首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
Abstract

Bayly (1993) introduced and investigated the equation (? t + v·▽-η ▽2)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.  相似文献   

2.
《水文科学杂志》2013,58(4):700-712
Abstract

The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r 2 Bh′ + Pr 2 ? PR 2 = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions.  相似文献   

3.
Abstract

Abstract Base flows make up the flows of most rivers in Zimbabwe during the dry season. Prediction of base flows from basin characteristics is necessary for water resources planning of ungauged basins. Linear regression and artificial neural networks were used to predict the base flow index (BFI) from basin characteristics for 52 basins in Zimbabwe. Base flow index was positively related to mean annual precipitation (r = 0.71), basin slope (r = 0.76), and drainage density (r = 0.29), and negatively related to mean annual evapotranspiration (r = –0.74), and proportion of a basin with grasslands and wooded grasslands (r = –0.53). Differences in lithology did not significantly affect BFI. Linear regression and artificial neural networks were both suitable for predicting BFI values. The predicted BFI was used in turn to derive flow duration curves of the 52 basins and with R 2 being 0.89–0.99.  相似文献   

4.
ABSTRACT

Much of New Hampshire and Vermont (combined area = 50 000 km2) has hilly to mountainous topography. Elevations range from 0 to 1900 m a.s.l. (average = 360 m), and many peaks exceed 1200 m. Mean annual precipitation increases strongly with elevation (adjusted for additional orographic effects and distance from moisture sources), as do mean monthly precipitation, snow depth, and snow water equivalents. Mean monthly temperatures decrease with elevation, largely masking latitudinal effects, and can be used with other information to show how potential evapotranspiration changes with elevation. These effects combine to produce strong elevational increases in mean annual streamflow and, more surprisingly, cause streamflow variability, both short term and annual, to decrease with mean drainage basin elevation. Low flows for a given exceedance probability increase markedly as mean basin elevation increases above 340 m. Flood peaks for a given return period also increase with mean basin elevation. Slope and aspect affect the timing of snowmelt runoff, but otherwise appear to have only second order effects on hydrology. The effect of elevation is so dominant in the region that it can be used as the single independent variable in predicting many streamflow parameters.  相似文献   

5.
It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σ 103dyne/cm2), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σ = 104 dyne/cm2, if the flow rate is greater than 105 g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.  相似文献   

6.
ABSTRACT

Irrigation equipment was used to create strong flows in agricultural drains of clayware and plastic pipes, the latter in both smooth and corrugated conformations. The piezometric heads at 10 m intervals along the drains were analysed to show that the inflow per unit length varied greatly. Both inflows and outflows were found; some drains had substantial inflows at the origin. For given conditions the flow rates were as much as 17 per cent less than flow rates determined for similar conditions in the laboratory.  相似文献   

7.
Abstract

The impulse response and the response to a unit step function of the onedirectional semi-infinite aquifer is given, derived from the approximate partial differential equation of the ground water flow. An example is presented.  相似文献   

8.
Abstract

The probability-distributed catchment model, as originally proposed by Moore &; Clarke (1981), is re-examined from a maximum statistical entropy viewpoint. The distribution of water within a catchment is treated as a problem of statistical inference and resolved using an entropy maximization technique. A simple runoff generating mechanism is employed, which, together with the catchment mass balance equation, yields a catchment model involving just one dynamic parameter, y, and two constants, k and λ. The parameter y determines the temporal variation of catchment storage V and runoff q. The latter is nonlinearly related to V through q = k(1—λyV), where y provides the nonlinear departure from the simple linear reservoir q = kV.  相似文献   

9.
ABSTRACT

The maximum rainfalls recorded at the Cherrapunji Observatory raingauge during various periods within the 57 years from 1903 to 1959 have been studied and the equation of the enveloping line has found to be R = 49 D0.485 where R is the rainfall in inches and D is duration in days. One-day maximum rainfalls for different periods from two to 100 years have also been worked out and the 100-year value has been found to be 2.1 times the 2-year value. The daily probable maximum precipitation (PMP), estimated by the Hershfield technique, is 78 in. A study of annual and monsoon rainfalls did not show any general linear trend but there was a gradual increase in amounts from 1944 to 1954.  相似文献   

10.
Abstract

We examine the role played in annulus flows by mechanisms dependent upon the Prandtl number, σ. Solutions are obtained at σ = 1 for both the real annulus system and for the hypothetical “free annulus” system (free slip lateral boundaries). These solutions are compared with previously obtained solutions at σ = 7.

In the free annulus, the solution at σ = 1 differs radically from that at σ = 7. The σ = 1 solution appears to be essentially a finite amplitude mode due to Solberg instability whereas the solution at σ = 7 manifests a flow caused by the diffusive overturning mechanism.

