HEC 25 - Tidal Hydrology, Hydraulics, and Scour at Bridges

Chapter 4 Tidal Hydraulic Modeling

4.1 Introduction

Dynamic modeling is recommended when complex geomorphic or hydraulic conditions make the basic methods of Chapter 3 unusable or when the simplifying assumptions of these above methods are violated to such a degree that the results are overly conservative. Complex geomorphic conditions include anabranching or multiple channel inlets or estuaries, large floodplain areas constricted by main channel and relief bridges, and complex channel geometry near bridges. For estuaries with large or vegetated floodplains, where the simple tidal prism method is overly conservative due to high flow resistance, dynamic modeling is most appropriate. Dynamic modeling is also most appropriate in the case of large bays where an assumed level water surface is overly conservative or where wind effects are significant.

In the Pooled Fund study (Ayres Associates 1994), UNET (HEC 1997) and FESWMS-2DH (Froehlich 1996) were recommended for dynamic tidal hydraulic modeling. UNET is a 1-dimensional model and FESWMS-2DH is a 2-dimensional model. While other 1- and 2-dimensional models are also applicable for tidal hydraulic modeling, the recommended models incorporate bridge, culvert, and road overtopping hydraulics. Therefore, these models were deemed most applicable for tidal bridge hydraulic and scour evaluations. HEC-RAS Version 3.X (USACE 2001) incorporates the UNET dynamic routing routines. Therefore it should be equally as applicable as UNET and much easier to apply.

Dynamic models perform hydraulic computations for channels, overbanks, bridges and culverts, and the models should be set-up to include areas filled during daily tides and areas of potential inundation during storm tides. Dynamic models yield the most accurate hydraulic analysis for scour computations and countermeasure design. The governing equations used in these models are the full dynamic equations for conservation of mass and momentum. One-dimensional modeling is applicable for estuaries with well defined channels and for bays with single or multiple inlets. When bays are crossed by numerous causeways, especially causeways with multiple bridge openings, 2-dimensional modeling is recommended. Estuaries with multiple anabranched channels can be modeled with 1-dimensional network models (such as UNET), but the complexity often warrants the use of 2-dimensional models.

4.2 Model Extent

The model extent (upstream and downstream model limits) for bridges in tidal waterways differ from the model extents typical for riverine hydraulic analyses. The minimum number of cross sections in a steady state riverine analysis include an upstream (Approach), downstream (Exit) and bridge cross sections. The water surface elevation is specified for the Exit cross section and a discharge is specified for the simulation. Additional upstream and downstream cross sections are often warranted to assess hydraulic impacts of the bridge design.

For tidal waterway analysis, the discharge is typically not known and the downstream stage is represented as time series (stage hydrograph) that is specified at the ocean. The hydraulic condition at the bridge is computed based on applying the dynamic model (either 1- or 2-dimensional) to as much of the tidal waterway as is necessary to establish accurate flow conditions. The limits, therefore, are the entire tidal waterway but, as a minimum, must extend sufficiently inland to accurately represent the dynamic flow conditions. If the upstream limit is too close to the ocean, the storage (or prism) will be under represented and the computed discharge will be less than actually occurs. The wave also cannot propagate inland and will reflect off the upstream boundary resulting in inaccurate results. Therefore, it is best to extend the model well inland so the upstream extent does not cause inaccuracies in the model results.

The downstream boundary of the model should be at a location where the tide and surge conditions are well defined. Although a tide conditions may be known at some distance up an estuary, the storm surge is probably best defined at the coastline. If a known tide that is located far inland from the coast is combined with an ocean surge, the results at the bridge are almost certainly conservative because the surge will probably dissipate as it travels inland. Therefore, to avoid overly conservative design hydraulic conditions at a bridge, the downstream boundary should be located at the ocean. However, it is often desirable to locate the downstream boundary some distance inland to reduce the modeling effort as long as this does not result in inland surge that is too conservative.

4.3 One-Dimensional Modeling

As illustrated in Figure 4.1, 1-dimensional models use a series of reaches to represent the network of channels that form the waterway. Each reach is represented by a series of cross sections that includes channel and overbank geometry. The cross sections provide a 2-dimensional representation of the channel geometry, elevation and distance. The distance between cross sections results in an overall representation of the waterway geometry. The model is considered 1-dimensional because the direction of flow is assumed along the channel perpendicular to the cross sections. Flow expansion and contraction occurs between cross sections and flow in the vertical direction is not simulated.

Figure 4.1. Illustration of 1-D model geometric layout.

One-dimensional models have the advantage of simplicity and speed over 2-D models. The advantage of speed is both in model setup and in the run-time of the computer simulation. Also, the results are more readily interpreted for design and scour computations. One-dimensional models are best suited for long estuaries. The more the tidal waterway looks like a river, the more suitable are 1-D models. One-dimensional models require the engineer to identify the flow direction and orient the cross sections perpendicular to the flow. This can be difficult in reversing flow conditions because areas that are ineffective during flood-tides may be effective during ebb-tides. Therefore, as flow conditions become more complex, 1-D models become less suitable.

