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1.
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
2.
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
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 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
5.
The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for
resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion
that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical
experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature
and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines
to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated
experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary
layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive,
unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow
boundary layers that form on the island itself. 相似文献
6.
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
7.
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
8.
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
9.
Lahcen Zouhri 《水文研究》2010,24(10):1308-1317
An electrical prospecting survey is conducted in the Rharb basin, a semi‐arid region in the southern part of the Rifean Cordillera (Morocco) to delineate characteristics of the aquifer and the groundwater affected by the marine intrusion related to Atlantic Ocean. Analysis and interpretations of electrical soundings, bi‐logarithmic diagrams and the geoelectrical sections highlight a monolayer aquifer in the southern part, a multilayer system in the northern part of the Rharb basin and lenticular semi‐permeable formations. Several electrical layers have been deduced from the analysis of bi‐logarithmic diagrams: resistant superficial level (R0), conducting superficial level (C0), resistant level (R), intermediary resistant level (R′), conducting level (Cp) and intermediary layer of resistivity (AT). Spatial distribution of the resistivity deduced from the interpretation of apparent resistivity maps (AB = 400 and 1000 m) and the decreasing of resistivity values (35–10 Ωm), in particular in the coastal zone show that this heterogeneity is related to several anomalies identified in the coastal area, which result from hydraulic and geological processes: (i) heterogeneous hydraulic conductivity in particular in the southern part of the Rharb; (ii) lateral facies and synsedimentary faulting and (iii) the relationship between the electrical conductivity and chloride concentration of groundwater shows that salinity is the most important factor controlling resistivity. The distribution of fresh/salt‐water zones and their variations in space along geoelectrical sections are established through converting subsurface depth‐resistivity models. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
Laboratory flume experiments were done to investigate bed load sediment transport by both steady and unsteady flows in a degrading channel. The bed, respectively composed of uniform sand, uniform gravel, or sand-gravel mixtures, always undergoes bulk degradation. It is found that both uniform and non-uniform bed load transport is enhanced greatly by unsteady flows as compared to their volume-equivalent steady flows. This enhancement effect is evaluated by means of an enhancement factor, which is shown to be larger with a coarser bed and lower discharges. Also, the fractional transport rates of gravel and sand in non-uniform sand-gravel mixtures are compared with their uniform counterparts under both steady and unsteady flows. The sand is found to be able to greatly promote the transport of gravel, whilst the gravel considerably hinders the transport of sand. Particularly, the promoting and hindering impacts are more pronounced at lower discharges and tend to be weakened by flow unsteadiness. 相似文献
11.
Summary The elastic response (i.e., displacement fields, strain and stress distributions) has been determined by structural matrix analysis for a homogeneous rock layer subjected to two-dimensional distributions of vertical displacement applied along a basal boundary. The results obtained compare favorably with biharmonic function solutions obtained bySanford [42]2) and the authors. The analysis was then extended: the effects of different magnitudes of superposed gravitationally-induced stresses, release of a constrained side boundary, and introduction of pronounced heterogeneity were each quantitatively evaluated. Each of these changed conditions effected important alterations in response characteristics, e.g., in configuration of stress trajectories, predicted locations and configurations of initial fracture surfaces, shear stress distributions, and displacement fields.These results are cited as an example of the utility of finite-element analysis (originally developed for evaluation of aeronautical structural components) for solutions of boundary value problems of a geological/geophysical nature. The breadth of specific physical problems succeptible to evaluation by this method is large and includes (i) behavior of rocks under static/dynamic loading, (ii) seismic response, (iii) heat and fluid flow, and (iv) distribution of potential. Most of the fundamental problems in geophysics, structural geology, geohydrology, geomorphology, glaciology, and engineering geology involve the above categories either directly or otherwise. The finite-element approach to these problems if bound to have enormous significance, for unlike classical mechanics, it can be readily adapted to solution of systems characterized by non-linear, anisotropic, heterogeneous material properties, of any exterior configuration, containing structural discontinuities, and subjected to any viable combinations of load/displacement boundary conditions. 相似文献
12.
Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
13.
S. E. Serrano T. E. Unny 《Stochastic Environmental Research and Risk Assessment (SERRA)》1987,1(4):281-296
Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to closure approximations (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient. 相似文献
14.
