate contributions from turbulence and meandering to the total dispersion. The turbulence is described by a Markov Chain Monte Carlo process based on the Langevin equation using the observed turbulence variances. The meandering motions, not the turbulence, are primarily responsible for the 1-h averaged horizontal dispersion as measured by the travel time dependence of the particle position variances. As a result, the 1-h averaged horizontal concentration patterns are often characterized by streaks and multi-modal distributions. Time series of concentration at a fixed location are highly nonstationary even when the 1-h averaged spatial distribution is close to Gaussian. The results show that meandering dominates the travel-time dependence of the horizontal dispersion under all atmospheric conditions: weak and strong winds, and unstable and stable stratification.