共查询到20条相似文献，搜索用时 968 毫秒
1.
Summary Unsteady boundary layer flows generated in an incompressible, homogeneous, nonrotating viscous fluid bounded by a rigid wavy plate are studied theoretically. The Laplace transform method is employed to obtain exact solutions of the unsteady boundary layer equations in a wavy plate configuration. The structures of the unsteady velocity distribution and the associated boundary layers are determined explicitly and several particular solutions are recovered as special cases of this analysis. The physical interpretation of the mathematical results are examined. 相似文献
2.
This article examines the conditions under which the pressure-work and viscous dissipation terms should be retained in the energy balance relation for single (liquid water or vapor) and two-phase (liquid water and vapor) fluid flow through porous media. It is shown that if one wishes to retain the pressure-work term, then one must also keep the viscous dissipation term in the energy balance. Consideration of steady non-isothermal radial flow demonstrates that both pressure-work and viscous dissipation are liable to have negligibly small effects in single phase liquid water and in two-phase liquid-vapor systems. This conclusion is, however, not generally valid for pure vapor systems; in this case, pressure-work and viscous dissipation can produce significant variations in the computed reservoir response. 相似文献
3.
Summary Unsteady boundary layer flows generated in a homogeneous, non-rotating viscous fluid are considered. The method of Laplace transform is used to obtain exact solutions of the unsteady boundary layer equations in a more general situation. The structures of the unsteady velocity field and the associated boundary layers are determined. Several particular solutions are recovered as special cases of the present general theory. The physical implications of the mathematical results are investigated. 相似文献
4.
Summary Some exact solutions are presented for the unsteady boundary layer flows of a homogeneous, viscous, incompressible fluid bounded by (i) an infinite rigid oscillating flat plate or (ii) two parallel rigid oscillating flat plates. An explicit representation of the velocity fields for both the configurations has been given. The structures of the associated periodic boundary layers are determined with physical interpretations. Several results of interest have been recovered as special cases of this general theory. The Heaviside operational calculus along with the theory of residues of analytic functions is adopted in finding the solutions. 相似文献
5.
L. W. Morland 《地球物理与天体物理流体动力学》2013,107(1-4):237-266
Abstract The flow of large natural ice masses under gravity is described by the mass, momentum, and energy balances of an incompressible, homogeneous, heat conducting, non-linearly viscous fluid in which the shear response includes a strongly temperature-dependent rate factor. Dimensionless analysis and co-ordinate stretching reflecting the long aspect ratio show that series expansions in a small parameter which determines the surface slope magnitude are uniformly valid even when temperature variation induces a strongly non-uniform mechanical response. The normalised energy balance shows that both horizontal and vertical advection are significant in thin and thick grounded sheets and in floating shelves, and that viscous dissipation can be significant in basal regions of a grounded sheet, and hence there is strong thermomechanical coupling. Moreover, though a thermal basal boundary layer may arise in a thick sheet, it would only give rise to significantly enhanced temperature and strain-rate gradients in extreme circumstances. The leading order relations for steady plane flow of a grounded sheet are reduced to a parabolic system for the temperature and two velocity components, which incorporates the unknown surface slope in coefficients and boundary conditions. This provides a useful starting point for numerical solution of the thermomechanically coupled problem. A fixed domain mapping is presented as an attractive alternative formulation when the bed topography is close to planar. 相似文献
6.
