Numerical modelling of residual flow and salinity in the Río de la Plata

The Río de la Plata discharges into the Atlantic Ocean. The particular characteristics of the study area, the variable width and shallowness of the river, the high fluvial discharges and the dynamic processes involving interactions between river discharges, tidal currents and wind, generate complex velocity and salinity fields. We applied the hydrodynamic model RMA-10 to examine the effects of various forcing (tides, flow discharge and winds) on residual currents and salinity fields in the Río de la Plata, focusing on the outer zone of the river. The RMA-10 code, developed by Ian King, is a multiparameter finite element model representing estuarine flow in three dimensions. In this study the model has been applied in a depth-averaged-baroclinic mode and a series of observed data is used for model calibration and verification. The model result shows that it is able to simulate velocity and the salinity fields with a reasonable accuracy. The analysis of residual currents in the river, when forced by freshwater discharge and astronomical tide, shows that the flow discharge takes place mainly over the shallower areas of the river and that the saline water is advected up-river through the deeper channels. The numerical simulations show that the winds from the South-West and North-East quadrants have a great influence over the salinity and velocity fields.     

A 3D hydrodynamic numerical model of the Río de la Plata and Montevideo’s coastal zone

The 3D hydrodynamic numerical model MOHID was applied in the Río de la Plata and Montevideo coastal zone in order to represent the main dynamics and to study its complex circulation pattern. The hydrodynamic model was calibrated and validated considering the following main forces: fresh water flow, astronomical and meteorological tides in the oceanic boundary, and wind acting on the water surface. A series of water levels measured at six coastal stations and vertical profiles of current velocity measured at four different locations in the estuarine zone of the Río de la Plata were used for calibrating and validating the hydrodynamic model. The calibration process was carried out in two steps. First the astronomical waves propagation was calibrated comparing harmonic constants of observed and computed sea surface elevation data. Next, both the astronomical and meteorological wave propagation was calibrated. Direct comparison of scatter plot and root-mean square errors of model results and field data were used when evaluating the calibration quality. The calibrated model shows good agreement with the measured water surface level in the entire domain with mean error values being minor than 20% of the measured data and correlation factors higher than 0.74. Also, the intensity and velocity direction observed in the currents data are well represented by the model in both bottom and surface levels with errors similar to 30% of the currents data components. Using the 3D calibrated model the bottom and surface residual circulation for a four month period of time was analyzed.     

Hydrodynamic numerical simulation at the mouths of the Parana and Uruguay rivers and the upper Rio de la Plata estuary: A realistic boundary condition

A hydrodynamic numerical study at the mouths of the Paraná and Uruguay rivers and the upper Río de la Plata is presented in this paper. Water Quality Mapping numerical model was implemented and realistic and very simple boundary conditions were specially developed for this complex estuarial system. A set of numerical experiments were carried out using different constant discharges for the Paraná and Uruguay rivers but unrealistic currents were generated. In order to obtain more realistic results, a set of numerical simulations were carried out imposing water level timeseries at the open boundaries. M₂, S₂, K₁ and O₁ harmonic constants were used to generate water levels at Zárate (Paraná river), Nueva Palmira (Uruguay river) and the eastern boundary of the domain (La Plata–Colonia). A mean water level equal to zero was set between La Plata and Colonia. Positive mean water levels (0.3–0.4 m) were imposed at Zárate and Nueva Palmira to simulate the hydraulic slope of both rivers and, consequently, to generate realistic and unsteady discharges. These boundary conditions, built by means of the addition of a mean water level and the astronomical tide, significantly improve the simulated currents at the northernmost region of the RDP estuary.     

Pre-operational forecasting of sea level height for the Río de la Plata

This paper presents the implementation and calibration of a pre-operational numerical model for the Río de la Plata river. This model is capable of predicting sea level variations in the Río de la Plata, and therefore constitutes a numerical tool of great value for the fluvial–maritime navigation and regional environmental management. A two-dimensional model (MOHID) with nested domains was used to simulate the hydrodynamics. This model was forced with a meso-scale atmospheric model (WRF) and a global tidal model (FES2004). The results obtained include astronomic and meteorological sea level variations in the Río de la Plata. Comparisons of modeled water levels with data have shown very good qualitative and quantitative agreement. The pre-operational test presented in this paper, a 4-day hydrodynamic forecast, was conducted in approximately 18 h.     

