MIKE 21C RIVER MORPHOLOGY - MIKE by DHI

M21C-SD/0400215/HGE DHI Water & Environment

MIKE 21C RIVER MORPHOLOGY

A Short Description

DHI Water & Environment M21C-SD/0400215/HGE

MIKE 21C River Morphology

A Short Description 1


INTRODUCTION TO THE SYSTEM

MIKE 21C is a generalised mathematicalmodelling system for the simulation of thehydrodynamics of vertically homogenous flows,and for the simulation of sediment transport. Themodelling system has the capability of utilisingboth a rectilinear and a curvilinear computationalgrid.

The modelling system, which is a part of theMIKE 21 software package from DHI Water &Environment, is composed of a number ofmodules relevant to sediment and morphologystudies in rivers:

• Hydrodynamic module• Advection-dispersion module• Sediment transport module• Flow resistance module• Bank erosion module• Large scale morphological module

These features are described in general terms inthe following sections.

The model components can run simultaneously,thus incorporating dynamic feedback fromchanging hydraulic resistance, bed topography andbank lines to the hydrodynamic behaviour of theriver.

For pre- and post-processing of input and output,the MIKE 21 PP-module (pre- and post-processor)from the MIKE 21 family is used. Special utilityprogrammes have been developed to handle datain a curvilinear grid format:

• Graphics-based and menu-driven gridgenerator to create curvilinear grids andmodel bathymetries

• Result-Viewer for 2D contour and vector plotsas well as time series plot

• Utility tools to extract time series, profiles,width-integrated discharge etc.

Application areas

The MIKE 21C is used for simulation of two-dimensional free surface flow and sedimenttransport in rivers where stratification can beneglected and where an accurate description of theflow along the banks as well as helical three-dimensional flow is important. Typical modelapplications comprise

• Protection schemes against bank erosion andbed scour measures to reduce or manageshoaling

• Structures including e.g. weirs, groynes,barrages, bendway weirs

• Alignments and dimensions of navigationchannels for minimizing capital andmaintenance dredging

• Sedimentation of water intakes, outlets, locks,harbors, reservoirs

• Bridge, tunnel and pipe line crossings• Restoration plans for optimal environmental

habitats in channel-floodplain systems• Monitoring networks based on morphological

forecasting

ELLIPTIC GRID GENERATOR

The general version of the MIKE 21 is based on arectilinear computational grid. For modelling ofthe open sea, and most estuaries and coastalapplications, such a grid provides sufficientaccuracy. In river application, however, anaccurate resolution of the boundaries is requiredwhich necessitates for the use of curvilinear orunstructured grids. Curvilinear grids have theadvantage over the unstructured grids that thecomputational schemes are much faster.

The benefits of using a curvilinear computationalgrid compared to a rectilinear grid are visualisedin Figure 1, where a river reach is described inboth a curvilinear and a rectilinear grid. In thisexample, the discretization in the curvilinear gridis based on 210 computational points, whereas therectilinear model uses 228 active (water) points.The curvilinear model provides a much betterresolution of the flow near the boundaries andthereby a higher modelling accuracy. Bigger timestep can be used in the curvilinear model becausegrid lines follow the streamlines. In the rectilinear


2 A Short Description


model, a total of 900 points is defined and stored,whereas for the curvilinear model, only 270 pointsare defined. Thus, the required storage capacity isrelatively larger in a rectilinear model.

Figure 1 Schematisation of a river inrectilinear and curvilinear grid.

MIKE 21C is based on a so-called orthogonalcurvilinear grid. This is created with a graphicalbased grid generator, which solves a set of ellipticpartial differential equations. The advantage ofusing an orthogonal grid is that the finitedifference equations describing the two-dimensional flow become substantially simplerthan if a general (non-orthogonal) curvilinear gridwas applied. This implies that the numerical

scheme becomes more accurate with anorthogonal grid and that the computational speedof the engine improves.

The orthogonal curvilinear grid used in MIKE21C is obtained from the following elliptic partialdifferential equations:

∂∂

∂∂

∂∂

∂∂

s

gx

s+

n

1

g

x

n= 0

0=n

y

g

1

n+

s

yg

s

∂∂

∂∂

∂∂

∂∂

wherex,y Cartesian co-ordinatess,n curvilinear co-ordinates (anti-clockwise

system)g "weight" function

The weight function is a measure of the ratiobetween the grid cell length in the s- and the n-direction, respectively.

The boundary condition for this system is the non-linear orthogonality condition:

0=n

y

s

y

n

x

s

x bbbb

∂∂

∂∂+

∂∂

∂∂

0=yxf bb ),(

where the former expresses the condition oforthogonality and the latter expresses the locationof grid points (x,y) on a specific curve describingthe boundary. A strongly implicit method isemployed for solving the partial differentialequations with a special Newton-Raphsonprocedure for the boundary conditions, see Stone(1968).

