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1.
ABSTRACT

The study presented herein forms part of a wider research project on dispersion prediction in open channel flows which include laboratory, field and numerical investigations. In this paper, a numerical model which uses finite elements in space and finite differences in time for the solution of the convective-dispersion equation is developed and verified. In the model, the dispersion coefficient is considered as a function of time (or distance) during the initial period. It is represented by a modified Fickian type model which has been calibrated by the authors using laboratory data. The numerical model has been used to predict concentration profiles of tracer studies carried out in the laboratory as well as in the field.  相似文献   

2.
Abstract

The steady nonlinear regime of Bénard convection in a uniformly rotating fluid is treated using a two-dimensional primitive-equation numerical model with rigid boundaries. Quantitative comparisons with laboratory heat transport data for water are made in the parameter ranges for which the experimental flows are approximately two-dimensional and steady. When an experimentally realistic spatial periodicity is imposed upon the numerical solution, the model simulates the experimental determinations of Nusselt number fairly accurately. In particular, it predicts the observed non-monotonic dependence on Taylor number. When spatial periodicities corresponding to those of the linear stability problem are specified, however, the accuracy of the simulation is less and the Taylor number dependence is monotonic.  相似文献   

3.
Dike breaking is a disaster that could cause extensive damage. It could lead to flood flows outside the dike and induce water level fluctuations in the main channel. Numerical models are increasingly used to simulate flood flows due to dike-break, because direct observations from field surveys and physical models are rather limited. Existing knowledge concerning dam-break flows cannot be applied directly to dike-break flows because the effect of channel discharge cannot be neglected in the latter. In this study,physical experiments are done in a large laboratory flume to simulate the process of dike-break induced flood wave propagation in the floodplain and flow fluctuations in the main channel. The variations of water levels and velocities are measured and recorded using an array of pressure sensors and two acoustic Doppler velocimetry devices. A numerical model has been set up according to the experimental layout. The experiments have high repeatability and the numerical model predictions agree closely with the physical model data. The experimental results provide reliable information for improving the understanding of dike-break flow dynamics and for the verification of numerical models.  相似文献   

4.
Abstract

An investigation is made of steady thermal convection of a Boussinesq fluid confined in a vertically-mounted rotating cylinder. The top and bottom endwall disks are thermal conductors at temperatures Tt and Tb with δT = Tt ? Tb >0. The vertical sidewall has a finite thermal conductance. A Newtonian heat flux condition is adopted at the sidewall. The Rayleigh number of the fluid system is large to render a boundary layer-type flow. Finite-difference numerical solutions to the full Navier-Stokes equations are obtained. The vertical motions within the buoyancy layer along the sidewall induce weak meridional flows in the interior. Because of the Coriolis acceleration, the meridional flows give rise to azimuthal flows relative to the rotating container. Strong vertical gradients of azimuthal flows exist in the regions near the endwalls. As the stratification effect increases, concentration of flow gradients in thin endwall boundary layers becomes more pronounced. The azimuthal flow field exhibits considerable horizontal gradients. The temperature field develops horizontal variations superposed on the dominant vertical distribution. As either the sidewall thermal conductance or the stratification effect decreases, the temperature distribution tends to the profile varying linearly with height. Comparisons of the sizes of the dynamic effects demonstrate that, in the bulk of flow field, the vertical shear of azimuthal velocity is supported by the horizontal temperature gradient, resulting in a thermal-wind relation.  相似文献   

5.
Abstract

The breakdown and separation or reattachment of boundary layers adjoining a mainstream are studied in the three related situations (i)-(iii) of the title. For (i) the classical steady boundary layer generally admits a logarithmic singularity in the displacement when breakdown occurs on a downstream-moving surface whereas the corresponding singularity for an upstream-moving surface can be logarithmic or of minus-one-sixth form. Conversely, the breakdown can be delayed to the onset of zero mainstream flow, in which case the displacement singularity is again logarithmic. In certain flows these singularities prove to be removable locally, yielding a breakaway separation or reattachment and including the first known successes of a classical strategy in describing large-scale separation. Other flows, by contrast, require an interactive strategy. Again, even on a fixed surface a breakdown different from Goldstein's can be produced if there is a moving section of surface further upstream. The application to (ii), semi-similar unsteady boundary layers, e.g. near an impulsively started wedge-like trailing edge, then follows readily and predicts analogous forms of singularity. The corresponding singularity in displacement predicted for fully unsteady classical boundary layers, (iii), occurs within a finite time and, like (i) (usually) and (ii), a three-tiered breakdown is involved at first. Subsequently interaction comes into play. Comparisons with numerical and/or earlier work are noted. In all three situations (i)-(iii), although the dynamics involved near breakdown, separation or reattachment are predominantly inviscid, the presence of small viscosity is of significance in enforcing smoothness of the local velocity profiles.  相似文献   