On the partial sums,Cesáro and de la Valleé Poussin means of convex and starlike functions of order 1/2

In this paper we study certain properties of partial sums, cesáro and de la valleé Poussin means of convex and starlike functions.     

Approximate Properties of the de la Vallee Poussin Means for the Discrete Fourier-Jacobi Sums

We consider the system of the classical Jacobi polynomials of degree at most N which generate an orthogonal system on the discrete set of the zeros of the Jacobi polynomial of degree N. Given an arbitrary continuous function on the interval [-1,1], we construct the de la Vallee Poussin-type means for discrete Fourier–Jacobi sums over the orthonormal system introduced above. We prove that, under certain relations between N and the parameters in the definition of de la Vall'ee Poussin means, the latter approximate a continuous function with the best approximation rate in the space C[-1,1] of continuous functions.     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

On approximations of the de Rham complex and their cohomology

For a commutative algebra R, its de Rham cohomology is an important invariant of R. In the paper, an infinite chain of de Rham-like complexes is introduced where the first member of the chain is the de Rham complex. The complexes are called approximations of the de Rham complex. Their cohomologies are found for polynomial rings and algebras of power series over a field of characteristic zero.     

Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models

The fluid structure interaction mechanism in vascular dynamics can be described by either 3D or 1D models, depending on the level of detail of the flow and pressure patterns needed for analysis. A successful strategy that has been proposed in the past years is the so-called geometrical multiscale approach, which consists of coupling both 3D and 1D models so as to use the former only in those regions where details of the fluid flow are needed and describe the remaining part of the vascular network by the simplified 1D model.In this paper we review recently proposed strategies to couple the 3D and 1D models, and within the 3D model, to couple the fluid and structure sub-problems. The 3D/1D coupling strategy relies on the imposition of the continuity of flow rate and total normal stress at the interface. On the other hand, the fluid–structure coupling strategy employs Robin transmission conditions. We present some numerical results and show the effectiveness of the new approaches.     

部分植被化矩形河槽紊流时均流速分布分析解

研究了部分植被化矩形河槽紊流的水深平均流速分布．植被被视为不可移动的刚性多孔介质,植被对水流的阻力以多孔介质理论加以考虑,并综合考虑部分植被存在时矩形河槽紊动水流二次流的作用,建立了紊流动量方程．针对恒定均匀流的特点,对动量方程进行了简化,沿水深方向积分并引入参考量,形成无量纲形式的基于多孔介质理论紊动水流控制方程,进而对其求解给出了水深平均纵向时均流速分布的分析解．研究表明,在不同水流条件下的二次流强度系数具有相同的数量级．为验证分析解的正确性,在实验室采用MicoADV测量了部分植被化矩形河槽水流的流速分布．数值解与实验资料和日本学者的相关实验资料的对比表明,该方法可以准确预测部分植被化矩形河槽紊流水流的水深平均流速分布．     

Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with Hall currents and inclined magnetic field influence

A numerical solution is developed for the viscous, incompressible, magnetohydrodynamic flow in a rotating channel comprising two infinite parallel plates and containing a Darcian porous medium, the plates lying in the x–z plane, under constant pressure gradient. The system is subjected to a strong, inclined magnetic field orientated to the positive direction of the y-axis (rotational axis, normal to the x–z plane). The Navier–Stokes flow equations for a general rotating hydromagnetic flow are reduced to a pair of linear, viscous partial differential equations neglecting convective acceleration terms, for primary velocity (u′) and secondary velocity (v′) where these velocities are directed along the x and y axes. Only viscous terms are retained in the momenta equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless ordinary differential equations are solved using a robust numerical method, Network Simulation Methodology. Full details of the numerics are provided. The present solutions are also benchmarked against the analytical solutions presented recently by Ghosh and Pop [Ghosh SK, Pop I. An analytical approach to MHD plasma behaviour of a rotating environment in the presence of an inclined magnetic field as compared to excitation frequency. Int J Appl Mech Eng 2006;11(4):845–856] for the case of a purely fluid medium (infinite permeability). We study graphically the influence of Hartmann number (Ha, magnetic field parameter), Ekman number (Ek, rotation parameter), Hall current parameter (Nh), Darcy number (Da, permeability parameter), pressure gradient (Np) and also magnetic field inclination (θ) on primary and secondary velocity fields. Additionally we investigate the effects of these multiphysical parameters on the dimensionless shear stresses at the plates. Both primary and secondary velocity are seen to be increased with a rise in Darcy number, owing to a simultaneous reduction in Darcian drag force. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) but there is a decrease in secondary velocity. The study finds important applications in magnetic materials processing, hydromagnetic plasma energy generators, magneto-geophysics and planetary astrophysics.     

