共查询到20条相似文献，搜索用时 500 毫秒
1.
E. R. Johnson 《地球物理与天体物理流体动力学》2013,107(2):143-164
Abstract Solutions of the steady, inviscid, non-linear equations for the conservation of potential vorticity are presented for linearly sheared geostrophic flow over a right circular cylinder. The indeterminancy introduced by the presence of closed streamline regions is removed by requiring that the steady flow retains above topography a given fraction of that fluid initially present there, assuming the flow to have been started from rest. Those solutions which retain the largest fraction in uniform and negatively sheared streams satisfy the Ingersoll (1969) criterion (that, in the limit of vanishingly small viscosity, closed streamline regions are stagnant) and so are unaffected by Ekman pumping. These flows are set up on the advection time scale. In positively sheared flows the maximum retention solutions do not satisfy the Ingersoll criterion and thus would be slowly spun down on the far longer viscous spin-up time. For arbitrary isolated topography, both the partial retention and Ingersoll problems are reduced to a one-dimensional non-linear integral equation and the solution of the Ingersoll problem obtained in the limit of strong positive shear. The stagnant region is symmetric about the zero velocity line and extends to infinity in the streamwise direction. Its cross-stream width is proportional to the rotation rate and fractional height occupied by the obstacle and inversely proportional to the strength of the shear, decreasing inversely as the square of distance upstream and downstream. 相似文献
2.
Michael S. Zhdanov Vjacheslav V. Spichak Leonid Yu. Zaslavsky 《Physics of the Earth and Planetary Interiors》1990,60(1-4):53-61
A method for numerical modeling of quasi-stationary electromagnetic fields in axially symmetric media is proposed. It is based on the direct finite-element method and the use of special basis functions. Assuming cylindrical coordinates r, φ, z, the three-dimensional solution is presented as a superposition of fields with the azimuthal dependence exp(inφ). For each case this results in a system of two equations of elliptical type in two scalar functions in the (r, z) plane.
The discretization leads to the conservative nine-points difference scheme. The system of linear equations is solved by means of the LU-decomposition technique, the band structure of the matrix being taken into account.
The program is tested using analytical results (DC asymptote) for a near-surface inhomogeneity. Comparison also is made with 2D results (H-polarization) for the model of a local well conducting inclusion in a three-layered Earth. 相似文献
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4.
M. Sankar Rao 《Pure and Applied Geophysics》1966,65(1):196-215
Summary In a coordinate system in which the ground is always a coordinate surface, climatic equations for axially asymmetric and symmetric atmospheric motions are derived. These are compared with their counterparts in the pressure coordinate system. Some qualitative predictions regarding solutions are given. 相似文献
5.
The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions. 相似文献
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7.
Fred T. Tracy 《Journal of Hydrology》1995,170(1-4):199-214
An excellent tool for checking numerical models of unsaturated flow in groundwater is analytical solutions. However, because of the highly nonlinear nature of the governing partial differential equation, only a limited number of analytical solutions are available. This paper first gives some simple 1-D solutions. Next, by use of a transformation, the nonlinear partial differential equation is converted to a linear one for a specific form of the moisture content vs. pressure head and relative hydraulic conductivity vs. pressure head curves. This allows both 2-D and 3-D solutions to be derived, which is done in this paper. Finally, computations from a finite element computer program are compared with results from one of the analytical solutions to illustrate the use of the derived equations. 相似文献
8.
We have analyzed the applicability of the approximation of the axially symmetric magnetic field created by the dipole field
and the currents flowing in the plasma for describing the Dst variation value during magnetic storms and the dependence of the position of the pressure maximum on the volumes of magnetic
flux tubes on the plasma pressure. We have determined the dependence of the disturbance in the field on the geocentric distance.
We have shown that the experimentally obtained dependence on the position of the pressure maximum on Dst is described in the assumption on the correctness of the adiabatic law on changes in pressure with a change in geocentric
distance. We have calculated the values of the magnetic field distortion and the value of the Dst variation for the experimentally determined radial pressure profile for three magnetic storms with Dst ∼ 100 nT. We have shown that, with allowance for nonlinear magnetic field distortions, the axially symmetric part of the
ring current makes the main contribution to the value of the Dst variation. 相似文献
9.
Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. The dynamo action of all solutions with fixed parameters (steady flows) is known from earlier studies. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions, leading to high diffusion. In addition, steady flows generate only steady or regularly reversing oscillatory fields and cannot therefore reproduce irregular geomagnetic-type reversal behaviour. Oscillations of the flow are introduced by varying the flow parameters in time, defining a closed orbit in the space ( D,?M ). When the frequency of the oscillation is small, the net growth rate of the magnetic field over one period approaches the average of the growth rates for steady flows along the orbit. At increased frequency time-dependence appears to smooth out flux concentrations, often enhancing dynamo action. Dynamo action can be impaired, however, when flux concentrations of opposite signs occur close together as smoothing destroys the flux by cancellation. It is possible to produce geomagnetic-type reversals by making the orbit stray into a region where the steady flows generate oscillatory fields. In this case, however, dynamo action was not found to be enhanced by the time-dependence. A novel approach is being taken to solve the time-dependent eigenvalue problem where, by combining Floquet theory with a matrix-free Krylov-subspace method, we can avoid large memory requirements for storing the matrix required by the standard approach. 相似文献
10.
The moments of time to first passage of the response process of the linear oscillator excited by a stationary wide-band process are obtained numerically for the symmetric two-sided barrier problem. A recursive set of partial differential equations governing the moments is solved using a Petrov-Galerkin finite element method. Stable, accurate solutions for the first few moments are calculated over a wide range of oscillator damping. 相似文献
11.
S. J. Jacobs 《Pure and Applied Geophysics》1989,130(4):743-749
A set of ordinary differential equations describing a mechanical system subject to forcing and dissipation is considered. A topological argument is employed to show that if all time-dependent solutions of the governing equations are bounded, the equations admitN steady solutions, whereN is a positive odd integer and where at least (N–1)/2 of the steady solutions are unstable. The results are discussed in the context of atmospheric flows, and it is shown that truncated forms of the quasigeostrophic equations of dynamic meteorology and of Budyko-Sellers climate models satisfy the hypotheses of the theorem. 相似文献
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13.
Magnetic reconnection at a three-dimensional null point is the natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a spiral null point, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. A steady magnetic field is assumed, as well as the existence of a localised diffusion region surrounding the null point. Outside the diffusion region the plasma and magnetic field move ideally. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flows are found to be rotational in nature, as is the change in connections of the magnetic field lines. 相似文献
14.
This paper investigates energy losses in compound channel under non-uniform flow conditions. Using the first law of thermodynamics, the concepts of energy loss and head loss are first distinguished. They are found to be different within one sub-section (main channel or floodplain). Experimental measurements of the head within the main channel and the floodplain are then analyzed for geometries with constant or variable channel width. Results show that head loss differs from one sub-section to another: the classical 1D hypothesis of unique head loss gradient appears to be erroneous. Using a model that couple 1D momentum equations, called “Independent Sub-sections Method (ISM)”, head losses are resolved. The relative weights of head losses related to bed friction, turbulent exchanges and mass transfers between sub-sections are estimated. It is shown that water level and the discharge distribution across the channel are influenced by turbulent exchanges for (a) developing flows in straight channels, but only when the flow tends to uniformity; (b) flows in skewed floodplains and symmetrical converging floodplains for small relative flow depth; (c) flows in symmetrical diverging floodplains for small and medium relative depth. Flow parameters are influenced by the momentum flux due to mass exchanges in all non-prismatic geometries for small and medium relative depth, while this flux is negligible for developing flows in straight geometry. The role of an explicit modeling of mass conservation between sub-sections is eventually investigated. 相似文献
15.
Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations 总被引：1，自引：0，他引：1
Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas where no water is present, as standard numerical methods may fail in the presence of these areas. These equations also have still water steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. In this paper we propose a high order discontinuous Galerkin method which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. A simple positivity-preserving limiter, valid under suitable CFL condition, will be introduced in one dimension and then extended to two dimensions with rectangular meshes. Numerical tests are performed to verify the positivity-preserving property, well-balanced property, high order accuracy, and good resolution for smooth and discontinuous solutions. 相似文献
16.