Generation of an orthogonal curvilinear grid is aniterative process in which boundaries aresmoothened and weight functions are adjusteduntil the computational grid is judged to be sound,i.e. without too large gradients in grid cell spacingand curvature of grid lines. Figure 2 shows anexample of a curvilinear grid obtained with theelliptic grid generator. The graphical based gridgenerator offers a number of flexible tools to tailor




the grid to the model area, for instance around anin-channel bar.

Figure 2 Example of curvilinear grid. Theweight function causes the grid to be concentratedin the deeper parts (depth adaptive grid)

InputInput for the grid generator is• Boundary lines, either imported from ASCII

files containing (x,y) co-ordinates or digitiseddirectly on top of a geo-referenced bitmapwithin the grid generator

• Specification of the required number of gridpoints along the river, and across the river

• River bed levels, defined as a set of discretevalues with bed level z at given (x,y) co-ordinates. Data can be imported from anASCII file or from another MIKE 21 dfs-file.

OutputOutput from the grid generator is two files, whichis required for a curvilinear model setup• A 2D map of the co-ordinates of every corner

point in each grid cell in the curvilinear mesh.(This file is a standard dfs2 file with two itemsx and y).

• A 2D map of the river bed level at everycentre point in the each grid cell in thecurvilinear mesh. (This standard dfs2 file issimilar to a bathymetry file in a general MIKE21 setup).

HYDRODYNAMIC MODEL

The hydrodynamic model simulates the waterlevel variation and flows in rivers and estuaries.Model simulations are based on a curvilinearcomputational grid covering the area of interest.The MIKE 21 hydrodynamic model has beenunder continuous development at DHI Water &Environment since 1970 whereas the curvilinearversion of MIKE 21 using the same solutionmethods was developed in 1990.

Basic EquationsThe hydrodynamic model solves the full dynamicand vertically integrated equations of continuityand conservation of momentum (the Saint Venantequations) in two directions. The following effectscan be included in the equations when used forriver applications:

• flow acceleration• convective and cross-momentum• pressure gradients (water surface slopes)• bed shear stress• momentum dispersion (through e.g. the

Smagorinsky formulation)• flow curvature and helical flow

The curvature of the grid lines gives rise toadditional terms in the partial differentialequations for the flow. The equations solved inMIKE 21C are:

∂∂

∂∂

∂∂

∂∂

p

t+

s

p

h+

n

pq

h+ 2

pq

hR+

p - q

hR+ gh

H

s+

g

C

p p + q

h= RHS

2

n

2 2

s2

2 2

2

∂∂

∂∂

∂∂

∂∂

q

t+

s

pq

h+

n

q

h+ 2

pq

hR+

q - p

hR+ gh

H

n+

g

C

q p + q

h= RHS

2

s

2 2

n2

2 2

2

∂∂

∂∂

∂∂

H

t+

p

s+

q

n-

q

R+

p

R= 0

s n

wheres,n co-ordinates in the curvilinear co-ordinate

systemp,q mass fluxes in the s- and n-direction,

respectivelyH water levelh water depthg gravitational accelerationC Chezy roughness coefficientRs, Rn radius of curvature of s- and n-line,

respectively.




RHS The right hand side describing a.o. Reynoldstresses (see MIKE 21 HydrodynamicModule)

Solution TechniqueThe equations are solved by implicit differencetechniques with the variables defined on a spacestaggered computational grid as shown in Figure3.

Two solution algorithms exist in MIKE 21C. Thefirst is the “classical” ADI (alternate directioniteration) scheme as applied in the general MIKE21, which is applicable for highly dynamic flow.The other scheme is based on quasi-steadyassumptions and is a predictor-corrector algorithmthat originates from methods for incompressiblefluid flow (Michelsen, 1989). The quasi-steadysolver is particular suitable for slowly varyingflow conditions in long-term simulations.

∆s

∆n

hj,k

zj,k

hj,k+1

zj,k+1

hj+1,k

zj+1,k

hj+1,k+1

zj+1,k+1

pj,k

qj,k

qj+1,k

pj,k+1

Figure 3 Space staggered grid used in thehydrodynamic model of MIKE 21C

Establishing a model setupThe setting up of a hydrodynamic river modelusing MIKE 21C involves the following threesteps:

• The extent of the modelling area is selectedand the computational grid is designed for theriver as described in the previous section. Theextent of modelling areas can vary from fewhundred metres to more than 100 km. The gridsize depends on the channel width (typicallynot less than 10 points across), the depth (notless than say two times the maximum depth),

flow direction (grid spacing in thelongitudinal direction is often two-three timesthe spacing across). Grid spacing of 100m x50m for larger rivers and 30m x 10m forsmaller rivers is typical.The bed levels areentered into the computational grid. Variousutilities in the grid generator performconversions, interpolation, extrapolation,smoothening etc.

• The simulation period is planned and theboundary conditions are specified, forinstance a time series of discharge at theinflow boundary, and a time series of waterlevel at the downstream model boundary. Thetypical length of simulation periods variesfrom days to several months (full dynamic)and several years (quasi-steady).

