Surface Flow Model Research Articles

Modelling floodplain flows using a two‐dimensional finite element model

AbstractA prototype two‐dimensional finite element flow model for depth‐averaged free surface flows was developed for floodplain environments. Limited refinement of the model's physical representation was undertaken and the enhanced scheme applied to an 11 km river channel/floodplain reach in the U.K. Preliminary model results indicate that this modelling approach can be used to identify dynamic variations in the flow field parameters over length scales of the order of 10‐100 m. Potentially, such data have the ability to permit detailed analysis of short‐term floodplain sedimentary dynamics.

Numerical Study of the Maximum Boundary Shear Stress Induced by Raindrop Impact

The magnitude, position, and timing of the instantaneous maximum boundary shear stress caused by a raindrop on a shallow pool of water are investigated using a series of computer simulation experiments in which the Navier‐Stokes equations are solved numerically. A dimensional analysis defines a set of parameters involving fluid properties and initial conditions relevant to the problem. Numerical simulations are performed over ranges of these parameters using a generic, two‐dimensional, incompressible, free surface flow model. Results of the simulations are summarized in simple algebraic relationships which serve to clarify the relative importance of the parameters. The algebraic relationships also serve as an efficient substitute for the numerical model in the estimation of the magnitude, position, and timing of the maximum boundary shear stress. Laboratory measurements of water‐droplet‐induced shear stress are used to demonstrate the validity of the algebraic relationships.

A perturbation analysis and finite element approximate model for free surface flow over curved beds

AbstractA perturbation analysis is developed for 1‐D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non‐linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep‐slope shallow water formulation corresponding to the model with zero curvature.

Ultrathin films in wetting evidenced by x-ray reflectivity.

The role of thin films in different situations of wetting has been investigated by x-ray reflectivity, a technique that allows an independent determination of their thicknesses, densities, and roughnesses, using a nonvolatile siloxane oil spreading on different kinds of surfaces. The spreading of a microscopic droplet involves at least two stages: the development of a ``tongue'' of molecular thickness controlled by the spreading parameter and the friction on the substrate is followed by a surface diffusion process. The final stages of spreading are shown to be largely dependent on the polymer-substrate interactions. Increasing the chain length of the polymer slows the process down, but does not lead to a qualitatively different behavior. This study has been complemented with capillary rise experiments in order to measure diffusion constants. The results are discussed using a simple model of surface flow.

Subsurface transport in water and gas

Current designs for nuclear-waste repositories rely primarily upon subsurface geologic barriers for long-term containment. Because water and air are generally considered to be the mechanisms most likely to transport radioactivity to the surface environment, flow and transport models are important tools in repository assessment. Most models assume that the geologic medium can be treated as a continuum. A substantial body of recent work has focused on applying these models to difficult-to-solve problems, such as the simulation of variably dense or variably saturated flow and transport, large and complex flow systems, sharp solute concentration fronts, and fractured rock systems. The complex chemical interactions between the transport fluid and solid particles within the system have been analyzed using geochemical flow models, most of which assume that the system is at chemical equilibrium. The role of colloids in contaminant transport is a relatively new area of research. The large-scale effects of small-scale variability within the geologic system have been the subject of intense investigation. Inherent limitations of the continuum approach have prompted the design of models in which the flow occurs in discrete fractures. The difficulty and complexity of simulating transport has led to the development of network transport models, which represent the flow field as a series of 1-D path segments. The widespread use of models for prediction and analysis has prompted investigations of their reliability and relative merits.

Penalty finite element analysis of free surface flows of power-law fluids

The penalty function method is used to formulate the finite element model of the free surface flows of incompressible, viscous, power-law fluids in plane and axisymmetric situations. Two different procedures of obtaining the free surface are presented, and application of the present finite element model to die-swell problems is discussed. The numerical results are compared with available experimental data and numerical results obtained by others.