The solutions of constant‐head and constant‐flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well‐known transient and steady‐state drawdown solutions, respectively, of the constant‐flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However, the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant‐head and constant‐flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite‐domain solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite‐domain solution by the infinite‐domain solution and the Thiem equation are investigated and presented. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
This work deals with the evaluation of the dynamic pressures and the associated forces on a pair of rigid vertical cantilever walls retaining a uniform, fully saturated poroelastic layer of soil. Hysteretic damping in the soil skeleton may also be present. Wall pressures and forces are induced by horizontal ground shaking harmonically varying with time and spatially invariant. The problem is solved analytically under conditions of plane strain. The governing partial differential equations of motion, after separation of variables and the simplifying assumptions of zero vertical normal stresses and zero horizontal variation of vertical displacements, reduce to a system of two ordinary differential equations for the amplitudes of the solid skeleton horizontal displacement and the pore water pressure, which are easily solved. The parameters examined include the ratio of the distance between walls to the height of the retained soil material and the soil material properties such as porosity, permeability and damping. The comprehensive numerical data presented indicate that the displacements, wall pressures and resultant forces are highly dependent on the distance between the walls for any values of porosity and permeability. 相似文献
18.
Decoupling of the coupled poroelastic equations for quasistatic flow in deformable porous media containing two immiscible fluids 总被引：1，自引：0，他引：1
The study of the poroelastic behavior of sedimentary materials containing two immiscible fluids in response to either applied stress or pore pressure change in a quasistatic limit, i.e., negligible second time-derivatives, is of great importance to many hydrogelogical problems, e.g., land subsidence caused by withdrawal of subsurface fluids. The poroelasticity models developed for analyzing these problems feature partial differential equations that are coupled in the terms describing viscous damping and strain field. To determine closed-form analytical solutions for induced volumetric strain (dilatation) of the solid framework and its interaction with fluid flows, the choice of normal coordinates whose transformation can be performed to decouple these poroelastic equations is highly desirable. In this paper, we show that normal coordinates for decoupling these equations are real-valued and equal to three different linear combinations of the dilatations of the solid and the fluids (or equivalently, three different linear combinations of two individual fluid pressures and solid dilatation). In contrast to fully saturated porous media, it is found that the viscous damping effect must be represented in normal coordinates in the presence of the second fluid. The resulting decoupled equations representing independent motional modes are a Laplace equation and two diffusion equations, which can be solved analytically under a variety of initial and boundary conditions. Thus, after inverse transformation of normal coordinates is performed, the closed-form analytical solutions for induced solid volumetric strain and excess pore fluid pressures can be obtained simultaneously from our decoupled partial differential equations. 相似文献
19.
P.A.C. Raats 《Journal of Hydrology》1974,21(4):357-369
A comprehensive analysis of steady flow patterns in saturated and unsaturated, possibly heterogeneous, isotropic soils is presented. It is shown that, at any point, the divergence of the unit tangent vector field to the streamlines is equal to the directional derivative along the streamlines of the orthogonal cross-sectional area of an infinitesimal stream tube divided by that area and also equal to the mean curvature of the surface of constant total head. Expressions are derived for the distribution of the flux, the water content, the velocity, the hydraulic conductivity, the total head, and the pressure head along a stream line or an infinitesimal, stream tube. Among the results is a simpler derivation, further interpretation, and extension of earlier work on calculating the hydraulic conductivity distribution from detailed measurements of the total head distribution in combination with measurements of the hydraulic conductivity at a few locations. In the last section, the jumps of various quantities at an interface are discussed. 相似文献
20.
Magnetic reconnection at a three-dimensional null point is a natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a null point with current directed parallel to the fan plane, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. The magnetic field is assumed to be steady, and a localised diffusion region surrounding the null point is also assumed, outside which the plasma is ideal. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flow is found to cross the spine and fan of the null, and thus transfer magnetic flux between topologically distinct regions. Solutions are also found in which the flow crosses either the spine or fan only. 相似文献