• Finally, the initial conditions in terms of waterlevels and fluxes at the beginning of thesimulation are defined. This can be done indifferent ways with for instance a hot-start ora warm-up period.

CalibrationThe calibration process for the MIKE 21Chydrodynamic model involves tuning of a numberof calibration factors, first of all the bed resistance(Chezy or Manning number) and the Eddyviscosity (constant, 2D map or Smagorinskyformulation). All the calibration factors have aphysical meaning and should not be arbitrarilygiven values outside their realistic ranges to obtainagreement with observed data. In Figures 4 and 5,some computational examples are presented.




Figure 4 Simulated flow pattern in a braidedriver (Brahmaputra River). The computational gridis depicted in Figure 2.

InputThe input for the menu-driven setup editor is• 2D map of the curvilinear mesh and a 2D map

of the bed levels (from the grid generator)• Time series of discharge at the upstream

boundary and water level at the downstreamboundary (ASCII file format, Excel or similar)

• 2D map of the initial surface water elevation(from the grid editor), or a constant

OutputThe output from a MIKE 21C hydrodynamicmodel comprises the following parameters in apredefined number of time steps during thesimulation period• 2D map of water depth• 2D map of water flux in two directions

(contours or vectors)

Derived results, which can be extracted by anumber of graphics based tools are• 2D maps of flow velocity in two directions

(contours or vectors),• and water surface elevation• Time series and profiles in selected

points/lines of discharge, water level, flowvelocity, depth etc.

Figure 5 Schematical example of acurvilinear grid and simulated flow distribution in astraight rectangular channel. The example showseffect of curvilinear terms.

SEDIMENT TRANSPORT

Helical Flow

Helical flow is a principal secondary flowphenomenon in rivers. Whilst it does not have anystrong influence on the general flow pattern inrivers with large width-depth ratios, it has asignificant influence on the sediment transportdirection and hence the morphological changes inthe river channel (see Olesen, 1987). The helicalflow is, therefore, calculated in connection withsediment transport simulations when larger scalemorphology is modelled. It is an importantingredient in the development of bend scour,confluence scour, and in formation of point barsas well as alternating bars.




Figure 6 Theoretical illustrations of helical (secondary) flow in a river bend.

The helical flows occur in curved flows,especially in river bends. It arises from theimbalance between the pressure gradient and thecentripetal acceleration working on a waterparticle moving along a curved path. Near theriverbed the helical flow is directed towards thecentre of flow curvature. The magnitude of thehelical flow (i.e. the transverse flow velocitycomponent) rarely exceeds 5-10 % of the mainflow velocity in natural rivers. A typical helicalflow pattern is shown in Figure 6.

Assuming a logarithmic main flow velocitydistribution over the vertical and a parabolic eddyviscosity distribution, the magnitude of thesecondary flow can be shown to be proportional tothe main flow velocity, the depth of flow and thecurvature of the main flow stream lines. In MIKE21C, the streamline curvature is calculatedexplicitly from the depth integrated flow field.The gradual adaptation of secondary (helical) flowto changing curvature is accounted for by solving

a first order differential equation along the streamlines with the strength of the helical flow as thedependent variable (see also de Vriend, 1981).The strength of the helical flow is used todetermine the direction of both bed and suspendedload.

With streamlines of radius Rs of curvature anddepth H, the helical flow intensity can beexpressed as (U is the main flow speed, C isChezys number):

U=i eh ⋅χ

where the helical flow strength was first derivedby Rozowsky, 1957:

R

H)

C

g-(1

2=

s2e ⋅

⋅κκχ

secondary

s

nprimary

(primary

(secondary)

Outer bank

Inner bank

Main flow

Secondaryflow

Bottom

n

s

TopMainDirection

sδ




Transport formulaeIn connection with detailed (two-dimensional)mathematical modelling of sediment transport andmorphology in rivers with large suspended loadtransports, it is necessary to distinguish betweenbed and suspended load in order to:

• simulate the dynamic development of bedform dimensions

• account for the effect of helical flow as wellas the bed slope on the sediment transportdirection

The relatively simple total load sediment transportformulas, such as Engelund & Hansen, 1967 andAckers & White, 1973 can therefore not be usedfor river applications with consideration of helicalflow and bed slope without a separatespecification of how the sediment is distributedbetween bed load and suspended load. It ispossible, though, to run simulations by MIKE 21Cwith a total transport formula only by disregardingthe effect of helical flow and bed slope.

The sediment transport models developed byEngelund & Fredsoe, 1976, and van Rijn, 1984,which distinguish between bed and suspendedload form the basis for the sediment transportdescription in MIKE 21C. The specification of thesediment transport formulas is, however, veryflexible. Specially developed sediment transportformulas (determined from for instance fieldmeasurements) can be specified separately for bedload and suspended load, respectively. With thisflexible sediment transport formulation, it is alsopossible to select formulas like Engelund-Hansen,Smart-Jaeggi, and Meyer-Peter.

If the suspended sediment transport is negligiblecompared to the bed load transport, the suspendedsediment model can be switched off, so only a bedload model (or a total load model) is employed.