A dissipative finite element model for free surface flow

A dissipative finite element model applicable to one-dimensional free surface flow is presented. The classical Galerkin formulation seems to be inappropriate to simulate open channel flow when discontinuities are introduced in the flow domain. A weighted residual formulation based on discontinuous weighting functions is presented, which provides better results than the standard Galerkin approximation. Thus the problem of the undesirable noise in the vicinity of the discontinuities is overcome and the finite element method becomes capable of simulating steep wave fronts. This dissipative model is applied to continuous flow in a section of the Axios river in Greece and it is also applied to discontinuous flow in a rough rectangular horizontal channel. The computational results are compared with those obtained by finite difference schemes and with experimental data.

A Computer Simulation Model of Surface and Subsurface Flows From Agricultural Areas

A deterministic computer model, to simulate the hourly surface and subsurface flows from agricultural fields in humid regions, is described. The model simulates all of the major hydrologic and hydraulic processes occurring both above and below the ground. Input data requirements include hourly rainfall, daily potential evapotranspiration, soil physical properties, field dimensions, open channel geometry and drainage system specifications. An example of model output is presented.

Delayed yield. An exact quasi-three dimensional model for free-aquifers

Quasi-three-dimensional models have been quite successful in the numerical treatment of leaky aquifers. Similar models are not available for free aquifers, except for Boulton's theory which can be properly interpreted as such. In the present paper a quasi-three-dimensional model of free surface flows is developed for free aquifers and waves. The zero-order approximation of this model yields Boulton's theory of delayed yield, elucidating in this manner the nature of the latter theory. The model presented here possesses numerical and theoretical possibilities which will be explored more thoroughly in further work.

Vadose Zone Permeability Tests: Steady State Results

Free surface and saturated-unsaturated flow models are applied to the problem of constant head borehole infiltrat1on tests for determining saturated hydraulic conductivity above a water table. The free surface model follows the same general approach employed to develop analytical solutions, but this model does not suffer from some of the many simplifying assumptions regarding boundary conditions. Nonetheless, the results of steady state simulations with the free surface model agree rather well with the analytical solutions. The free surface approach provides a distorted view of the infiltration process. Saturated-unsaturated models used to simulate quasi-steady state conditions indicated that only a small volume of soil in the vicinity of the borehole is completely saturated with water. Based on saturated-unsaturated simulations in four different homogeneous, isotropic soils, an empirical solution is developed for deep water table conditions to estimate saturated hydraulic conductivity with improved accuracy. Due to the effects of borehole geometry unsaturated soil characteristics, water table depth, heterogeneity, and anisotropy, it is extremely difficult to develop a completely general formula.

Driver gas flow with fluctuations

A shock tube's driver gas can apparently provide flow with turbulent bursts. The fluctuations are interpreted using a boundary layer model of contact surface flow and results from a kinetic theory of turbulence. With this, a lower limit of 4 on the ratio of maximum to minimum turbulent intensities in contact surface instabilities has been estimated.

A model for surface flow in cartilage

The creep behavior of articular cartilage in joints when loaded in compression depends on the availability of a path for flow between the cartilage surfaces. Normal waviness in surface contour seen in unloaded cartilage which persists to some extent during compression can provide a meandering path for fluid flow along the loaded surface. An idealized model can be used to determine when this surface flow becomes less favourable than a flow predominantly parallel but entirely within the cartilage. The model also estimates the pressure of liquid in this film in comparison to the deep tissue liquid pressure.