6.
Abstract

A theoretical model is described for estimating the impacts of changes in Lake Victoria levels on river flows, lake levels and swamp areas in the upper White Nile basin. The basis of the model is to represent the main river channel by a series of interconnected lakes and swamps, whose water balances are described by differential equations relating outflows to levels, areas and the net basin supply at each point. Closed form solutions are obtained for two situations: (a) a long-term change in the mean level of Lake Victoria, and (b) a return to equilibrium levels following an initial disturbance in Lake Victoria levels. A simple model for the net basin supply to Lake Victoria is also used to relate these changes in levels to changes in climate and runoff in the basin. The results illustrate the extreme sensitivity of White Nile flows to changes in Lake Victoria levels and outflows, and in particular to variations in the direct rainfall on the lake surface. Estimates are also presented for the various time scales and time delays which affect the White Nile system.  相似文献   

7.
Seasonal and event variations in stream channel area and the contributions of channel precipitation to stream flow were studied on a 106‐ha forested headwater catchment in central Pennsylvania. Variations in stream velocity, flowing stream surface width and widths of near‐stream saturated areas were periodically monitored at 61 channel transects over a two‐year period. The area of flowing stream surface and near‐stream saturated zones combined, ranged from 0·07% of basin area during summer low flows to 0·60% of total basin area during peak storm flows. Near‐stream saturated zones generally represented about half of the total channel area available to intercept throughfall and generate channel precipitation. Contributions of routed channel precipitation from the flowing stream surface and near‐stream zones, calculated using the Penn State Runoff Model (PSRM, v. 95), represented from 1·1 to 6·4% of total stream flow and 2·5–29% of total storm flow (stream flow–antecedent baseflow) during the six events. Areas of near‐stream saturated zones contributed 35–52% of the computed channel precipitation during the six events. Channel precipitation contributed a higher percentage of stream flow for events with low antecedent baseflow when storm flow generated by subsurface sources was relatively low. Expansion of channel area and consequent increases in volumes of channel precipitation with flow increases during events was non‐linear, with greater rates of change occurring at lower than at higher discharge rates. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

8.
Laboratory experiments are used to illustrate how steady convective flows, while efficient at stirring an initial heterogeneity within a single cell, do not produce dispersal of heterogeneous material over scales large compared to the depth. Long-range dispersal requires that the flow be time dependent on a time scale comparable to the overturn time. Convection in an internally heated layer has this property and numerical solutions are used to study the way in which it disperses a set of neutrally buoyant particles that were initially confined to a small space. The horizontal dispersal of these particles is reasonably well represented by an effective diffusivity of 0.3 cm2/s for a Rayleigh number of 106. The concept of an effective diffusivity is then applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems with spatial variations generated by horizontal variations in degree of melting 1.8×109 years ago. The present-day average ε value one would measure in such a system depends on the average degree of melting, the amplitude and length scale of variations in partial melt, and the effective diffusivity assumed. Especially in the case of Nd the differences in average ε value between a uniform and a spatially variable (but with the same average) melting case can be significant. The range of ε values about the average is controlled by the competing effects of generation by the differences in enrichment factor and decay due to the effective diffusivity.  相似文献   

9.
A 1:50 scale hydraulic model was designed, based on Froude number similarity and using hydrological and sediment data from a small braided gravel-bed river (the North Branch of the Ashburton River, Canterbury, New Zealand). Eighteen experiments were conducted; seven using steady flows, and eleven using unsteady flows. The experiments were carried out in a 20 m × 3 m tilting flume equipped with a continuous sediment feed and an automated data acquisition and control system. In all experiments water at 30°C was used to reduce viscosity-related scale effects. Analyses of the experimental data revealed that bedload transport rates in braided channels are highly variable, with relative variability being inversely related to mean bedload transport rate. Variability was also found to be cyclic with short-term variations being caused by the migration of bedforms. Bedload transport was found to be more efficient under steady flow than under unsteady flow, and it was postulated that this is caused by a tendency for channel form to evolve towards a condition which maximizes bedload transport for the occurring flow. Average bedload transport rate was found to vary with channel form, although insufficient measurements were made to define a relationship.  相似文献   