The variation with σ of the real annulus flow is not so fundamental but some differences in the dynamical structures are noted.  相似文献   

11.
ABSTRACT

The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content.

Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data.

Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme.

Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate.  相似文献   

12.
Abstract

In this paper an analytical method to study the hydrodynamic stability of simple barotropic, non-divergent flows is discussed. The method is based on the variational approach introduced by Arnold and derived from the Lyapunov stability criteria. In this context, the sufficient condition for the stability of a steady barotropic flow ψ(x,y) is obtained when dP(ψ)/dPψ = ψ, the derivative of the absolute vorticity P(ψ), is positive definite. In this case, we discuss the effect of higher derivatives dnP(ψ)/dψnψψ = ψ on the non-linear stability. Then we show that some classical examples of oceanic non-divergent flows (i.e. lee waves downstream an Island, steady flows through a Strait, the Fofonoff gyre) are stable to finite-amplitude perturbations.  相似文献   

13.
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   

14.
We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε2 being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k c . For waves, the largest growth rate is of the order ε4/3. In the case of Eckhaus instability the growth rate is of the order of α2.  相似文献   

15.
Abstract

The linear stability of a non-divergent barotropic parallel shear flow in a zonal and a non-zonal channel on the β plane was examined numerically. When the channel is non-zonal, the governing equation is slightly modified from the Orr-Sommerfeld equation. Numerical solutions were obtained by solving the discretized linear perturbation equation as an eigenvalue problem of a matrix. When the channel is zonal and lateral viscosity is neglected the problem is reduced to the ordinary barotropic instability problem described by Kuo's (1949) equation. The discrepancy between the stability properties of westward and eastward flows, which have been indicated by earlier studies, was reconfirmed. It has also been suggested that the unstable modes are closely related to the continuous modes discretized by a finite differential approximation. When the channel is non-zonal, the properties of unstable modes were quite different from those of the zonal problem in that: (1) The phase speed of the unstable modes can exceed the maximum value of the basic flow speed; (2) The unstable modes are not accompanied by their conjugate mode; and (3) The basic flow without an inflection point can be unstable. The dispersion relation and the spatial structure of the unstable modes suggested that, irrespective of the orientation of the channel, they have close relation to the neutral modes (Rossby channel modes) which are the solutions in the absence of a basic shear flow. The features mentioned above are not dependent on whether or not the flow velocity at the boundary is zero.  相似文献   

16.
Abstract

A new nonlinear stability criterion is derived for baroclinic flows over topography in spherical geometry. The stability of a wide class of exact three-dimensional nonlinear steady state solutions subject to arbitrary disturbances is established. The resonance condition, at the highest total wavenumber, for the steady state solutions and the stability criteria for baroclinic flow in the absence of topography provide the boundaries of the regions of stability in the presence of topography. The analogous results for flow on periodic or infinite beta planes incorporating non-orthogonal function large scale flows are also discussed.  相似文献   

17.
Abstract

Fresh-water lenses are formed in unconfined saline aquifers in response to deep percolation from rainfall, artificial recharge, and seepage from irrigation waters and/or in response to injecting fresh water through vertical or horizontal wells. An approximate differential equation is derived in terms of the depth of the fresh-salt water interface below the initial position of the saline-water table. This equation is analogous to that of the ground-water motion in two dimensions. The wealth of knowledge available from solving the latter equation is used to obtain approximate expressions for the movement of the fresh-salt water interface in several flow systems wherein this interface does not reach the bottom of the aquifer. These approximate solutions as well as others for related quantities of interest may afford useful tools for rationally planning the extraction of usable waters from such flow systems.  相似文献   

18.
Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief.

On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 ()).  相似文献   

19.
Formulated as an inverse problem, the diffusion parameters associated with length-scale dependent eddy diffusivities can be viewed as the unknowns in the mass conservation equation for coastal zone transport problems. The values of the diffusion parameters can be optimized according to an error function incorporated with observed concentration data. Examples are given for the Fickian, shear diffusion and inertial subrange diffusion models. Based on a new set of dyeplume data collected in the coastal zone off Bronte, Lake Ontario, it is shown that the predictions of turbulence closure models can be evaluated for different flow conditions. The choice of computational schemes for this diagnostic approach is based on tests with analytic solutions and observed data. It is found that the optimized shear diffusion model produced a better agreement with observations for both high and low advective flows than, e.g., the unoptimized semi-empirical model, Ky=0.075 σy1.2, described by Murthy and Kenney.  相似文献   

20.
ABSTRACT

The hydrological data available for the Lower Mekong River are presented in directly usable form for design purposes by means of a regional frequency study of the annual maximum daily mean flows (floods) and by means of the annual mean minimum flows for various durations (droughts). In addition, a regional analysis is given of the annual dry season recession hydrograph. The only information required to apply these results is the size of the drainage area or the distance along the river upstream from Phnom-Penh.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号