《Advances in water resources》2001,24(7):793-801
Topological groundwater hydrodynamics is an emerging subdiscipline in the mechanics of fluids in porous media whose objective is to investigate the invariant geometric properties of subsurface flow and transport processes. In this paper, the topological characteristics of groundwater flows governed by the Darcy law are studied. It is demonstrated that: (i) the topological constraint of zero helicity density during flow is equivalent to the Darcy law; (ii) both steady and unsteady groundwater flows through aquifers whose hydraulic conductivity is an arbitrary scalar function of position and time are confined to surfaces on which the streamlines of the flow are geodesic curves; (iii) the surfaces to which the flows are confined either are flat or are tori; and (iv) chaotic streamlines are not possible for these flows, implying that they are inherently poorly mixing in advective solute transport. 相似文献
15.
Marijan Dravinski 《地震工程与结构动力学》1983,11(3):313-335
Scattering of plane harmonic SH, P, SV and Rayleigh waves by several inclusions of arbitrary shape, completely embedded into an elastic half-space, is considered. Perfect bonding between the half-space and the inclusions is assumed. The problem is investigated for linear, isotropic and homogeneous elastic materials. The displacement field is evaluated throughout the elastic medium so that the continuity conditions between the half-space and the inclusions are satisfied in mean-square sense. Numerical results of the surface displacement field are evaluated for single and two elliptic inclusions. The results show the following: (a) presence of a subsurface inhomogeneity may lead to large amplifications of the surface ground motion; (2) different surface displacement patterns emerge for different incident waves; (3) the presence of an additional inclusion may change significantly the surface displacement response of a single inclusion; (4) the surface motion extremes strongly depend upon (i) angle of incidence; (ii) frequency of incident field; (iii) embedment depth of the inclusions; (iv) separation distance between the inclusions; (v) material properties of the half-space and the inclusions; and (vi) location of observation point on the surface of the half-space. 相似文献
16.
Land subsidence due to subsurface fluid (water, gas, oil) withdrawal is often predicted by either finite element or finite difference numerical models based on coupled poroelastic theory, where the soil is represented as a semi-infinite medium bounded by the traction-free (ground) surface. One of the variables playing a most important role on the final outcome is the flow condition used on the traction-free boundary, which may be assumed as either permeable or impermeable. Although occasionally justified, the assumption of no-flow surface seems to be in general rather unrealistic. A permeable boundary where the fluid pressure is fixed to the external atmospheric pressure appears to be more appropriate. This paper addresses the response, in terms of land subsidence, obtained with a coupled poroelastic finite element model that simulates a distributed pumping from a horizontal aquifer confined between two relatively impervious layers, and takes either a permeable boundary surface, i.e., constant hydraulic potential, or an impermeable boundary, i.e., a zero Neumann flow condition. The analysis reveals that land subsidence is rather sensitive to the flow condition implemented on the traction-free boundary. In general, the no-flow condition leads to an overestimate of the predicted ground surface settlement, which could even be 1 order of magnitude larger than that obtained with the permeable boundary. 相似文献
17.
Pampanin DM Camus L Gomiero A Marangon I Volpato E Nasci C 《Marine pollution bulletin》2005,50(12):512-1557
The aim of this study was to evaluate the susceptibility to pollutant mediated oxidative stress of the Mediterranean mussel Mytilus galloprovincialis in the Venice lagoon (Italy).
In June 2003, mussels from a farm were transplanted to eight sites in the lagoon for five weeks. Oxidative stress responses were measured by: (i) total oxyradical scavenging capacity (TOSC) assay, for an overall evaluation of the oxidative stress response capability; (ii) catalase (CAT), as a key enzyme involved in the antioxidant defence system; (iii) malondialdehyde (MDA), as an indicator of lipid peroxidation, to evaluate an oxidative damage; (iv) metallothioneins (MTs), as they play a role in the antioxidant defence.
The TOSC analysis revealed a reduced capability to eliminate: (i) peroxyl radical in mussels transplanted at Palude della Rosa, Valle Millecampi and Chioggia; (ii) hydroxyl radical at Campalto and Valle Millecampi; (iii) peroxynitrite at Valle Millecampi.