Takashi Ichiye 《Pure and Applied Geophysics》1971,85(1):324-353
Summary The equations of conservations of momentum and energy scaled with the characteristic values of the mantle indicate the presence of the upper boundary layer to produce the estimated rate of the ocean floor spreading by convection and the importance of the frictional heating. The depth of the upper boundary layer can be estimated from the balance of the viscous force with the horizontal pressure gradient at the sea floor. It is of the orders of 100 km and becomes deeper for the Pacific than for the Atlantic Ocean and also with frictional heating than without it. The frictional heating increases the surface heat flow of the heat conduction by ten to twenty percent for the Pacific Ocean but only by a few percent for the Atlantic Ocean. The similarity solutions are determined for the temperature and horizontal velocity in the upper boundary layer. These solutions are expressed in power series of the variabley x
–n
, wherex, y, andn are horizontal and vertical coordinates and numerical constant, respectively. Both temperature and horizontal velocity within the boundary layer are higher for the Pacific than for the Atlantic Ocean. When a larger viscosity is applied, it causes the increase of horizontal velocity below the surface because of the surface boundary conditions of the finite velocity and of vanishment of the velocity shear. The higher horizontal velocity generates higher temperature because it advects hotter material from the mid-ocean ridge site. The direct effect of frictional heating on the temperature distribution of the similarity solution is almost negligible, since the shear zone is deep and near the lower boundary of the upper boundary layer. In the similarity solution, the surface heat flow which is increased by the frictional heating is given as the boundary value. The effect of the frictional heating is important below the mid-ocean ridge. 相似文献
7.
Summary In this paper, an investigation is made of the unsteady flow generated in a viscous, incompressible and homogeneous fluid bounded by (i) an infinite horizontal porous plate atz=0, or (ii) two infinite horizontal porous plates atz=0 andz=D. The fluid together with the plate(s) is in a state of solid body rotation with a constant angular velocity about the z-axis normal to the plate(s), and additionally, the plate(s) performs non-torsional elliptic harmonic oscillations in its (their) own plane(s). A uniform suction or injection is introduced in the configurations through the porous plate(s) and its influence on the unsteady flow and the associated boundary layers is examined. The unsteady flow field as well as the associated boundary layers is obtained explicitly. In contrast to the unsteady rotating flow without suction, solutions of the present problem with suction exhibit no resonant phenomena. It is shown that the suction is responsible for making the boundary layers thinner and for the elimination of the resonant phenomena. It is confirmed that the velocity field and the associated multiple boundary layers are significantly modified by suction. Physical significances of the mathematical results are discussed. Several limiting cases of interest are recovered from this analysis. The initial value problem for both the configurations is exactly solved by the Heaviside operational calculus combined with the theory of residues. 相似文献
8.
The dissipation method, the method preferred for estimating scalar surface fluxes over open water has not traditionally been used by agronomists, whereas the surface renewal (SR) theory in conjunction with the analysis of the scalar time trace offers tremendous advantages for estimating fluxes over agronomic crops. For a steady and horizontally homogeneous flow, it is shown that the dissipation method and SR analysis are closely related. As a consequence, a new dissipation–SR analysis expression for estimating scalar surface fluxes was derived. The new equation requires no calibration, and the scalar time trace measured at a frequency capable of identifying canopy‐scale coherent structures (typically 4–10 Hz in agriculture) is the only input required. Sensible and latent heat flux estimates obtained from 10 Hz air temperature and water vapour concentration measurements in the inertial sub‐layer (2 m height) over short, homogeneous rangeland grass at a site where similarity does not hold gave similar results to those measured with the eddy covariance (EC) method. For unstable cases, the new equation provided a root mean square error of 57 W m?2 for the surface energy‐balance closure. For stable cases, the performance was difficult to evaluate because the EC fluxes were similar in magnitude to the sensor error. It is concluded that the proposed method can contribute to a better understanding of hydrological processes and water requirements by providing an accurate, less costly, alternative method to indirectly estimate evapotranspiration as the residual of the energy balance equation. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
9.
In this paper we derive some similarity solutions of a nonlinear equation associated with a free boundary problem arising
in the shallow-water approximation in glaciology. In addition we present a classical potential symmetry analysis of this second-order
nonlinear degenerate parabolic equation related to non-Newtonian ice sheet dynamics in the isothermal case. After obtaining
a general result connecting the thickness function of the ice sheet and the solution of the nonlinear equation (without any
unilateral formulation), a particular example of a similarity solution to a problem formulated with Cauchy boundary conditions
is described. This allows us to obtain several qualitative properties on the free moving boundary in the presence of an accumulation-ablation
function with realistic physical properties. 相似文献
10.