Handling ineffective flow areas can be a major issue in the use of 1-D models. Ineffective flow areas are areas that flood, but do not convey flow along the channel. The engineer can specify ineffective flow areas in UNET and HEC-RAS models. In these models, ineffective flow areas are included for storage (they fill and empty during the tide or surge) but flow is not conveyed through an ineffective flow area.

The advantages of 1-D models are that they are relatively easy to develop and they are much faster to run. One-dimensional models provide excellent results for many tidal or river flow conditions provided that the 1-D modeling assumptions are not violated. These assumptions include (1) flow perpendicular to the entire cross section, (2) level water surface across the entire cross section, (3) discharge is distributed within a cross section based on the conveyance distribution and (4) the energy slope is uniform across the entire cross section. Therefore, the limitation of 1-D models is the fact that they are not 2-D models. As hydraulic conditions become more complex, the 1-D model assumptions listed above will be violated and 2-D modeling should be used.

4.4 Two-Dimensional Modeling

Two-dimensional models use either finite difference or finite element computational methods. Models are considered 2-dimensional in the sense that they compute velocity magnitude and direction (two horizontal components) and ignore any vertical component of flow. Figure 4.2 is an example of a portion of a 2-D finite element network at an inlet. The network is developed to accurately represent the waterway geometry. Velocity magnitude and direction are computed at nodes located at the corners and sides of each element. Examples of 2-dimensional models that are applicable to tidal modeling are FESWMS (Froehlich 1996) and RMA-2 (USACE 1997). Finite difference methods typically represent geometry using a regular grid of ground elevations. Finite element methods typically represent geometry with a network of three- and four-sided elements that are not restricted to a regular pattern. Finite difference models have the advantage of faster computational speed and finite element models have better flexibility in representing geometry. With the finite element method, smaller elements are used in areas of complex geometry and complex flow patterns. The elements can also be oriented along the curved channel while in a finite difference grid orientation is less flexibility.

Although 2-D models require greater effort to develop and longer computer time to perform a simulation, they are well suited for complex hydraulic conditions. While they required greater effort, in some respects they require less judgment from the engineer. For example, the model determines flow direction so the concept of cross section orientation is not a consideration in 2-D modeling. Ineffective flow is also directly determined in 2-D models. If an area is not effective in conveying flow along the channel, the 2-D model will compute still water or an area of flow circulation. If that area becomes effective as the flow conditions change, the 2-D model will automatically account for this change. Therefore, the advantage of 2-D models is that they more accurately simulate areas of complex flow patterns.

Figure 4.2. Example of 2-D model layout and results.

Two-dimensional models are best suited for waterways with multiple bridge openings, wide floodplains and large bays, especially bays with multiple causeways. Two-dimensional models are also best suited to simulating the effects of wind stresses although some 1-D models incorporate wind conditions.

One approach that combines the advantages of 1- and 2-D models is performing a 1-D analysis of the entire system and using the results as input to a detailed 2-D model of the local site. Assuming a 1-D model provides a reasonable representation of the entire system, this combined approach provides more detailed flow distribution information than a 1-dimensional model while reducing data requirements and total modeling effort compared to a system level 2-dimensional model. The 2-D model is run either in steady-state mode for the worst-case conditions from the 1-D analysis or run in dynamic mode using the temporal results of the 1-D analysis. The 2-D model then provides better information on flow distributions and more accurate estimates of roadway overtopping.

The advantage of 2-D models is that they compute velocity magnitude and direction throughout the model network. Therefore, complex flow conditions and flow transfer between channel and floodplain are simulated much more accurately. Two-dimensional models remove some of the judgment required for 1-D modeling since decisions related to cross section location and orientation is not required. The disadvantages of 2-D modeling are that they require relatively greater effort to develop, require more computer time to perform a simulation, and tend to have more problems with numerical instability, especially in areas of wetting and drying. As computer speeds increase and advances are made to network development software, these disadvantages become less significant.

4.5 Model Selection

Guidance on the selection of appropriate methods for tidal hydraulic analysis of bridges is provided in Section 3.5. In general, hydrodynamic models should be used as the size and complexity of the tidal waterway increases. Two-dimensional models should be used for wide floodplains, large tidal marshes, floodplains with significant variability in topography or ground cover, multiple bridge openings, parallel roads and railroads (especially when the bridges or piers are not well aligned), areas with significant wind effects, skewed embankments, crossings with significant road overtopping, and extreme channel sinuosity near the bridge opening. Once the decision has been made for 1- or 2-dimensional modeling, there may be several models to choose from. The user should consider the particular strengths and weaknesses of the models and the user's familiarity with the models in making this decision. The U.S. Army Corps of Engineers HEC-RAS model will be applicable for many 1-dimensional conditions. Other 1-dimensional hydrodynamic models include UNET and DYNLET. HEC-RAS and UNET include several useful features, such as bridge, culvert, other hydraulic structures, and storage areas, but do not include any wind modeling. DYNLET includes wind modeling, although wind modeling is generally simulated with 2-dimensional models.