Numerical solution of the generalized Stokes problem for the flow in a channel

In this article we introduce the separation of variables in the two-dimensional generalized Stokes problem. −νΔu + αu + inverted delta p = f, for the flow in a channel. Also for the first time, we discuss the implementation of the Incremental Unknowns Method with a data structure of Compressed Column Storage. Two examples of application of the Incremental Unknowns method for this problem are presented in which we compare the CPU times of three methods: Conjugate Gradient (CG), Incremental Unknowns (IU), and Uzawa Algorithm (Uzawa). © 1997 John Wiley & Sons, Inc.     

Hamiltonian model for coupled surface and internal waves in the presence of currents

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ‘wave’ variables and the equations of motion are calculated. The resultant equations of motion are then analysed to show that wave–current interaction is influenced only by the current profile in the ‘strips’ adjacent to the surface and the interface. Small amplitude and long-wave approximations are also presented.     

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.     

Early work of N.G. (Dick) de Bruijn in analysis and some of my own

There are parallels between de Bruijn’s early work in analysis and that of the author. However, Dick’s work soon became much broader and deeper. While the present paper reviews several topics of common interest, its main content is a short version of Dick’s important article related to Riemann’s Hypothesis, entitled ‘The roots of trigonometric integrals’ [N.G. de Bruijn, The roots of trigonometric integrals, Duke Math. J. 17 (1950) 197–226]. The associated ‘de Bruijn–Newman constant’ is also discussed.     

On the volume and the Gauss map image of spacelike hypersurfaces in de Sitter space

In this paper we prove that a complete spacelike hypersurface in de Sitter space such that its image under the Gauss map is contained in a hyperbolic geodesic ball of radius is necessarily compact and its -dimensional volume satisfies , where denotes the volume of a unitary round -sphere. We also characterize the case where these inequalities become equalities. As an application of our result, we also conclude that Goddard's conjecture is true under the assumption that the hyperbolic image of the hypersurface is bounded.

     

The Potential Fluid Flow Problem and the Convergence Rate of the Minimal Residual Method

In the paper the potential fluic flow problem in porous media using Darcy's law and the continuity equation is solved. Mixed-hybrid finite element formulation based on general trilateral prismatic elements is considered. Spectral properties of resulting symmetric indefinite system of linear equations are examined. Minimal residual method for the solution of systems with a symmetric indefinite matrix is applied. The rate of convergence and the asymptotic convergence factor which depend on the eigenvalue distribution of the system matrix are estimated.     

Numerical modeling of the movement of a rigid particle in viscous fluid

Modeling the movement of a rigid particle in viscous fluid is a problem physicists and smathematicians have tried to solve since the beginning of this century. A general model for an ellipsoidal particle was first published by Jeffery in the twenties. We exploit the fact that Jeffery was concerned with formulae which can be used to compute numerically the velocity field in the neighborhood of the particle during his derivation of equations of motion of the particle. This is our principal contribution to the subject. After a thorough check of Jeffery's formulae, we coded software for modeling the flow around a rigid particle based on these equations. Examples of its applications are given in conclusion. A practical example is concerned with the simulation of sigmoidal inclusion trails in porphyroblast.     

广义de Bruijn有向图及其叠线图的支撑树与欧拉环游的计数

给出了一类特殊的广义deBruijn有向图的支撑树与欧环游的数目的简洁表示式，并得到了广义deBruijn有向叠线图的支撑树与欧拉环境数目的计算公式。