Bed LoadIn MIKE 21C, the bed load transport is calculatedexplicitly from one of the selected formulas, eg.Engelund-Fredsøe, van Rijn, or Meyer-Peter.These formulas relate the transport rate to the bedshear stress and the grain diameter.

On a horizontal bed, the transport direction willcoincide with the direction of the bed shear stress.The direction of the bed shear stress may,however, deviate from the direction of the depth-averaged flow due to the helical flow as describedin a previous section. If δ is the angle of deviationdue to the helical flow and χ is the helical flowstrength, the following relation exists:

χδ =tan

On sloping beds, the gravity will have influenceon the transport direction as sketched in Figure 7.The description of the effect of gravity and bedslope on the transport direction is as describedbelow in MIKE 21C. Due to bed slope effects theangle of deviation, α, is (G and a are coefficients,I transverse bed slope):

IG= a ⋅⋅ −θαtan

The bed slope is I, the angle of deviation is α, θ isnon-dimensional bed shear stress and G and a arecalibration parameters. Typical values of G and aare 0.66 and 0.5, respectively. Most of theserelations have, however, only been verifiedagainst data from laboratory tests and are,therefore, not necessarily applicable to naturalrivers with large suspended load, see alsoTalmon/Struiksma/van Mierlo 1995. Theapplicable relation is therefore often determinedvia calibration of the model. Corrections in thecalculated bed load transport due to sloping riverbed in the main flow direction is also done inMIKE 21C.

Stream line

Bed contours

x

y

s

n

β

δ

α

Fbs

Fg

Fbn

Figure 7 Shear stress on bed load sedimentparticles is composed of three “drag” components:Force due to main flow Fbs, force due tosecondary flow Fbn, force due to gravity on asloping riverbed.




Suspended LoadStandard methods for calculation of suspendedload are not applicable in the case of detailed (ie.high resolution) modelling of rivers. It isnecessary to include the time-space lag in thesediment transport response to changes in localhydraulic conditions. Consider, for instance, anincrease of flow velocity in a river (eg. aconstriction). As the flow velocity increases, theentrainment at the river bed will increasecorrespondingly, but it will take some time (andhence some distance) for the sediment entrained atthe bottom to disperse all through the watercolumn. This means that the actual suspended loadis not only a function of local hydraulicconditions, as it is normally assumed in mostmathematical sediment transport models, but it isalso a function of what takes place upstream andearlier in time.

A relevant time scale for the time lag (T) is thesettling time for a sediment grain in the watercolumn:

T = h*/ws

where h* is the effective fall height (depends onthe shape of the vertical concentration profile and,thus, on the fall velocity and eddy dispersion) andws is the fall velocity.Correspondingly, a length scale for the space lagis

L = T⋅U

where U is the flow velocity. Assuming h*=8 m,ws=0.02 m/s, U =2 m/s, the time and length scalesare 400 s and 800 m, respectively. Consequently,the space lag is important for river applications .

The space lag effect is modelled in MIKE 21C bya depth-averaged convection-dispersion modelwhich represents the transport and the verticaldistribution of suspended solids and flow. Thismodel is an extension of the model first developedfor one dimension by Galappatti (1983) and laterin two dimensions by Wang (1989). The model byWang, however, was primarily developed forestuarine applications and did not include theeffect of helical flow. This effect is essential in thecase of river applications because the suspendedload direction will be different from the main flow

direction due to helical flow, as shown in Figure7.

The secondary flow profile is computed in MIKE21C and used together with the primary flowprofile and the concentration profile when thesuspended load is integrated over the depth. Asthe concentration is highest near the river bed, thesuspended load transport will be deflected towardsthe centre of flow curvature. In contrast to bedload, the transverse river bed slope does notinfluence the direction of suspended loadtransport.

The depth averaged convection-dispersion modelrequires an expression for the equilibriumconcentration. The models by eg. Engelund &Fredsøe (1982) or van Rijn (1984) can be used forthat purpose. The empirical formulas implementedin MIKE 21C can also be used assuming that theequilibrium concentration equals the suspendedload transport divided by the water flux.

Supply-limited sediment transportAn important feature of the MIKE 21C is tosimulate supply-limited sediment transport, i.e. asediment layer on the riverbed of finite thickness.Below a pre-defined equilibrium thickness(usually associated with the height of sand dunesin sandy rivers), the sediment transport is reducedaccording to the availability of sediment. Erosioncan only take place, as long as there is sedimentavailable on the riverbed. A 2D map of the initialsediment layer thickness can be defined. Thefeature is used in connection with for instancerepresentation of river training works (revetments,groynes, weirs etc.) or fine sediment transportover a rock bed.

Graded sediment transportThe MIKE 21C is capable of simulating severalfractions of sediment, each with a characteristicgrain size. Each grain fraction is simulatedseparately with due consideration to the inter-action between the various grain components atthe riverbed (shielding, armouring). Thus, thegraded sediment model is applied in conjunctionwith defined sediment layers, each composed withdefined percentages of each sediment fraction.With this model, it is possible to simulate thesorting in space and time of graded sediment.