For 2-dimensional applications, FESWMS and RMA-2 are frequently used. Each of the 2-dimensional models includes wind and storm wind modeling. In storm wind modeling the model generates a wind field based on user specified hurricane properties, such as forward speed and radius of maximum wind. FESWMS also includes specialized features, such as pier drag and roadway overtopping, that the current version of RMA-2 does not. FESWMS does not simulate the flow field around a pier directly, but includes an additional force, caused by pier drag, in the solution of the momentum equation for the element containing the pier.

The models referenced above are not an exhaustive list of model that are applicable to tidal hydrodynamic modeling for bridges. It is important to recognize each model's strengths and weaknesses, and to apply models that incorporate the hydraulic conditions, structure hydraulics and boundary conditions for the specific application.

4.6 Model Calibration and Troubleshooting

4.6.1 Model Calibration

Overbank and channel roughness coefficients (Manning's n) are typically determined using tabulated values, ground cover and geomorphic data, and engineering judgment. However, due to the high degree of variability inherent in tidal systems, these roughness values should be adjusted when possible to calibrate the model to actual conditions.

Calibration of a hydrodynamic model requires sufficient data to perform a dynamic simulation. The dynamic calibration simulation should be long enough to render any initial condition error insignificant at interior observation points. The minimum simulation time of the calibration will vary with the size and type of the model, but should generally simulate at least two lunar days (approximately 50 hours).

Overbank roughness calibration is not typically practical in the absence of observed storm surge stage and velocity hydrographs at all open model boundaries and at interior locations in the model. The minimum data required to calibrate main channel roughness for a hydrodynamic model are observed stage hydrographs at all tidally influenced model boundaries and at least one interior point in the model. If daily riverine inflows to the system significantly influence hydraulic conditions, then upland flows are also required. The calibration can also be improved by using channel velocity measurements at interior points in the model.

The stage hydrographs may be developed using water level recorders (tide gages) placed as close as possible to the actual model boundaries. Each gauge should be surveyed into a fixed modeling datum and should be set to allow synchronization of the stage time series with the other stage and velocity measurements. Interior water level gauges should be placed at a minimum of one point. The entire gauge network should operate long enough to provide sufficient data for the calibration simulation. Five-minute water surface elevation readings will adequately characterize the hydrographs for calibration purposes. In addition, because water surface elevations are less sensitive to small changes in roughness than channel velocities, channel velocities should be measured over a full tide cycle for at least one interior point of interest while the tide gauge network is active.

The model should be run using the observed boundary condition hydrographs and the computed results at the interior observation points compared to the observed velocity and stage hydrographs taken at those points. Channel roughness should be adjusted to match computed velocity magnitude, tide phase shift and attenuation to observed values. This simulation and roughness adjustment procedure should be iterated to minimize the difference between predicted and observed interior channel velocities and tide height, range, and phase shift. If the model calibration procedure results in unreasonable roughness values or if it is impossible to adequately calibrate predicted conditions to observed conditions, then the model network should be examined to determine if it adequately represents the actual system.

4.6.2 Model Troubleshooting

Tidal hydrodynamic modeling can be an extremely challenging endeavor. The waterways and adjacent land areas can be extremely large, potentially extending over 100 miles in length. It is also necessary to obtain detailed hydraulic results at a bridge, or often many bridges, within a model that covers and extensive area. There are numerous computational problems that can occur during the simulation. Since each simulation may require many computer hours, even days, to run, the time required for model calibration and production runs can be extensive even if other modeling problems have been avoided. If there are other modeling problems, such as numerical instability, troubleshooting these problems will require additional effort. The following categories of modeling problems and potential troubleshooting solutions are discussed in this section.

• Model fails to execute
• Numerical instability
• Model doesn't calibrate
  
  

Execution Failure. If the numerical model fails to execute, meaning that it doesn't run at all, then there is almost certainly a problem with the data entry. Depending on the level of error checking that is internal to the program and the level error messages that the program includes in the output, this type of problem can be very difficult to trace. Correcting this problem may require a painstaking review of all of the model input files to determine whether they are complete and consistent. There may be required data that are missing, or even a required input file that is missing. It is also possible that the boundary condition file is either internally inconsistent or inconsistent with the model geometry. An example of an internal inconsistency is identifying one time period or starting date for the dynamic run, and providing boundary conditions for another time period. An external inconsistency would include setting an initial water surface elevation that is below the ground elevations in the model or that is significantly different that the tide water surface elevations. For a storage area in HEC-RAS, the user must set an initial water surface elevation. The default water surface elevation is one foot above the lowest elevation in the storage area. If this default results in a water surface elevation lower than the tide elevations the simulation could fail instantly due to the large head differential at the start of the simulation. Similar problems can occur in 2-dimensional models because an initial water surface must be consistent with the boundary condition water surface. The problems may also exist due to errors in the model geometry. For example, in 1-dimensional models, the user may need to identify how the various channel reaches connect and an error in the connections could result in a model that cannot execute. In summary, when a model immediately fails to execute, then the user should check:

