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Stream Function (stream + function)
Selected AbstractsSimulation of Indian summer monsoon: sensitivity to cumulus parameterization in a GCMINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 8 2007S. K. Deb Abstract Hindcasts for the Indian summer monsoons (ISMs) of 2002 and 2003 have been produced from a series of numerical simulations performed with a general circulation model using different cumulus parameterization schemes. Ten sets of ensemble simulations have been produced without using any vegetation scheme but by prescribing the monthly observed SST from the ECMWF (European Centre for Medium Range Weather Forecasts) analyses. For each ensemble, ten simulations have been realised with different initial conditions that are also prepared from the ECMWF data: five each from the April and May analyses of both the years. Stream function, velocity potential with divergent winds at 200 hPa, winds at 850 hPa and rainfall patterns with their anomalies have been analysed and interpreted. The large-scale upper and lower level circulation features are simulated satisfactorily. The spatial structure of predicted July monsoon rainfall over India shows a fair agreement with the GPCP (observed) pentad rainfall distribution. The variability associated with all-India June,July simulated rainfall time series matches reasonably well with the observations in 2003, but the model fails to simulate the observed variability in July 2002. Further evaluation of the model-produced precipitation in seasonal simulations is done with the help of empirical orthogonal functions (EOFs) of the GPCP rainfall over India. Since the first four EOFs explain a significant part of the total variance of the observed rainfall, the simulated precipitation is projected on to these modes. Thus, the differences in simulated and observed rainfall fields manifest in the time series of their expansion coefficients, which are utilised for inter-comparison/evaluation of model simulations. Copyright © 2006 Royal Meteorological Society [source] Hydrologic and geochemical controls on soluble benzene migration in sedimentary basinsGEOFLUIDS (ELECTRONIC), Issue 2 2005Y. ZHANG Abstract The effects of groundwater flow and biodegradation on the long-distance migration of petroleum-derived benzene in oil-bearing sedimentary basins are evaluated. Using an idealized basin representation, a coupled groundwater flow and heat transfer model computes the hydraulic head, stream function, and temperature in the basin. A coupled mass transport model simulates water washing of benzene from an oil reservoir and its miscible, advective/dispersive transport by groundwater. Benzene mass transfer at the oil,water contact is computed assuming equilibrium partitioning. A first-order rate constant is used to represent aqueous benzene biodegradation. A sensitivity study is used to evaluate the effect of the variation in aquifer/geochemical parameters and oil reservoir location on benzene transport. Our results indicate that in a basin with active hydrodynamics, miscible benzene transport is dominated by advection. Diffusion may dominate within the cap rock when its permeability is less than 10,19 m2. Miscible benzene transport can form surface anomalies, sometimes adjacent to oil fields. Biodegradation controls the distance of transport down-gradient from a reservoir. We conclude that benzene detected in exploration wells may indicate an oil reservoir that lies hydraulically up-gradient. Geochemical sampling of hydrocarbons from springs and exploration wells can be useful only when the oil reservoir is located within about 20 km. Benzene soil gas anomalies may form due to regional hydrodynamics rather than separate phase migration. Diffusion alone cannot explain the elevated benzene concentration observed in carrier beds several km away from oil fields. [source] Piecewise divergence-free discontinuous Galerkin methods for Stokes flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2008Peter Hansbo Abstract In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix,Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Treatment of Neumann boundaries in the complex variable boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2004Kozo Sato Abstract For potential flow, the complex variable boundary element method (CVBEM) is formulated in terms of the velocity potential , and the stream function ,. In actual flow problems, , and ,,/,n are given along Dirichlet and Neumann boundaries, respectively. In the CVBEM, the Neumann-type condition ,,/,n is not directly handled, and, instead, , is used to define Neumann boundaries. Owing to this discrepancy, numerical difficulties are raised along Neumann boundaries. The current study addresses two such difficulties: (1) multiple Neumann boundaries and (2) branch cuts across Neumann boundaries. The first problem is due to the fact that , along multiple boundaries cannot be specified a priori, and the second problem is due to the discontinuous jump inherent in , for sink/source singularities. To overcome these difficulties, a new formulation of the CVBEM to solve for the unknown , values and a proper way of branch-cut placement are proposed, and these techniques are verified against example problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] A Hermite finite element method for incompressible fluid flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010J. T. Holdeman Abstract We describe some Hermite stream function and velocity finite elements and a divergence-free finite element method for the computation of incompressible flow. Divergence-free velocity bases defined on (but not limited to) rectangles are presented, which produce pointwise divergence-free flow fields (,·uh,0). The discrete velocity satisfies a flow equation that does not involve pressure. The pressure can be recovered as a function of the