Summary An investigation is carried out on the unsteady boundary layer induced in an incompressible, homogeneous, viscous fluid bounded by (i) an infinite horizontal porous plate aty=0, or (ii) two parallel horizontal rigid porous plates aty=0 andy=d. The unsteady motion is generated in the above fluid configurations by moving the plate(s) impulsively in its (their) own plane with a prescribed time-dependent velocity. Solutions for the unsteady velocity field are exactly solved by the Laplace transform treatment combined with the theory of residues. The structures of the associated boundary layers are determined. The effects of suction on the solutions and the boundary layers are investigated in detail, the limiting behaviour of the unsteady solution as timet is examined and Physical interpretations of the mathematical results are given. Finally, the frictional stresses on the plates are stated without detailed calculation. 相似文献
11.
Abstract The adjustment of a nonlinear, quasigeostrophic, stratified ocean to an impulsively applied wind stress is investigated under the assumption that barotropic advection of vortex tube length is the most important nonlinearity. The present study complements the steady state theories which have recently appeared, and extends earlier, dissipationless, linear models. In terms of Sverdrup transport, the equation for baroclinic evolution is a forced advection-diffusion equation. Solutions of this equation subject to a “tilted disk” Ekman divergence are obtained analytically for the case of no diffusion and numerically otherwise. The similarity between the present equation and that of a forced barotropic fluid with bottom topography is shown. Barotropic flow, which is assumed to mature instantly, can reverse the tendency for westward propagation, and thus produce regions of closed geostrophic contours. Inside these regions, dissipation, or equivalently the eddy field, plays a central role. We assume that eddy mixing effects a lateral, down-gradient diffusion of potential vorticity; hence, within the closed geostrophic contours, our model approaches a state of uniform potential vorticity. The solutions also extend the steady-state theories, which require weak diffusion, by demonstrating that homogenization occurs for moderately strong diffusion. The evoiution of potential vorticity and the thermocline are examined, and it is shown that the adjustment time of the model is governed by dissipation, rather than baroclinic wave propagation as in linear theories. If dissipation is weak, spin-up of a nonlinear ocean may take several times that predicted by linear models, which agrees with analyses of eddy-resolving general circulation models. The inclusion of a western boundary current may accelerate this process, although dissipation will still play a central role. 相似文献
12.
《Advances in water resources》1996,19(4):207-213
It is shown that from any solution of the linear diffusion equation, we may construct a solution of a realistic form of the Richards equation for unsaturated flow. Compared to the usual direct linearization method, our inverse approach involves a quite different sequence of transformations. This opens the possibility of exact solutions with a wider variety of continuously varying flux boundary conditions. Closed-form solutions are presented for two examples. In these, the varying water flux boundary conditions resemble (i) the passage of a peaking storm and (ii) the continuous opening of a valve preceding a steady water supply. Unlike earlier more systematic approaches to this problem, our method does not require the numerical solution of an integral equation. 相似文献
13.
P.W. France 《Journal of Hydrology》1974,21(4):381-398
A numerical method is presented for analysing either steady state or transient three-dimensional groundwater flow problems. The governing equation is formulated in terms of the finite element process using the Galerkin approach, and cubic isoparametric elements are used to simulate the flow domain as these permit accurate modelling of curved boundaries. Particular attention is paid to the time dependent movement of the phreatic surface where an iterative technique based on the replacement of the original transient problem by a discrete number of steady state problems is used to effect a solution. Furthermore, in tracing the movement of the surface use is made of the element formulation theory in order to compute the normal to the boundary.The validity of the technique is first established by analysing a radially symmetrical problem for which an alternative analytical solution is available. Finally, a general three-dimensional flow system is studied for which there is no known analytical solution. It is shown that relatively few elements are required to yield practical solutions. 相似文献
14.