• Program output error messages
• Missing input data
• Incorrect input data
• Missing input files
• Inconsistent input data
  
  

Numerical Instability. Numerical instability occurs when a model does not converge to a solution during the number of iterations specified for a specific time step. The computed values of velocity or depth may oscillate without convergence or the changes from one iteration to the next may amplify until the model "blows up." Occasionally, the model may exhibit minor convergence problems for a few time steps and then get past cause of the instability and continue without further problems. The cause of numerical instability may be related to computational time step length, lack of geometric refinement, wetting and drying problems, or structure hydraulics. It is often necessary to use computational time steps of 6 minutes or less for storm surge simulations. One minute time steps may be necessary during the rapid rise and fall of a storm surge. Some models allow one time step for computation and another for output in order to limit output file size. Very short time steps tend to increase run times, although there are cases when decreasing the time step can decrease the total simulation run time. This can occur if the model requires only 2 iterations to converge for a short time step but may require many more iterations for the longer time step. Model stability can also be affected by selection of the implicit weighting factor, theta, used for the time derivatives. A theta value of one is the most stable, but a lower value, usually around 0.6, produces a more accurate solution. It is usually better to reduce time step than to use values of theta approaching 1.0.

In some cases, lack of geometric refinement can produce numerical instability. This is especially true for 2-dimensional models in area where flow separation is occurring and a large scale eddy should form. If the model lacks sufficient geometric refinement, the model may not converge because the flow field may be poorly defined. This type of instability can also occur in 1-dimensional models if, due to a severe constriction, the flow velocity changes too rapidly between cross sections. In either case (1- or 2-D), the solution is to further refine the model in the area of instability. In most cases, the area can be easily determined because the location of greatest change is identified in the model output.

Another type of geometric problem occurs as areas of the model wet (become inundated) or dry. In 2-dimensional models, wetting and drying requires elements to activate or de-activate. The inclusion of these extra elements can create a shock to the solution of the simultaneous equations. A similar problem can occur in 1-dimensional models based on the fact that a small increase in stage may produce a large increase in flow area if the floodplain is wide and relatively flat. Decreasing the computation time step length is one way to reducing problems with wetting and drying. Some 2-dimensional models include methods of maintaining elements active even if the water surface is not higher than the entire element. For examples, the RMA-2 model includes "marsh porosity" and the FESWMS model includes "storativity." A simple explanation of these methods is that they keep elements active by included some very small flow area associated with the element at all times. The amount of flow in these artificially wet elements does not significantly affect the model results.

Another common source of model instability is weir flow. If the model includes roadway overtopping, the initiation of flow over the road can be sudden and the change in flow from one time step to the next can be extreme. The number of iterations required to converge to a solution may be very large when road overtopping occurs. Alternatively, the time step length should be reduced to reduce the amount of change, in both head and flow, from one time step to the next.

In summary, the causes of numerical instability are:

• Computational time step too long
• Lack of geometric refinement
• Wetting and drying problems
• Weir flow
  
  

Calibration Problems. Calibration is usually conducted for astronomical tide conditions because the data are more easily obtained than for storm surge conditions. However, there are many problems associated with model calibration even for astronomical tide conditions. With an accurate representation of the tidal waterway geometry and boundary conditions, the model should calibrate very well. Calibration is usually conducted by comparing model tide range and timing with observations at a tide gage at several locations in the modeled area. It is recommended that velocity measurements also be obtained at key locations, especially the bridge crossing, to compare with the model results. The primary variable that needs to be calibrated is the Manning n of the areas below high tide. The Manning n should only be adjusted within a reasonable range for the bed conditions. If the bed is sand, then Manning n should range from 0.018 to 0.025, although for some small, less regular channels, values up to 0.035 may be acceptable. If the model does not calibrate using a reasonable range of Manning n values, then other areas should be investigated. Most frequently, problems with calibration are associated with inaccurate bathymetry, although insufficient upstream extent, improper conversions between datums, unmodeled wind effects, or incorrect upstream flow can also cause a model to not calibrate.

If the model does not include the entire tidally affected area, then wave propagation and volume of the tidal prism will be misrepresented and model calibration will not be possible. Even if the tide range and timing could be matched fairly well with observations, flow velocities could not be matched. Since tide propagation is primarily controlled by flow depth, errors in the model bathymetry will result in errors in calibration. This can occur if out-of-date hydrographic surveys are used to develop the model and there has been general filling or lowering of the channel in the interim. Another source of inaccurate bathymetry is in conversion between datums. If the original bathymetry is recorded in a tidal datum such as mean lower low water, then the bathymetry should be converted to a fixed datum.

The tides that were used for boundary conditions and for calibration must all be in the same datum as the bathymetry. This generally requires that the gages be surveyed. In many cases, NOAA tide gage data include information on conversion to fixed datums.