10.
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   

11.
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   

12.
In this paper, a second order space discontinuous Galerkin (DG) method is presented for the numerical solution of inviscid shallow water flows over varying bottom topography. Novel in the implementation is the use of HLLC and kinetic numerical fluxes1 in combination with a dissipation operator, applied only locally around discontinuities to limit spurious numerical oscillations. Numerical solutions over (non-)uniform meshes are verified against exact solutions; the numerical error in the L2-norm and the convergence of the solution are computed. Bore–vortex interactions are studied analytically and numerically to validate the model; these include bores as “breaking waves” in a channel and a bore traveling over a conical and Gaussian hump. In these complex numerical test cases, we correctly predict the generation of potential vorticity by non-uniform bores. Finally, we successfully validate the numerical model against measurements of steady oblique hydraulic jumps in a channel with a contraction. In the latter case, the kinetic flux is shown to be more robust.  相似文献   

13.
This paper presents a three-dimensional (3-D) numerical model to simulate morphological changes in alluvial channels due to bank erosion. A method for the simulation of bank erosion is established. This is incorporated into a 3-D mathematical model for turbulent flow and non-uniform, non-equilibrium sediment transport. This model is applied to simulate morphological changes in the Shishou bend of the middle Yangtze River in China, where serious bank erosions occurred during the last two decades. The double-layer sediment structure of the riverbank on the middle Yangtze River is taken into account in the bank erosion module. Both cohesive and non-cohesive bank material in the different layers are considered. The bank erosion module also includes other factors affecting the rate of bank erosion, such as the longitudinal length of failed bank, the thickness of each layer in the double-layer structure, and the erosion-resisting effect of cohesive material from the top layer of failed bank. A locally-adaptive grid system is proposed to efficiently simulate the lateral migration of alluvial channel due to bank erosion. The predictive capability of the 3-D model is examined by laboratory data. Simulated processes of bank erosion agree with field observations in the Shishou bend during the period of October 1996–October 1998, and the bank erosion module plays a significant role in simulating morphological changes of the study reach. In addition, the equivalent channel-forming discharge, which is defined as a constant discharge that can create the same amount of bank erosion in an alluvial channel as that created by natural runoff processes during the same period of time, is proposed to improve calculation efficiency for feasibility studies.  相似文献   

14.
A general model for Mt. Ruapehu lahars   总被引：1，自引：1，他引：1  
A mathematical model of the motion of lahars is presented. Lahar flows and travel speeds are calculated using a kinematic wave model which equates gravitational accelerations to frictional losses. A chezyor Manning-type law of friction is assumed, in which lahar flow rate is a simple power function of lahar depth, multiplied by another simple power of the chanel slope. Use of the model requires knowledge of essentially only one parameter which appears to be relatively insensitive for flows down a given channel. Variable channel slope effects are removed by a longitudinal scaling which applies to all flows down a given channel. For lahars generated by a single explosive event it is unnecessary to perform numerical calculations to predict lahar flow and travel time, but for lahnars produced by multiple sources in which different lahar flows are interacting, numerical calculations appear necessary. The model is applied to all recorded lahar flows from Mt. Ruapehu, and satisfactorily described all lahar flows generated by a single explosive mechanism. Such flows depend essentially only on total lahar volume. The 1968 Mt. Ruapehu lahar, generated by a series of smaller eruptive mechanisms, was modelled as the interaction of seven point sources of fluid originating from positions mathematically extrapolated up the mountain. Good agreement was obtained between the predicted times of formation of these 1968 lahars, and the times of greatest seismic amplitude.  相似文献   

15.
The characteristics and forcing mechanisms of high-frequency flow variations (periods of minutes to days) were investigated near Gladden Spit, a reef promontory off the coast of Belize. Direct field observations and a high-resolution (50-m grid size) numerical ocean model are used to describe the flow variations that impact the initial dispersion of eggs and larvae from this site, which serves as a spawning aggregation site for many species of reef fishes. Idealized sensitivity model experiments isolate the role of various processes, such as internal waves, wind, tides, and large-scale flow variations. The acute horizontal curvature and steep topography of the reef intensify the flow, create small-scale convergence and divergence zones, and excite high-frequency oscillations and internal waves. Although the tides in this area are relatively small (∼10-cm amplitude), the model simulations show that tides can excite significant high-frequency flow variations near the reef, which suggests that the preference of fish to aggregate and spawn in the days following the time of full moon may not be coincidental. Even small variations in remote flows (2–5 cm s−1) due to say, meso-scale eddies, are enough to excite near-reef oscillations. Model simulations and the observations further suggest that the spawning site at the tip of the reef provides initial strong dispersion for eggs, but then the combined influence of the along-isobath flow and the westward wind will transport the eggs and larvae downstream of Gladden Spit toward less turbulent region, which may contribute to enhanced larval survival.  相似文献   