Cohesive sedimentA simple version of cohesive sediment descriptionis included in the MIKE 21C sediment transportmodel allowing the user to specify sedimentfractions in a graded sediment model over a widerange from mud to silt, sand, gravel and cobbles.This is relevant for instance in connection withmodelling of reservoir sedimentation with largerparticles depositing in the upper part of thereservoir and finer particles depositing in thelower (and deeper) part of the reservoir.

InputTo summarise, the main input parameters for theMIKE 21C sediment transport model is• Grain size (2D map or constant in the enture

area)• The percentage and grain size for all fractions

in case a graded sediment model is applied• Initial concentration of sediment (if required.

Default is nil).• Transport formulae for bed load and/or

suspended load

The main calibration coefficients are• Coefficient for helical flow intensity• Calibration factors for sediment formulae• Dispersion coeffients

OutputThe output parameters for the MIKE 21Csediment transport model in a predefined numberof time steps during the simulation period are• 2D map of concentration of suspended

sediment• 2D map of bed load transport, suspended load

transport and total load transport in twodirections (contours or vectors)

• 2D map of net sedimentation

Derived results, which can be extracted by anumber of graphics based tools are• Time series and profiles in selected

points/lines of concentration and sedimenttransport rates.

ALLUVIAL RESISTANCE

It is far more complex to determine the hydraulicresistance in alluvial rivers than in channels with afixed bed. This is because a large part of thehydraulic resistance in alluvial rivers is caused bybed form drag. The bed forms have aconfiguration determined by the sedimenttransport and flow. The hydraulic resistance willtherefore exhibit both temporal and spatialvariations.

Generally, the hydraulic resistance is divided intothat caused by drag on the bed forms (formfriction) and due to shear forces on the bed (skinfriction). The skin friction is relatively accuratelydetermined from a logaritmic boundary layerequation based on the median grain size of thebed. The form friction, however, can only bedetermined analytically if the size of the bedforms is known.

Ripples

Dunes

Plane bed

Anti dunes

Figure 8 Development of bed forms as theflow velocity increases.

Several hydraulic resistance predictors for alluvialrivers have been proposed, including those ofEngelund-Hansen and Ackers & White. Both ofthese models are semi-empirical linking thehydraulic resistance to the local instantaneousflow conditions. However, there can be asignificant lag between the form friction (ie. thebed form size) and the hydraulic conditions. Forinstance, in many tropical rivers, with distinct dry




and wet periods, the sand dunes found at the riverbed during the dry season have been formedduring a receding flood at the end of the floodseason. In such rivers, the hydraulic resistancewill often be relatively larger during the dryseason. It is therefore important to account for thistime lag.

In MIKE 21C, the dynamic development of thebed form size (height and length) has beencalculated in some projects with the modeldeveloped by Fredsøe (1979). In a subsequentstep, the form friction is calculated using a Carnottype formula for expansion loss. The skin frictionis determined from a logarithmic boundary layerequation. In quasi-steady flow, this modelsuggests that as the flow velocity increases, thedune size and hence the hydraulic resistanceincreases. As the flow velocity increases further,the bed form height and water depth first increaseat more or less the same rate and hence thehydraulic resistance only changes slowly until thesand dunes are washed away relatively abruptlyand the hydraulic resistance decreases rapidly.These features are illustrated in Figure 8.

For some applications, the differences in bedresistance due to rapidly changing bed levels maybe more important than the differences in bedresistance due to increase of decrease in the flowrate. Thus, use of a simpler alluvial bed resistancemodel was found to be operational in most cases.This model reads (C is the Chezy number, h is thelocal depth, a and b are calibration constants):

bha=C ⋅For b=1/6, the model simply equals the Manningformula, whereas for b=0, the model is the Chezyformula. In the morphological model, the depth hwill change both as a result of bed level changesand due to water level changes.

InputThe input parameter for the MIKE 21C alluvialresistance model is• Calibration constants• Minimum and maximum allowed values of

computed bed resistance

OutputThe output from the MIKE 21C alluvial resistancemodel is

• 2D map of bed resistance in a predefinednumber of timesteps during the simulationtime.

BANK EROSION

An important aspect of river morphologicalprocesses is bank erosion. For natural riverswithout protection of the riverbanks, appropriatedescription of bank erosion may be vital to get afull picture of the overall morphology of the area.In MIKE 21C, the bank erosion can be simulatedin parallel with the sediment transport andhydrodynamic simulations. In each time step, theeroded bank material is included in the solution ofthe sediment continuity equation. The followingbank erosion model is incorporated.

γβα +h

S+

t

z-=Eb ⋅

∂∂⋅

whereEb the bank erosion rate in m/s,z local bed levelS near bank sediment transporth local water depthα,β,γ calibration coefficients specified in the

model

The extra sediment which is discharged into theriver from this source and which is included in thesediment continuity equation is (hb height of thebank above the water level):

)h+(hE=S bbe ⋅∆

Figure 9 Definition of bank erosion rate E,which in the present model depends on bed levelchange, sediment transport and depth near theriverbank.