If the modeling does not include wind effects, but the tides are significantly affected by wind, then calibration will not be successful. Another external control, or boundary condition, that will effect calibration is upstream inflow. In most cases, upstream inflow is small in comparison to tidal flows, especially for daily tides and normal daily upstream inflows. An example of a case where inflow was significant is a model of the Cooper River in South Carolina. The flow from upstream reservoir releases was consistently higher than normal during the time when tide gages were installed. Without the appropriate inflow, the model would not calibrate with the measured tides. Once the correct inflow was obtained from USGS records and included in the model, the model calibrated without further adjustment.

In summary model calibration will be affected by:

• Appropriate model extents
• Accuracy of model bathymetry
• Correct datum conversions for bathymetry
• Correct datum conversions for tide gages
• Inclusion of wind effects
• Inclusion of appropriate upstream inflow
  
  

4.6.3 Evaluating Results

Just because a model runs doesn't mean the model results accurately represent the real world. The model input and output files should be reviewed in order to assure that appropriate input variables have been used and that the model results are realistic. The first step in evaluating the model results is to review the output file for any error or warning messages. A warning may indicate that some corrective action, such as additional geometric refinement or a shorter time step, is required. The warning message may indicate that a hydraulic condition, such as excessive weir flow, has been computed. The weir flow should be checked manually to check whether the model result is reasonable.

The model results should also be checked to ensure that the solution is numerically stable. Scan the output file to check whether convergence is achieved for each time step. Also plot hydrographs from several locations to determine whether there are oscillations or sudden changes in the stage or flow hydrographs. For 2-dimensional model, plot the velocity magnitudes and vectors to determine whether there are any areas of apparent instability. At times, an area my appear unstable because the velocity vectors appear randomly oriented. Make sure that the velocity vectors are scaled relative to the velocity magnitude because the velocity in this area may actually be near zero and the results are valid.

4.7 Physical Modeling in Coastal Engineering

This section provides an overview of the capabilities and limitations of physical models and the facilities required for analyzing coastal engineering problems, including wave, tidal, and littoral processes. Bridges and highways cross or parallel estuaries and inlets and, in some cases, must be protected by coastal structures such as seawalls or jetties. Consideration of the complex hydrodynamic and sediment transport processes of the coastal zone may require the use of physical modeling and the hydraulic laboratory facilities required are quite different from those used for riverine models. This section highlights those difference to aid in the selection of an appropriate hydraulics laboratory, if physical modeling is required to meet project objectives. The information in this section is drawn, primarily, from two sources: U.S. Army Corps of Engineers Coastal Engineering Research Center Special Report No. 5, "Coastal Hydraulic Models" (Hudson et al. 1979) and a more recent text on "Physical Models and Laboratory Techniques in Coastal Engineering" by S.F. Hughes (1993) of the Coastal Engineering Research Center.

4.7.1 Coastal Engineering Models

The field of coastal engineering involves providing reliable and economic design solutions to support man's activities in the coastal zone. Coastal engineers must study and attempt to understand such diverse topics as wave mechanics and wave climate prediction, shoreline erosion and protection methods, harbor design and design of protective structures, geological and geotechnical aspects of foundation design, dredging technology, estuarine processes, hurricane and storm surge effects, and environmental impacts of coastal projects. Laboratory investigations play an important role in many of these areas (Hughes 1993).

Coastal engineers rely on three complementary techniques to deal with the complex fluid flow regimes typical of many coastal projects. These techniques are field measurements and observations, laboratory measurements and observations, and mathematical calculations. Laboratory studies are generally termed physical models because often they are miniature reproductions of a physical system. In parallel to the physical model is the numerical model, which is a mathematical representation of a physical system, as described in previous sections.

Measurements and observations of hydrodynamic phenomena made at a specific site are often critical for understanding the hydrodynamic regime and its impact on existing or planned coastal projects. These measurements can be used to quantify the hydraulic flows, to specify hydrodynamic forcing conditions for numerical or physical model studies, or to verify the correct formulation and operation of numerical or physical model simulations.

Numerical modeling has shown steady growth and utility over the past decade. Large physical models of tidal estuary systems have now been almost totally replaced with numerical models that can predict flows with a good degree of success. Numerical models are also practical for cases where wave refraction, shoaling, and diffraction are the only important hydrodynamic characteristics, and considerable success has been shown in accurately simulating nearshore circulation with numerical models (Hughes 1993).

However, many flow conditions and problems in coastal engineering are not amenable to mathematical analysis because of the nonlinear character of the governing equations of motion, lack of information on wave breaking, turbulence or bottom friction, or numerous connected water channels. In these cases it is often necessary to resort to physical models for predicting prototype behavior or observing results not readily examined in nature.

4.7.2 Advantages and Limitations of Physical Models

A review of the historical development of hydraulics and hydraulic models indicates that the scale model played an increasing role in the design of hydraulic structures and coastal works in the United States from about 1930 to about 1970 (Hudson et al. 1979). Important model techniques and procedures were developed, instrumentation was improved, and simulation of more complicated phenomena became possible through experience and basic research. For many of the complex problems in coastal engineering, especially those concerning the effects of wave action, the best approach to the problem of obtaining the optimum balance between the functional, stability, and economical aspects of design is the use of scale models. However, as noted above, since the 1970s numerical modeling techniques have improved sufficiently to permit accurate and economical numerical simulation of the estuarine processes of most interest to the highway engineer.