AN APPLICATION RUNOFF MODEL STRATEGY FOR UNGAGED WATERSHEDS1

ABSTRACT: Mathematical models for predicting watershed surface flow responses are available, most of which are elaborate nonlinear numerical surface and channel flow models linked with infiltration models. Such models may be used to make predictions for ungaged areas, assuming an acceptable fitting of the model to the topography and roughness of the real system. For some application purposes, these models are impractical because of their complexity and expensive computer solutions. A procedure is developed that uses a complex model of an ungaged area to derive a simpler parametric nonlinear system model for repetitious simulation with input sequences. The predicted flow outputs are obtained with the simpler model at significant savings of money and time. The procedures for constructing a complex kinematic model of a 40 acre (161,880 m2) reference watershed and deriving the simpler system model are outlined. The results of predictions from both models are compared with a selected set of measured events, all having essentially the same initial conditions. Peak discharges ranged from 3 to 118 ft3/sec (0.085 to 3.34 m3/sec), which includes the largest event of record. The inherent limitations of lumped systems models are demonstrated, including the bias caused by their inability to model infiltration losses after rainfall ceases. Computer costs and times for the models were compared. The derived simple model has a cost advantage when repeated use of a model is required. Such an applications hydrologic model has an engineering tradeoff of reduced accuracy, and lumping bias, but is more economical for certain design purposes.

Determination of design hydrographs on small catchments by the state variable model

Derivation of a design hydrograph from rainfall data is a typical problem when dealing with small catchments; in most cases there are no streamflow data available. Numerical solutions of unsteady flow equations are difficult to adopt for flow on natural catchments because of the uncertainity about the initial and boundary conditions. A simplified approach is suggested in which a catchment topography is characterized by a number of planes and channels. Flow over the planes and the channel flow are computed by a numerical solution of the state variable equations of unsteady gradually varied flow. The state variable model of surface flow offers simplicity and calculating speed compared with the numerical solutions of the complete unsteady flow equations, yet it maintains a reasonable approximation of the physical reality. Example problems of the use of the model in derivation of a design hydrograph for a small catchment, using rainfall intensities and durations as inputs, are presented. The computer program is provided at a nominal charge from the Depository of Unpublished Data, CISTI, National Research Council of Canada, Ottawa, Canada K1A 0S2.

Nonlinear response of a small drainage basin model

A surface flow model utilizing the kinematic wave theory was applied to a third-order stream system which represented conditions in Williamson and Johnson Counties, Illinois. The model drainage basin was considered as a distributed hydrologic system with the stream network, channel characteristics and overland flow lengths as distributed hydrologic variables. Different order channel lengths, channel cross-sections and channel slopes were treated as spatially distributed. The results of the hydrologic response of the model small agricultural drainage basin showed that various time parameters are affected by change in rainfall-excess intensity. The peak flow rates for a given rainfall-excess duration showed a nonlinear response with the rainfall-excess intensities. The base or time duration of a direct run-off hydrograph increased with an increase in rainfall-excess intensity and duration.

Formulation of Mathematical Watershed-Flow Model

In a macroscopic hydrodynamic approach, a set of one-dimensional spatially varied unsteady flow equations, that include terms for lateral mass flux, lateral momentum flux, overpressure head due to raindrop impact, and boundary shear, are derived from the equation of continuity and the Navier-Stokes equations for the three-dimensional flow of viscous incompressible fluid in cooperation with the kinematic and dynamic boundary conditions on the water and ground surfaces of a watershed. The Darcy-Weisbach equation is employed to evaluate the friction slope, and the laminar uniform flow equation for the Darcy-Weisbach friction coefficient coupled with the Karman-Prandtl logarithmic resistance equation for turbulent flow is used to simulate, as a first approximation, the unknown function of the Darcy-Weisbach friction coefficient for watershed surface flow. The proposed mathematical model for watershed surface flow consists of a set of quasilinear partial differential flow equations of hyperbolic type with the appropriately prescribed initial and boundary conditions.

The synthesis of distributed inputs for hydrograph predictions

A surface flow model based on kinematic wave theory is applied to a flow system derived from the geomorphic properties of the watershed in question. This model facilitates the inclusion of conventional hydraulic methods for computations and avoids one of the major sources of error in watershed modeling: the lumping of input (rainfall excess). Input can be introduced as a distributed variable. The hydrograph synthesis process is evaluated by an objective function based on observed hydrograph peak flow. An example is used to illustrate the modeling process and its application.