In addition to the formula above, a number ofalternative formulations have been tested and isavailable as hidden features in the MIKE 21C.

The accumulated bank erosion causes a retreat ofthe bank line position and thereby also in theextent of the modelling area. The MIKE 21Cincorporates these plan form changes by re-generating the curvilinear grid during thesimulation when the bank line changes exceed acertain pre-defined threshold. In this manner, themorphological model becomes a plan form model.

InputThe input parameter for the MIKE 21C planformmodel is• The number and location of eroding banks

within the model area (land/water boundarywhich must follow a curvilinear grid line)

• The erosion characteristics of each erodingbank

• Update frequency of the computational griddue to moving bank lines

OutputThe output from the MIKE 21C planform model is• 2D map of bank erosion in the model area• 2D map of the co-ordinates of every corner

point in each grid cell in the curvilinear meshat a predefined number of timesteps during thesimulation time.

The latter file is similar to the file created with thegrid generator, and is applied to depict modelresults in a movable curvilinear grid.

LARGE SCALE MORPHOLOGY

Large scale in this context means changes in thegeneral bed level within the model boundaries aswell as plan form changes due to bank erosion.

The bed and suspended load sediment transportmodels described earlier in this section predictsediment transport rate and direction. The changeof bed level is, therefore, easily determined byintegrating the net inflow or outflow within acontrol volume causing either deposition or scour.

This integration is explicit, due to the non-linearcharacter of the sediment transport relations

applied. This implies that the large-scalemorphological model needs to be subjected to arigorous stability criterion for the time step.However, a time step substantially larger than thetime step in the hydrodynamic model cangenerally be applied. In addition, the MIKE 21Chas the capability to simulate hydrodynamicsassuming quasi-steadiness. With this feature, it ispossible to simulate very long time series (years)with even very detailed 2-D models. Finally, thetime step for sediment transport simulation canvary automatically by specifying a maximumacceptable sediment transport courant numberrather than the time step it self. This option isuseful when simulating time series with largevariations from low to high flow conditions.

Three kinds of boundary conditions can bespecified for the morphological model at theupstream boundary: Total sediment transport, bedlevel changes, or concentration of suspendedsediment (in which case, bed load is calculatedexplicitly from local hydraulic condition at theboundary). The boundary conditions may varyboth in space and time along the boundaries. Theeffect of bank erosion is included in the sedimentcontinuity equation, ie. the eroded bank material isincluded as a lateral boundary condition.

The output from the large-scale morphologicalmodel is sediment transport (bed load as well assuspended load), the bed level and bed levelchanges at every grid point and at every time step.Also accumulated bank erosion and new grid co-ordinates are output from the model if the bankerosion and grid update module is activated.

InputThe input parameter for the MIKE 21C Largescale morphology is• Time series of sediment transport rate,

concentration of suspended sediment or bedlevel changes at the upstream boundary(ASCII file format, Excel or similar).Constants can be defined as well (e.g. bedlevel changes = 0)

• The number of sediment layers on the riverbed

• 2D map (or constant) of the initial sedimentlayer thickness




• 2D map (or constant) of the initial percentageof each sediment fraction in each layer, ifgraded sediment is applied.

OutputThe output from the MIKE 21C Large scalemorphology at a predefined number of timestepsduring the simulation time is• 2D map of bed levels• 2D map of bed level changes• 2D map of layer thickness and mean grainsize

Derived results, which can be extracted by anumber of graphics based tools are• Time series and profiles in selected

points/lines of bed levels, bed level changes,layer thickness etc.

MODEL VERIFICATION

The MIKE 21C is specially designed formodelling of river morphology. Therefore, it mustbe able to simulate the development of bendscour, which is one of the main features ofmeandering rivers as well as development of point

bars and alternating bars. In the following, twoexamples of model applications are presented:One of a flume in a lab, and another of a braidedriver.

By testing against physical scale modellingresults, it is possible to follow the developmentfrom a flat, horizontal riverbed. At DelftUniversity of Technology, an extensive number ofmobile bed model tests with a curved laboratoryflume has been carried out. The results obtainedby e.g. Olesen (1987) and Talmon, 1992, havebeen used for verification of the performance ofMIKE 21C.

The u-shaped flume is shown in Figure 9. Thewidth of the flume is 0.50 m. The inflow section(which is straight) has a length of 11 m, the arclength of the bend is 12.9 m, and the radius ofcurvature of the centre line along the curvedsection is 4.1 m. The inflow at the upper boundaryis constant (5.7 l/s), the average longitudinal slopeis 0.0034, the mean depth is 0.048 m, the meanvelocity is 0.24 m/s, and the median grain size ofthe sand in the flume bottom is 0.088 mm.

Figure 9 Mathematical model of a laboratory flume. The simulated bed level changes are shown in aplan view together with longitudinal profiles of the time development of the relative depth.