Physical models constructed and operated at reduced scale still offer an alternative for examining coastal phenomena that may presently be beyond our analytical skills (Hughes 1993). There are several distinct advantages gained by using physical models to replicate nearshore processes:

1. The physical model integrates the appropriate equations governing the processes without simplifying assumptions that have to be made for analytical or numerical models.

2. The small size of the model permits easier data collection throughout the regime at a reduced cost, whereas field data collection is much more expensive and difficult, and simultaneous field measurements are hard to achieve.

3. The degree of experimental control with physical models allows simulation of varied or sometimes rare environmental conditions at the convenience of the investigator.

4. The ability to get a visual feedback from the model gives the investigator an immediate qualitative impression of the physical processes which in turn can help to focus the study and reduce the planned testing.

Although there are distinct advantages in favor of laboratory experimentation and physical modeling, physical hydraulic models have some serious drawbacks, most notably (Hughes 1993):

1. Scale effects occur in models that are smaller than the prototype if it is not possible to simulate all relevant variables in correct relationship to each other. A common scale effect in coastal models is viscous forces that are relatively larger in the scale model than in the prototype.

2. Laboratory effects can influence the process being simulated to the extent that suitable approximation of the prototype is not possible. Typical laboratory effects arise from the inability to create realistic forcing conditions and from the impact model boundaries have on the process being simulated. A common laboratory effect arises when unidirectional waves are generated in the model to approximate multidirectional waves that occur in nature.

3. Sometimes all forcing functions and boundary conditions acting in nature are not included in the physical model, and the missing functions and conditions need to be assessed and accounted for in evaluation of model results. For example, wind shear stresses acting on the free surface may generate significant nearshore circulation currents in nature that would be absent in any model which included only mechanical wave generation.

4.7.3 Types of Physical Models in Coastal Engineering

In terms of their physical characteristics, physical models used to study nearshore coastal processes can be divided into two classes: fixed-bed models and movable-bed models (Hughes 1993).

Fixed-bed models have solid boundaries that cannot be modified by the hydrodynamic processes ongoing in the model. Fixed-bed models are used to study waves, currents, or similar hydrodynamic phenomena in the laboratory under controlled circumstances. They are also used to study the interaction of hydrodynamic forces with solid bodies, such as pilings, breakwaters, harbor basins, etc. The scaling effects associated with fixed-bed models are reasonably well understood and much confidence can be given to the results of carefully-conducted fixed-bed model studies.

Examples of fixed-bed model studies in 2-dimensional facilities include wave tank tests to examine wave propagation and transformation, studies of wind wave generation in flumes, breakwater stability tests, studies on wave/current interaction, measurement of hydrodynamic forces on structures, and examination of fluid kinematics.

Three-dimensional fixed-bed models are more involved, and they examine such coastal engineering problems as wave penetration into harbors, harbor seiching response to short waves, transformation of directionally-spread irregular waves, interaction of oblique waves and currents, stability of complex coastal structures, and other challenging engineering problems.

Moveable-bed models, as the name implies, have a bed composed of material that can react to the applied hydrodynamic forces. The scaling effects inherent in movable-bed physical models used for studying sedimentary problems are not as well understood as they are for fixed-bed models. Consequently, movable-bed model results must be carefully reviewed in the context of previous, similar models that have demonstrated success in reproducing prototype bed evolution.

Examples of 2-dimensional movable-bed coastal models include studies of beach profile evolution, dune erosion, ripple development, scour at the toes of coastal structures, response of beach fills to storms, response of cobble beaches to wave action, and bedform translation under unidirectional currents.

Three-dimensional movable-bed models are much rarer, due in part to the high costs associated with these models. Examples include studies of erosion of oil drilling sand islands, littoral drift induced by oblique wave approach, formation of sand spits, 3-dimensional ripple formation, and scour holes in the vicinity of structures such as highway bridge piers.

A final characteristic that can be assigned to either fixed-bed or movable-bed models is whether the model is "short-term" or "long-term." Short-term models examine response of the project or physical system to short-duration (hours to days), high intensity events, such as storms. Long-term models determine system changes that occur over extended time periods (days to years). Short-term physical models are far more practical to conduct.

4.7.4 Modeling of Estuary Processes

Estuary modeling is usually restricted to modeling water-related problems where tidal action provides the major source of system energy (Hudson et al. 1979). In some cases, other phenomena such as river flow, wind waves, and storm surges are of major importance, with tidal action merely a part of the physical processes that control the system.

Estuary modeling techniques have been applied to two major problem types: (a) predicting effects of construction in areas subject to tidal action, and (b) establishing base-line conditions against which future changes can be measured. Predicting the effects of changes caused by construction has been the major use of estuary modeling. Establishing base-line conditions in areas of anticipated changes has been a more recent application which has grown from the need for guidelines against which possible future developments may be compared. A typical estuary model layout is shown in Figure 4.3.