velocity if needed. The method is formulated in primitive variables and applied to the stationary lid-driven cavity and backward-facing step test problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical implementation of Aristov,Pukhnachev's formulation for axisymmetric viscous incompressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010N. P. Moshkin Abstract In the present work a finite-difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112,115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross-flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross-flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in-depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical study of an inviscid incompressible flow through a channel of finite lengthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009Vasily N. Govorukhin Abstract A two-dimensional inviscid incompressible flow in a rectilinear channel of finite length is studied numerically. Both the normal velocity and the vorticity are given at the inlet, and only the normal velocity is specified at the outlet. The flow is described in terms of the stream function and vorticity. To solve the unsteady problem numerically, we propose a version of the vortex particle method. The vorticity field is approximated using its values at a set of fluid particles. A pseudo-symplectic integrator is employed to solve the system of ordinary differential equations governing the motion of fluid particles. The stream function is computed using the Galerkin method. Unsteady flows developing from an initial perturbation in the form of an elliptical patch of vorticity are calculated for various values of the volume flux of fluid through the channel. It is shown that if the flux of fluid is large, the initial vortex patch is washed out of the channel, and when the flux is reduced, the initial perturbation evolves to a steady flow with stagnation regions. Copyright © 2008 John Wiley & Sons, Ltd. [source] 2D thermal/isothermal incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005Alfredo Nicolás Abstract 2D thermal and isothermal time-dependent incompressible viscous flows are presented in rectangular domains governed by the Boussinesq approximation and Navier,Stokes equations in the stream function,vorticity formulation. The results are obtained with a simple numerical scheme based on a fixed point iterative process applied to the non-linear elliptic systems that result after a second-order time discretization. The iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems. Thermal and isothermal examples are associated with the unregularized, driven cavity problem and correspond to several aspect ratios of the cavity. Some results are presented as validation examples and others, to the best of our knowledge, are reported for the first time. The parameters involved in the numerical experiments are the Reynolds number Re, the Grashof number Gr and the aspect ratio. All the results shown correspond to steady state flows obtained from the unsteady problem. Copyright © 2005 John Wiley & Sons, Ltd. [source] Chebyshev super spectral viscosity solution of a two-dimensional fluidized-bed modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003Scott A. SarraArticle first published online: 13 MAY 200 Abstract The numerical solution of a model describing a two-dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite-difference method. The mixed SSV/finite-difference method produces physically shaped bubbles, on a very coarse grid. Fine scale details, which were not present in previous finite-difference solutions, are present in the solution. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical simulation of vortical ideal fluid flow through curved channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003N. P. Moshkin Abstract A numerical algorithm to study the boundary-value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co-ordinate system. The convergence of the finite-difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka,Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two-dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented. Copyright © 2003 John Wiley & Sons, Ltd. [source] Highly accurate solutions of the bifurcation structure of mixed-convection heat transfer using spectral methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2002M. Selmi Abstract This paper is concerned with producing highly accurate solution and bifurcation structure using the pseudo-spectral method for the two-dimensional pressure-driven flow through a horizontal duct of a square cross-section that is heated by a uniform flux in the axial direction with a uniform temperature on the periphery. Two approaches are presented. In one approach, the streamwise vorticity, streamwise momentum and energy equations are solved for the stream function, axial velocity, and temperature. In the second approach, the streamwise vorticity and a combination of the energy and momentum equations are solved for stream function and temperature only. While the second approach solves less number of equations than the first approach, a grid sensitivity analysis has shown no distinct advantage of one method over the other. The overall solution structure composed of two symmetric and four asymmetric branches in the range of Grashof number (Gr) of 0,2 × 106 for a Prandtl number (Pr) of 0.73 has been computed using the first approach. The computed structure is comparable to that found by Nandakumar and Weinitschke (1991) using a finite difference scheme for Grashof numbers in the range of 0,1×106. The stability properties of some solution branches; however, are different. In particular, the two-cell structure of the isolated symmetric branch that has been found to be unstable by the study of Nandakumar and Weinitschke is found to be stable by the current study. Copyright © 2002 John Wiley & Sons, Ltd. [source] On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy,Riemann equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2006D. Constales Abstract In this paper, we study the growth behaviour of entire Clifford algebra-valued solutions to iterated Dirac and generalized Cauchy,Riemann equations in higher-dimensional Euclidean space. Solutions to this type of systems of partial differential equations are often called k -monogenic functions or, more generically, polymonogenic functions. In the case dealing with the Dirac operator, the function classes of polyharmonic functions are included as particular subcases. These are important for a number of concrete problems in physics and engineering, such as, for example, in the case of the biharmonic equation for elasticity problems of surfaces and for the description of the stream function in the Stokes flow regime with high viscosity. Furthermore, these equations in turn are closely related to the polywave equation, the poly-heat equation and the poly-Klein,Gordon equation. In the first part we develop sharp Cauchy-type estimates for polymonogenic functions, for equations in the sense of Dirac as well as Cauchy,Riemann. Then we introduce generalizations of growth orders, of the maximum term and of the central index in this framework, which in turn then enable us to perform a quantitative asymptotic growth analysis of this function class. As concrete applications we develop some generalizations of some of Valiron's inequalities in this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] Further results on the asymptotic growth of entire solutions of iterated Dirac equations in ,nMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2006D. Constales Abstract In this paper, we establish some further results on the asymptotic growth behaviour of entire solutions to iterated Dirac equations in ,n. Solutions to this type of systems of partial differential equations are often called polymonogenic or k -monogenic. In the particular cases where k is even, one deals with polyharmonic functions. These are of central importance for a number of concrete problems arising in engineering and physics, such as for example in the case of the biharmonic equation for the description of the stream function in the Stokes flow regime with low Reynolds numbers and for elasticity problems in plates. The asymptotic study that we are going to perform within the context of these PDE departs from the Taylor series representation of their solutions. Generalizations of the maximum term and the central index serve as basic tools in our analysis. By applying these tools we then establish explicit asymptotic relations between the growth behaviour of polymonogenic functions, the growth behaviour of their iterated radial derivatives and that of functions obtained by applying iterations of the , operator to them. Copyright © 2005 John Wiley & Sons, Ltd. [source] Dynamics of jet streaks in a stratified quasi-geostrophic atmosphere: Steady-state representationsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 600 2004Philip Cunningham Abstract The structure and dynamics of jet streaks in the extratropical upper troposphere are examined in the context of a continuously stratified quasi-geostrophic (QG) framework. It is hypothesized that jet streaks may result from the superposition of monopolar or dipolar vortices of mesoscale dimensions with the enhanced potential-vorticity gradients constituting the tropopause. Based on this hypothesis, steady-state monopolar and dipolar vortices in a uniform zonal background flow on an f -plane are investigated for their applicability as idealized dynamical representations of jet streaks. The representations of jet streaks satisfy the nonlinear governing equations of the continuously stratified QG framework: the monopolar vortex is specified in terms of axisymmetric distributions of QG potential vorticity in the interior of the domain and perturbation potential temperature on upper (tropopause) and lower (surface) boundaries, whereas the dipolar vortex is adapted from a closed-form analytical solution for the geostrophic stream function. Through the incorporation of vertical structure and divergent circulations, these representations of jet streaks extend those presented previously by the authors using a non-divergent barotropic model. It is shown that these vortex representations display characteristic signatures similar to those observed in atmospheric jet streaks. In particular, both the monopole and the dipole exhibit an ageostrophic wind directed towards lower geopotential height in the entrance region of the streak and towards higher geopotential height in the exit region. For the monopole, this ageostrophic wind is entirely rotational and there is no vertical motion. For the dipole, the rotational part of the ageostrophic wind dominates the divergent part; the latter is associated with a four-cell pattern of vertical velocity similar to that described in conceptual models of straight jet streaks. For both the monopole and the dipole, the jet streak is induced by the vortex structure such that the wind speed maximum translates at the same speed as the individual vortices; this translation speed is slower than the maximum wind speed in the core of the speed maximum, consistent with observations of jet streaks. It is proposed that the above representations provide a formal theoretical foundation for the conceptual models of jet streaks prevalent in the literature; these conceptual models typically are based on heuristic kinematic or parcel arguments and not on consistent solutions to a physically plausible set of equations. The representations also provide a foundation upon which to explore the unsteady behaviour of jet streaks in terms of the superposition of monopolar and dipolar vortices with non-uniform zonal background flows. Copyright © 2004 Royal Meteorological Society. [source] | |||||||||||||