Analytical solutions describing the concentration distribution along one-dimensional unsteady seepage flow through adsorbing saturated finite porous medium have been obtained. An exponential function concentration is enforced at the source of the dispersion, while the change in the concentration is zero at the other boundary. A new time variable has been introduced to solve the unsteady flow problem and the solution is illustrated. 相似文献
15.
１ＩＮＴＲＯＤＵＣＴＩＯＮＲｉｖｅｒｓｉｎＴａｉｗａｎａｒｅｒｅｌａｔｉｖｅｌｙｓｔｅｅｐｅｒｃｏｍｐａｒｅｄｔｏｔｈｏｓｅｉｎｏｔｈｅｒｃｏｎｔｉｎｅｎｔ．Ｌｏｃａｌｙｏｃｕｒｅｄｓｕｐｅｒｃｒｉｔｉｃａｌｆｌｏｗａｒｅｆａｉｒｌｙｃｏｍｍｏｎｉｎ... 相似文献
16.
The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial–boundary value problem, becomes self‐similar are investigated by utilizing one‐parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self‐similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self‐similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial–boundary value problem of a one‐dimensional unsteady open channel flow process in a prototype domain can be self‐similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal–horizontal and transverse–horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross‐section because the width‐to‐depth ratio and the inclination angles of the banks are conserved in a cross‐section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
17.
Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν0 + ν1 exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 107 and Rayleigh numbers of up to 108 are studied.For intermediate viscosity contrasts (around 103), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth zr (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 1015?5 × 1016 m2 s?1 for viscosity in the thermal boundary layer below the plate. 相似文献
18.
Farhad YAZDANDOOST 《国际泥沙研究》2005,20(4):358-365
1 INTRODUCTION Rivers as a source of life can at the same time impose devastating conditions on the environment. It is , therefore, imperative to analyse and predict river behaviour for different given conditions and engineering activities. Therefore, the use of simulation tools in this field has become a necessity. Many computational tools for simulation of sediment transport in rivers are now available that can be used for prediction and design under different flow conditions. However, … 相似文献
19.
Abstract Stability analysis is formulated for a two-layer fluid model in which the upper and lower layers are convectively stable and unstable, respectively. With discontinuities in viscosity and conductivity at the interface, the exchange of stability does not generally hold and overstability is possible. A detailed analytical treatment is presented for the case of small viscosity and conductivity in which viscous and conducting boundary layers are formed at the interface. The usual damping effect due to the energy dissipation by viscosity and thermal conductivity exists irrespective of whether the mode is the convection or the gravity wave, but, for larger horizontal wave lengths, the effect of the boundary layer can become more important. The jump in the thermal conductivity in the boundary layer can give rise to overstability of the gravity wave in agreement with Souffrin and Spiegel (1967). The jump in the viscosity provides a self-catalytic action for the unstable flow if the viscosity is assumed to be the nonlinear turbulent viscosity due to the motion itself. The effect, however, is not strong enough to overcome the usual viscous damping. 相似文献
20.
从洋中脊上升的地慢物质带上来的大量热量,使在洋中脊裂谷处的海底热流及温度最高,向海沟逐渐减小．由于热胀冷缩,海底地势在洋中脊处最高．作者根据板块模型由一维运动物体的热传导方程推出裂谷处上升物体的温度分布公式．用此分布公式作为垂直边的边界条件,严格地求解了运动板块的二维运动物体热传导方程．用此方程研究了各参数与观测量之间的关系．通过改变公式中的参数值,使计算的理论曲线与实测海底热流一年龄及海底深度一年龄曲线拟合,从而求出了板块的厚度Ｌ＝９７ｋｍ,地幔上升速度ｕ＝３．ｇｍｍ／ａ,热膨胀系数ａ＝３．３７×１０－５／℃及温度分布．该方法克服了在洋中脊处理论热流值趋于无限大的问题,并可以计算出地幔上升流的速度及宽度． 相似文献