All models of estuaries have one common characteristic, i.e., the models cannot be a completely accurate simulation of all of the complex phenomena inherent in tidal waterways. To approximate complete model-prototype similarity, a hydraulic model of an estuary should reproduce the geometry and boundary roughness of the prototype and be able to simulate the following (individually and collectively) as they vary with tidal cycle time at all points in the system:

• Water surface elevations
• Current velocities and directions
• Salinities
• Physical characteristics of sediments
• Transportation, deposition, and scour of sediments
• Parameters reflecting water quality, such as dissolved oxygen, temperature, viscosity, diffusion of introduced pollutants, etc.
• Freshwater and saltwater discharges into the estuary and the turbulent intermixing within the water mass
• Effects of winds on setup, waves, local water currents, mixing, diffusion, etc.

Simulation of all of these estuarine phenomena is unnecessary to solve every problem. In model studies of certain problems, some of the phenomena would be completely irrelevant and others would be so nearly irrelevant as to be negligible. The recommended approach to the design of an estuary model would be to first select the prototype phenomena which would significantly affect, or be affected by, the problem to be studied (or by possible solutions), and then to design the model to simulate the selected phenomena with acceptable accuracy.

4.7.5 Modeling Coastal Erosion and Coastal Structures

Movable-bed scale-model investigations of coastal erosion and coastal sediment transport phenomena are probably the most difficult hydraulic models to conduct (Hudson et al. 1979). However, such model studies are feasible in certain circumstances (e.g., littoral transport, onshore-offshore transport, scour, or erosion around structures). Careful planning is required, and the acquisition of extensive and accurate prototype data is necessary. Numerous scale-model laws can be derived by making various assumptions regarding the physical processes governing sediment motion.

The most important phase in this type of scale-model study is to obtain the quantity and quality of prototype data required for model verification. Some of the many problems that must be dealt with in model operation are model circulation, type of bottom sediment, model size, and rapid measurements and remodeling of bottom topography. Although nearly quantitative moveable-bed scale-model investigations of some coastal erosion and coastal sediment transport problems are considered feasible, a considerable amount of additional applied research is necessary before such studies become routine.

Figure 4.3. Columbia River estuary model (Hudson et al. 1979).

In contrast, hydraulic modeling techniques are routinely applied to coastal structure design. In preliminary design stages, many coastal structures can be designed using empirical formulae and nomograms developed from parametric small-scale physical model tests of generic structures (Hughes 1993). This initial design is often sufficient to estimate approximate costs or to select the most appropriate type of structure to meet project needs. However, designs of larger, more expensive coastal structures are usually tested and optimized using a physical hydraulic model. The relative cost of performing a model study is minor compared to the expense of an over-designed structure or a structure that requires frequent repair.

Coastal structures are intended to protect shorelines or navigation channels from the effects of waves and other hydrodynamic forces. Design must consider a range of likely wave heights and periods combined with water level variations composed of tide, storm surge, and wind setup. Some structures are designed to reflect wave energy, while other structures attempt to decrease most wave energy through wave breaking and dissipation upon and within a permeable structure.

The most common type of coastal structures include rubble mound structures and vertical wall structures (seawalls). The most common purposes for conducting stability models of coastal structures include:

1. Examine the stability of rubble-mound armor layers protecting the slopes, toes, and/or crowns when exposed to wave attack at different water levels.

2. Determine the hydrodynamic forces exerted on monolithic structures by wave action.

3. Optimize the structure type, size, and geometry to meet performance requirements and budget constraints.

4. Investigate structure characteristics such as wave run-up, rundown, overtopping, reflection, transmission, absorption, and static/dynamic internal pressures for different structure types, geometries, and/or construction methods.

5. Develop and/or test methods of repairing damage on existing structures or improving the performance of an existing structure.

6. Determine the effects of a proposed modification on an existing structure's stability and performance.

Physical model tests directed at any of the above purposes will yield quantitative results provided the model is correctly scaled and operated, and scale effects are determined to be minor.

Coastal structure physical models can be 2-dimensional (2-D) or 3-dimensional (3-D). The more expensive 3-D models are used to obtain optimum positioning, length, height, and alignment for a protective coastal structure such as a harbor breakwater. Also, oblique wave attack and jetty head stability can be studied in a 3-D model. A typical 2-D model of a breakwater is shown in Figure 4.4.

