Three-dimensional morphological modelling in Delft3D-FLOW

Transcription

1 Three-dimensional morphologial modelling in Delft3D-FLOW G. R. Lesser, J. van Kester, D.J.R. Walstra and J.A. Roelvink WL delft hydraulis Abstrat Computer modelling of sediment transport patterns is generally reognised as a valuable tool for understanding and prediting morphologial developments. In pratie, state-of-the-art omputer models are to-dimensional (depth averaged) and have a limited ability to model many of the important three-dimensional flo phenomena found in nature. This paper reports the implementation and validation of non-ohesive sediment transport formulations ithin the proven DELFT3D three-dimensional (hydrostati) flo solver. The paper briefly disusses the operation of the DELFT3D-FLOW module, presents the formulations implemented to model both suspended and bed-load sediment transport, and desribes the morphologial updating sheme. The modelling of the three-dimensional effets of aves is also disussed. Folloing the details of the implementation the results of a number of validation studies are presented. The model is shon to perform ell in a number of theoretial, laboratory, and real-life situations. Introdution In river, estuarine, and oastal environments sediment is transported by floing ater. Although muh of the sediment is transported lose to the bed, a signifiant quantity may be transported higher in the flo. In addition, the magnitude and diretion of the shear stress the flo exerts on the bed, hih is important for determining the magnitude and diretion of the sediment transport, annot alays be determined from the depth-averaged flo veloity as signifiant three-dimensional effets may our. Examples of these three-dimensional effets inlude the spiral flo pattern ommonly found in river bends, and the underto hih is espeially strong in breaking aves. While the boundaries of to-dimensional (depth-averaged) morphodynami modelling are onstantly being pushed bak, predominantly by adding to the refinement of the hydrodynami ave and flo models inorporated ithin the models, they ill alays suffer from the fat that they rely on depth-averaged estimates of sediment transport rates. These depth-averaged estimates are, in turn, based on assumptions regarding the vertial veloity profile and turbulent mixing profile. The simplest of the to-dimensional models assume a logarithmi veloity profile and a paraboli, or paraboli-onstant turbulent mixing profile. More advaned models, so-alled quasi threedimensional models, ontain additional parameters in order to attempt to adapt these general veloity and turbulent mixing profiles in situations here they are no longer valid, for example in highly stratified flos, or in areas ith signifiant ave ation or ith rapidly aelerating or deelerating flos. The next logial step is the development of fully three-dimensional morphologial models. These models alulate the veloity of ater flos, along ith the transport of sediment in all three spatial dimensions. This means that relatively fe parameterizations are required to desribe flo phenomena that our in three dimensions - spiral flo in river bends for example - and thus the model atually beomes simpler, as ell as being physially more aurate. The main disadvantage of three-dimensional modelling is the relatively large amount of omputational effort required to solve the signifiantly larger systems of equations. While omputing poer is obviously a onsideration that must be kept in mind hen ontemplating a large omputer model, the ongoing rapid inreases in omputing poer readily available to the professional user mean that desk-top personal omputers are no apable of running moderate-size three-dimensional simulations in an aeptable time. This is a situation that an only be expeted to improve over the oming months and years. This abstrat desribes the development and validation of just suh a three-dimensional morphodynami omputer model; it is developed by inorporating sediment transport formulations into the already-advaned DELFT3D hydrodynami flo modelling system. A full paper ith the same title and authors is in preparation. The Delft3D-FLOW module Delft3D-FLOW is the 2DH or 3D hydrostati flo solver ithin the Delft3D system (see.ldelft.nl/soft/d3d/flo) It an be operated in stand-alone mode or as a module of the Delft3D-MOR system. 1