The simulated development of bend scour isclearly seen from Figure 9: Erosion has taken

place along the outer bank, and deposition at theinner bank. In the straight reach downstream the




curved section, shifting point bars have developeddue to the abrupt change in flow (and bank line)curvature. The over-shooting phenomenon in bedlevels along river bends is very clearly seen fromthe results. Finally, the bed level fluctuations(point bars) downstream of the river benddemonstrate the limited numerical damping in themathematical model and the ability to form ameandering pattern of the channel.

The pattern and magnitude of the bed level changeis similar to the observed bed level change fromthe laboratory flume, see Talmon (1992). Asexpected, modelling results are sensitive to thechosen parameters for bed slope effect and helicalflow effect. From the comparison between thelaboratory flume results and the mathematical

modelling results, it is evident that the MIKE 21Cis capable of reproducing the equilibrium riverbend scour as well as the dynamic developmentbend scour to its mature state.

In the second example, see Figure 10, the modelhas been used to simulate the development of abraided river. Initially, a completely uniformriverbed with constant slope, discharge, grain size,width, depth, bed resistance has been assumed.Subsequently, the model simulates thedevelopment of channels and bars using modelparameters similar to those used for calibration ofa model of a real river, the Jamuna River inBangladesh. The simulation covers 30 years.

Figure 10 Simulation of a braided river starting with completely uniform conditions (left). The timedevelopment is shown after 0, 3, 6, 12, 18, 24, and 30 years. The real braided river (Jamuna River inBangladesh), from which model parameters were calibrated, is depicted to the left.

Accurate long-term predictions of the morphologyof braided rivers cannot be achieved with any

model due to the inherent chaotic nature of suchrivers. However, in this ultimate test, the MIKE




21C proves to be capable of reproducing thecharacteristics of the braided river in terms ofwave length, braiding intensity, channel width,

shape and size of main bars. Only the number ofmodel grid points sets the limit of the resolution ofminor channels and bars.




EXAMPLES OF MIKE 21CAPPLICATIONS

Measurements from the following monsoon weresubsequently employed to validate the modelsimulations (hindcasts) and improve thecalibration before the model was applied foranother new forecast.

After completion of the bridge, the model is beingused to support in Operation and Maintenance ofthe bridge.

Bank Erosion for Different Flood EventsLeft Bank

0

100

200

300

400

500

600

675 680 685 690 695 700 705 710 715 720 725Distance along bank (km)

Ban

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osio

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)

1988 Flood

1994 Flood

1995 Flood

1996 Flood

1997 Flood

Jamuna River, Bangladesh.

Mathematical modelling was established toprovide forecast of critical morphological and

hydrodynamic conditions during construction ofthe Jamuna Multipurpose Bridge 1995-1998.

Measurements of river bathymetry was carried outevery year after the monsoon. Subsequently, amodel was established of a 36 km reach of theriver and applied for predicting flow velocities,water levels, erosion- and deposition rates, bedlevels, bank lines etc. in the coming monsoon.

As the actual hydrograph was unknown at the timeof simulation, several historical time series ofdischarge were simulated to cover the possiblerange of monsoon events.

In addition to short-term predictions of criticalconditions within the next year, the model ofJamuna was applied to investigate the impact ofthe bridge project in terms of induced erosion nearthe river training structures as well as inducedincrease in water level and flow velocities.

Long-term simulations with MIKE 21C covering30 years were applied to assess changes in theoverall characteristics of the braided Jamuna riverdue to the bridge.

(Client: World Bank,1995-99)




Snake River, USA(right)The Pine Bar area in the Snake River, Idaho, isconsidered one of the most important on the riverwith respect to fish habitat. Also, the sandy barlocated on the right riverbank is considered ofvery high recreational value.

The hydrodynamic model was applied for fishhabitat modelling. Simulated results of flowvelocities and depths were extracted from theMIKE 21C model to a separate fish habitat model.Sediment transport was modelled as being supplylimited because of the presence of a fine sandfraction accumulating in small bars on thearmoured gravel riverbed. It was demonstratedhow the sediment transport model predicts theimpact of reservoirs in terms of effect of adifferent sediment supply.(Client: Idaho Power Company, 2000-2002)

Skjern River, Denmark(left)River Skjern was straightened and confinedbehind embankments through a major regulationin the 60s, which caused a number of negativeeffects on the environment. In 2001, therestoration of River Skjern was completed- thelargest project of its kind in northern Europe. Thekey objective of the project was to restore theriver's original meandering course, to createpermanent wetlands, to increase the biodiversityin the river valley, to improve the conditions fortrout and salmon and to increase the nutrientturnover in the meadows. MIKE21C was used toassess the morphological equilibrium of therestored river course. (Client: Ministry ofEnvironment, 1998-1999)




Loire River, France(above)

In connection with major dredging and rivertraining works in the Loire Estuary, a 2-D modelbased on MIKE21 CMT was established forpredicting changes in hydrodynamics and mud

transport. The tidal model was applied forsimulating several weeks dynamically in order toevaluate sediment transport patterns over a spring-neap tidal cycle. Boundary conditions were derivedfrom a 1-D MIKE 11 model.