16.
A high resolution (3–8 km grid), 3D numerical ocean model of the West Caribbean Sea (WCS) is used to investigate the variability and the forcing of flows near the Meso-American Barrier Reef System (MBRS) which runs along the coasts of Mexico, Belize, Guatemala and Honduras. Mesoscale variations in velocity and temperature along the reef were found in seasonal model simulations and in observations; these variations are associated with meandering of the Caribbean current (CC) and the propagation of Caribbean eddies. Diagnostic calculations and a simple assimilation technique are combined to infer the dynamically adjusted flow associated with particular eddies. The results demonstrate that when a cyclonic eddy (negative sea surface height anomaly (SSHA)) is found near the MBRS the CC shifts offshore, the cyclonic circulation in the Gulf of Honduras (GOH) intensifies, and a strong southward flow results along the reef. However, when an anticyclonic eddy (positive SSHA) is found near the reef, the CC moves onshore and the flow is predominantly westward across the reef. The model results help to explain how drifters are able to propagate in a direction opposite to the mean circulation when eddies cause a reversal of the coastal circulation. The effect of including the Meso-American Lagoon west of the Belize Reef in the model topography was also investigated, to show the importance of having accurate coastal topography in determining the variations of transports across the MBRS. The variations found in transports across the MBRS (on seasonal and mesoscale time scales) may have important consequences for biological activities along the reef such as spawning aggregations; better understanding the nature of these variations will help ongoing efforts in coral reef conservation and maintaining the health of the ecosystem in the region.  相似文献   

17.
In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and two-dimensional cases. A systematic derivation of the equations in tensor notation is presented, resulting in a unified formulation for the shallow water equations that covers all orthogonal horizontal grid types of practical interest. This includes spherical curvilinear orthogonal co-ordinate systems on the globe. Computational efficiency can be achieved in a single computer code. Furthermore, a single numerical algorithmic code implementation satisfies. All co-ordinate system specific metrics are determined as part of a computer-aided model grid design, which supports all four orthogonal grid types. Existing intuitive grid design and visual interpretation is conserved by appropriate conformal mappings, which conserve spherical orthogonality in planar representation. A spherical curvilinear co-ordinate solution of wind driven steady channel flow applying a strongly distorted grid is shown to give good agreement with a regular spherical co-ordinate model approach and the solution based on a β-plane approximation. Especially designed spherical curvilinear boundary fitted model grids are shown for typhoon surge propagation in the South China Sea and for ocean-driven flows through Malacca Straits. By using spherical curvilinear grids the number of grid points in these single model grid applications is reduced by a factor of 50–100 in comparison with regular spherical grids that have the same horizontal resolution in the area of interest. The spherical curvilinear approach combines the advantages of the various grid approaches, while the overall computational effort remains acceptable for very large model domains.  相似文献   

18.
The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.  相似文献   

19.
Abstract

In this paper we examine the behaviour of oceanic unsteady flow impinging on isolated topography by means of numerical simulation. The ocean model is quasigeostrophic and forced by an oscillatory mean flow. The fluid domain is of the channel type and open-boundary numerical conditions are used to represent downstream and upstream flow.

In certain cases, vortex shedding, either cyclonic or anticyclonic, is observed in the lee of obstacles. Such shedding can be explained as the consequence of both an enhanced process of vorticity dissipation over the topography which locally affects the balance of potential vorticity on the advective timescale, and a periodic dominance of advective effects which sweep the fluid particles trapped on the seamount. For refined resolution and smallest viscosity the model will predict flows in which the shed eddies are coherent structures with closed streamlines.

The model suggests a mechanism by which topographically generated eddies may be swept away from a seamount in the ocean.  相似文献   

20.
It has been suggested that there exists a stably stratified electrically conducting layer at the top of the Earth's outer fluid core and that lateral temperature gradients in the lower mantle is capable of a driving thermal-wind-type flow near the core–mantle boundary. We investigate how such a flow in a stable layer could influence the geomagnetic field and the geodynamo using a very simple two-dimensional kinematic dynamo model in Cartesian geometry. The dynamo has four layers representing the inner core, convecting lower outer core, stable upper core, and insulating mantle. An α2 dynamo operates in the convecting outer core and a horizontal shear flow is imposed in the stable layer. Exact dynamo solutions are obtained for a range of parameters, including different conductivities for the stable layer and inner core. This allows us to connect our solutions with known, simpler solutions of a single-layer α2 dynamo, and thereby assess the effects of the extra layers. We confirm earlier results that a stable, static layer can enhance dynamo action. We find that shear flows produce dynamo wave solutions with a different spatial structure from the steady α2 dynamos solutions. The stable layer controls the behavior of the dynamo system through the interface conditions, providing a new means whereby lateral variations on the boundary can influence the geomagnetic field.  相似文献   

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