4.7.6 Modeling Tidal Inlets

The tidal inlet is a complex part of the coastal environment. The three primary forces of importance to the coastal inlet are lunar-dominated ocean tides, winds, and freshwater inflow (Hudson et al. 1979). These forces interact in the ocean, bay, and inlet proper to produce many phenomena that affect the inlet. Among these phenomena are: (a) tidal currents, (b) littoral currents, (c) wind waves, (d) density currents, (e) changes in water levels due to lunar tides, (f) wind wave run-up, (g) currents generated by wind-water surface interaction, (h) littoral transport of material to the inlet, (i) wind transport of material to the inlet, and (j) freshwater transport of material to the inlet. A true physical model requires the accurate simulation of all of these phenomena active at a particular inlet. This simulation is not only beyond the capability of present physical modeling, but beyond the capabilities of any known simulation technique. The physical model does, however, provide a means of investigating the effects of a significant number of these phenomena. For many cases, this will allow an effective understanding of what does or could occur at a tidal inlet.

Figure 4.4. Typical 2-dimensional coastal structure model (Hughes 1993).

Studies in tidal inlet models are generally directed to development of methods for maintaining an effective navigation channel through the inlet, but often other aspects must also be investigated. Problems that can be investigated by physical inlet models are:

• Stabilization of navigation channel dimensions and location
• Structural dimensions of jetties, etc., and location and configuration
• Bridge scour and stability if a highway crosses an inlet
• Sand-bypassing techniques
• Shoaling and scouring trends
• Tidal prism changes
• Navigation conditions
• Salinity effects

Modification of the inlet by a proposed plan of improvement could result in changes to the tidal prism, i.e., the magnitude of flow into and out of the bay system, or changes to current patterns and the location of predominant currents within the bay system. Effective analysis of a potential plan of improvement dictates consideration of these aspects. A typical model layout for analyzing the effects of jetties on a tidal inlet bridge crossing is shown in Figure 4.5.

Figure 4.5. Details of jetty plans, Shrewsbury Inlet.

4.7.7 Physical Model Facilities

The facilities required to conduct a physical model for coastal engineering applications (estuaries, erosion, structures, inlets), are significantly different from those needed for a typical riverine model study. If a hydraulic model is required to support design for a bridge or highway project in the coastal zone, investigations may be necessary to locate a government, university, or private hydraulics laboratory with the necessary facilities and experience to conduct such studies.

For riverine studies the hydraulics laboratory at Colorado State University can be considered typical (Figure 4.6). CSU's indoor Hydraulics Laboratory is 280-feet long by 120-feet wide with a maximum ceiling clearance of 32 feet. Covered laboratory space for testing and models exceeds 20,000 square feet. Figure 4.6is a photograph of the Hydraulics Laboratory with a river model shown during testing in the center of the picture. The river model was constructed in a 20- by 100-foot flume.

In contrast, coastal hydraulic models generally involve the effects of waves and currents in the coastal region. Wave motions can be separated into two logical divisions: short waves which have wave periods in nature between 1 - 20 seconds and long waves which can have periods ranging between minutes and days (Hughes 1993). The division of waves by period is well suited to modeling (both physical and numerical) because in each case certain terms in the governing equations are dominant while other terms are less important. This simplifies model scaling requirements to better fit the assumption that dynamic similarity is achieved by a balance between only two dominant forces.

Figure 4.6. Photograph of hydraulics laboratory with river model during testing (center of photograph).

Short-wave models are used to study wind wave and swell effects on coastal projects, beaches, and navigation; and long-wave models are used to study the effects of tides, tsunamis, and other long-period waves on harbors, ports, estuaries, and tidal inlets. Some coastal engineering projects such as design of a harbor, must evaluate both short- and long-wave impacts. Short waves can enter the harbor and create a "chop" that makes small-craft mooring and navigation difficult and dangerous. On the other hand, long-wave energy can excite the harbor at a basic mode of oscillation that can cause difficulties for larger moored vessels. Generally, both types of wave motion cannot be investigated in the same physical model unless the harbor is quite small (Hughes 1993).

The realm of short-wave hydrodynamic models used in coastal engineering is quite varied. Studies can be conducted in laboratory wave tanks with the understanding that the model presents a 2-dimensional (2-D) viewpoint of the wave processes (Figure 4.7), or they can be conducted in wave basins where the width is large enough that waves can have an oblique approach to the beach and 3-dimensional (3-D) processes can be studied (Figure 4.8). Short-wave physical models can be used to study specific, real-world situations, or they can be used to examine systematically generic, idealized cases with the purpose of developing physical insight or engineering design guidance. Model waves can be generated as regular waves closely approximating theoretical formulations, or they can be made irregular to provide a more realistic simulation of nature (Hughes 1993).

The wave tank is the traditional tool of the coastal engineer and it enables less expensive examination of problems that can be approximated as 2-D processes. Wave basins provide the capability to study evolution of the wave field over nonuniform bathymetry or at particular sites as the waves undergo refraction, diffraction, shoaling, and breaking.

Long-wave hydrodynamic fixed-bed models are used primarily in the study of rivers, estuarine systems, or very large harbor complexes and hence, they are almost exclusively conducted in large wave basins. Tides are usually reproduced in coastal harbor models as a static water level over the duration of wave action; however, when necessary, time varying tide elevations can be reproduced (Hughes 1993).

Figure 4.7. Typical laboratory wave tank (Hughes 1993).

Figure 4.8. Typical laboratory wave basin (Hughes 1993).

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