(Client: BCEOM, 1997)

Øresund, Denmark(left)

A bridge/tunnel link is being constructed acrossthe strait between Sweden and Denmark.Numerous modelling studies have been carried outfor design and EIA studies. The present modellingsystem was applied to investigate the detailedflow pattern around the corners (training walls) ofan artificial island in the middle of the strait. Theflow is controlled by the water level differencesbetween the Baltic Sea and the North Sea. Acurvilinear model was constructed over a largerarea (25x20 km) with increasing grid cell intensitytowards the training walls under investigation.The minimum grid resolution (5 m) alloweddetailed eddy formations to be accuratelysimulated.

(Client: Øresundskonsortiet, 1998)




Gorai River, Bangladesh(right)The supply of fresh water to the South-Westregion of Bangladesh comes from the Gorai Riverwhich is a tributary of the Ganges River. The off-take from the Ganges River has been subject tosevere sedimentation in recent years causing theGorai River to be completely dry in severalmonths each year. With aid from internationaldonors, the Government of Bangladesh haslaunched a major dredging/river training project toensure the river stays open.

The MIKE 21C model is applied to 1) assist themain consultant in design of river training worksand dredging, 2) assist the dredging company inforecast of short-term morphological conditions,3) investigate the short-term and long-term impactof river training and dredging.

(Client: Surface Water Modelling Centre, Ministryof Water Resources in Bangladesh, and TheWorld Bank, 1998-99)

Songwe River, Tanzania/Malawi(left)The meandering Songwe River forms part of thephysical boundary between the Republic of Malawiand the United Republic of Tanzania and has alength of approximately 200 km. The combinationof multi-purpose reservoirs in the upper river basinsand bank protection works along the lower reacheshas been investigated at a feasibility level.Morphological model tests with MIKE 21C showthat management of the frequency and duration ofshort-term flood events (by means of reservoirs inthe middle and upper part of the Songwe RiverBasin) has a pronounced effect on the overall bankerosion and thereby river stability in downstreamreaches.

(Client: Nordic Development Fund, 2001-2003)



NN/fileserv/wrd/manuals/M21C-SD/990715/HGE/nck Dansk Hydraulisk Institut/Danish Hydraulic Institute

REFERENCES

Ackers, P. and Whit, W.R. (1973) SedimentTransport: New approach and analysis, Proc.ASCE, JHD, 99, HY11 pp. 2041-2060

Engelund, F. and Fredsoe, J. (1982) Hydraulictheory of alluvial rivers, Advances in HydroScience, Vol.13, pp.187-215

Engelund, F. and Hansen, E. (1967) A monographon sediment transport in alluvial streams, TekniskForlag, Copenhagen

Fredsøe, J. (1979) Unsteady flow in straight alluvialstreams; modifications of individual dunes, J. FluidMech.,Vol. 91, pp 497-512

Galappatti, R. (1983) A depth integrated model forsuspended load, Communications on Hydraulics83-7, Dept. Civil Eng. Delft Univ. Tech, TheNetherlands

Michelsen, J.A. (1989) Solution of the Navier-Stokes equations on general non-orthogonalmeshes, FTU/STVF pr J.nr. 95 83 02, Departmentof Fluid Mechanics, Technical University ofDenmark, pp 1-45.

Olesen, K.W. (1987) Bed topography in shallowriver bends, Faculty of Civil Eng., Delft Univ.Tech., Report 87-1

Ribberink, J.S. (1987) Mathematical modelling ofone-dimensional morphological changes in riverswith non-uniform sediment"

Rijn, van L.C. (1984a) Part I: Bed load transport, J.Hydraulic Eng., 110, 10, October

Rijn, van L.C. (1984a) Part II: Suspended loadtransport, J. Hyd.Eng, 110, 11, November

Talmon, A.M.; Struiksma, N.; van Mierlo,M.C.L.M.; "Laboratory Measurements of theDirection of Sediment Transport on TransverseAlluvial-bed Slopes, Journ. of Hydraulic Res., Vol.33 (1995) no.4

Talmon, A.M. (1992) Bed topography of riverbends with suspended sediment transport, Facultyof Civil Eng., Delft Univ. Tech., Report 92-5

Vriend, J.J. de (1981) Steady flow in shallow riverbends, Comm. on Hydraulics 81-3, Dept. CivilEng.,Delft Univ. Tech., The Netherlands

Wang, Z.B. (1989) Mathematical Modelling ofmorphological processes in estuaries, Report No.89-1, Faculty of Eng.,Delft Univ. Tech., TheNetherlands

Stone (1968) Iterative Solution of ImplicitApproximations of Multidimentional PartialDifferential Equations, SIAM Journal Num.Anal., Vol. 5, No. 3, pp 530-559

MIKE 21C RIVER MORPHOLOGY - MIKE by DHI

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