Inhibition in CAT activity, observed in all the monitored sites, confirms the presence of an oxidative pressure in transplanted mussels.
In addition, Pearson correlation analysis was performed in order to observe possible links between the various parameters. The PCA was a powerful tool to discriminate impacted sites, suggesting that the mussels transplanted throughout the Venice lagoon were subjected to different levels of oxidative pressure. Furthermore, it provided an easy and useful tool to summarize the obtained results. 相似文献
18.
S. S. Kevorkyants 《Izvestiya Physics of the Solid Earth》2006,42(8):702-711
Forward seismic problems are solved for elastic media by rigorous methods (i.e., methods with controllable accuracy). Analysis of the current state of research on this subject suggests that the most promising methods are based on integral and integro-differential equations, notwithstanding the rather modest results of their application to solving forward problems in the theory of elastic vibrations. The second Green integral theorem for seismic waves, formulated and proven in the paper, yields a system of two boundary (surface) integral equations for the displacement vector u(M 0) and the normal (to the boundary surface) vector component of the stress tensor tn(M 0). The integrands of the surface integrals in terms of which the function tn(M 0) is expressed on both sides of the interface between the medium and the heterogeneity contain the second derivatives of the Green’s tensor functions ? e (M 0, M) and ? i (M 0, M), respectively, which are responsible for a cubic singularity (third-order singularity) if the integration point M coincides with the observation point M 0. An original method of eliminating the cubic singularity proposed in the paper involves special tensor normalization of the integrals on the outer and inner sides of the interface and subsequent subtraction of one integral from another in order to construct the second integral equation. 相似文献
19.
An ensemble-based approach is developed to conduct optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where an ensemble of deterministic predictions is used to model and quantify uncertainty. In an operational setting, much about dynamics, topography, and forcing of the ocean environment is uncertain. To address this uncertainty, the flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each of the resulting realizations of the uncertain current field, we predict the path that minimizes the travel time by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of the sampling strategy and to develop insight into extensions dealing with general circulation ocean models. In particular, the ensemble method enables us to perform a statistical analysis of travel times and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows. 相似文献
20.
James D. L. White 《Bulletin of Volcanology》1996,58(4):249-262
The subaqueous phases of an eruption initiated approximately 85 m beneath the surface of Pleistocene Lake Bonneville produced
a broad mound of tephra. A variety of distinctive lithofacies allows reconstruction of the eruptive and depositional processes
active prior to emergence of the volcano above lake level. At the base of the volcano and very near inferred vent sites are
fines-poor, well-bedded, broadly scoured beds of sideromelane tephra having local very low-angle cross-stratification (M1
lithofacies). These beds grade upward into lithofacies M3, which shows progressively better developed dunes and cross-stratification
upsection to its uppermost exposure approximately 10 m below syneruptive lake level. Both lithofacies were emplaced largely
by traction from relatively dilute sediment gravity flows generated during eruption. Intercalated lithofacies are weakly bedded
tuff and breccia (M2), and nearly structureless units with coarse basal layers above strongly erosional contacts (M4). The
former combines products of deposition from direct fall and moderate concentration sediment gravity flows, and the latter
from progressively aggrading high-concentration sediment gravity flows. Early in the eruption subaqueous tephra jetting from
phreatomagmatic explosions discontinuously fed inhomogeneous, unsteady, dilute density currents which produced the M1 lithofacies
near the vent. Dunes and crossbeds which are better developed upward in M3 resulted from interaction between sediment gravity
flows and surface waves triggered as the explosion-generated pressure waves and eruption jets impinged upon and occasionally
breached the surface. Intermingling of (a) tephra emplaced after brief transport by tephra jets within a gaseous milieu and
(b) laterally flowing tephra formed lithofacies M2 along vent margins during parts of the eruption in which episodes of continuous
uprush produced localized water-exclusion zones above a vent. M4 comprises mass flow deposits formed by disruption and remobilization
of mound tephra. Intermittent, explosive magma–water interactions occurred from the outset of the Pahvant eruption, with condensation,
entrainment of water and lateral flow marking the transformation from eruptive to "sedimentary" processes leading to deposition
of the mound lithofacies.
Received: 10 October 1995 / Accepted: 18 April 1996 相似文献