2 The latter is applied in situations here various Delft3D modules are interating. In version disussed here sediment transport and morphologial updating is fully integrated ithin the flo module. In ase aves are inluded the Delft3D-MOR makes alternating alls to the ave module and the flo module. Suspended sediment transport At eah time step the three-dimensional transport of sediment is alulated by solving the three-dimensional advetion-diffusion (mass-balane) equation for the suspended sediment t x u y v z ( ) ª º º ( ) > ( H, H, H, º 0 (1) ª s «s x» s y sz x x ¼ y y ª ¼ z ¼ An important aspet of solving this equation is the speifiation of the loal turbulent sediment mixing omponents (Hs,x, Hs,y, Hs,z). The horizontal omponents are user-speified, the vertial omponent is taken from the turbulene losure model used to alulate the diffusion of mass and momentum in hydrodynami alulation. The user may selet an algebrai, k L, or k H turbulene losure model. Wave effets are aounted for folloing van Rijn (1993) for the algebrai model or Walstra et al. (2000) for the k H model. The loal hindered partile fall veloity ( s ) is alulated using the formulations presented by van Rijn (1993) inluding the effets of hindered settling. Boundary onditions are also required, these are implemented as follos: x x at the free surfae; vertial diffusion is set to zero at open lateral boundaries; horizontal diffusion is set to zero, the quantity of sediment adveted inard through an open boundary is determined by speifying a vertial onentration profile. An option is available to set sediment onentration profiles at inflo boundaries to their equilibrium values, based on the loal flo veloity and turbulent mixing profile. x at the bed; vertial advetion and diffusion are set to zero. Hoever a series of sediment soure and sink terms are inluded in the bottom omputational layer in order to simulate the exhange of sediment ith the bed. The resulting system of equations is solved using the same numerial solver as is used for omputing the transport of onservative onstituents. Bed-load sediment transport The alulation of bed-load sediment transport of sand sediment frations is inluded in the modified DELFT3D- FLOW module, generally folloing the method desribed by van Rijn (1993). Ativation of the bed-load transport option auses the bed-load transport vetor to be alulated at eah omputational point at eah time step. Spatial gradients in bed-load transport ill ause erosion and aretion of the bed hih may also be taken into aount hen performing on-line morphologial omputations, as desribed in the next setion. The bed-load sediment transport vetor inludes an adjustment for the effet of longitudinal and transverse bed slopes. Morphologial updating The bed level is updated during eah time step of the flo omputation, taking into aount the exhange ith the suspended sediment vertial and the gradient of the bed load transport. Both terms an be multiplied by a morphologial saling fator. The effet of fixed layers an be taken into aount; the verial exhange term and the bed load transports are gradually redued to zero as the sand layer thikness approahes zero. Three-dimensional ave effets The alulation of the vertial sediment diffusion oeffiient has been signifiantly improved in situations inluding aves. In order to affet these hanges the oeffiient for the vertial diffusion of sediment partiles is no stored separately from the vertial diffusion oeffiient for momentum and all other onstituents. The alulation of the vertial sediment diffusion oeffiient no depends on the type of sediment, the hoie of turbulene losure model, and hether aves are present. Wave effets are aounted for folloing van Rijn (1993) for the algebrai model or Walstra, Roelvink.and Groeneeg (2000) for the k H model. z 2

3 Validation A large number of validation tests have been arried out to test various aspets of the implemented proesses. To start ith, a series of tests as arried out for a long flume in a urrent -only situation, to verify that the equlibrium profile is reprodued orretly and to test the sensitivity various settings, suh as grid sizes, vertial distirbution of grid size, turbulene model. Next, to flume tests ere hindast: a trenh migration test by Van Rijn (1987) for urrent only, and a flume test by Dekker and Jaobs (2000). Results for the trenh ase are shon in Figure 1, shoing exellent agreement for both flo profiles and onentration profiles. Quite satisfatory results ere also found for the aves plus urrent test. 1 &RPSDULVRQ RI QXPHULFDO VLPXODWLRQ DQG IOXPH WHVWV.HSVLORQ WXUEXOHQFH PRGHO /D\HUV Computed veloity Computed sediment onentration Measured veloity Measured sediment onentration Height, z (m) Distane, x (m) Figure 1 Comparison of omputed and measured profiles of veloity and onentration, trenh ase. More realisti 3D ases ere also simulated: a test of erosion around a groin in a straight hannel, a omparison beteen quasi-3d and 3D morphologial modelling of a part of the Western Sheldt, over a period of a month, a simulation of the effet of the Eijerland dam in the north of the island of Texel and a simulation of a river bend utoff during a flood event. These simulations all sho robust and realisti behaviour. Comparisons beteen the 3D and the 2DH or Q3D odes sho similar patterns on a large sale but differenes on a smaller sale. A ontinuing validation effort is required to assess the overall auray of the ne approah in ompariison ith existing (mostly 2DH) methods. As a first test of the ombined modelling of aves, urrents and morphologial hanges in 3D, a test ase from literature as taken, viz. the offshore breakater test reported in Niholson et al. (1997). In Niholson et al., this test ase as run using five different 2DH morphodynami models, among hih Delft3D-MOR. The only driving fore in the tests are the aves, hih enter perpendiular to the oast. The aves drive a double irulation pattern hih tends to bring sand to the area behind the breakater, leading to the formation of a tombolo or salient. The initial flo field is shon in Figure 2 (left). It shos the overall pattern of to irulation ells in opposite diretions, hih are driven by set-up gradients. On top of that, e see a lear differene in flo pattern beteen the top and bottom layers, due to helial flo, hih pushes the upper-layer veloities outard, and underto, hih gives an seaard omponent near the bed in the surf zone. The final bathymetry is shon in Figure 2 (right). At first sight, the results are quite similar to the results from 2DH models, as given in Niholson et al. (1997). A big differene hoever is that the aretion behind the breakater goes at the expense of erosion at the beah at the sides of the lee zone, hereas in 2DH models the erosion takes plae mainly near the ends of the breakaters. In the 3D ase, some erosion takes plae there, but not nearly as muh as in the 2DH ase. 3

4 Figure 2 Left: Initial bathymetry and flo field in top (red) and bottom (blak) layer. Right: bathymetry after 1 day. Conlusions and reommendations A ne 3D morphodynami model has been developed and tested for a range of appliations. The model has shon to be robust and relatively easy to use. Future extensions should inlude the effet of ave asymmetry on the bed load transport, and inorporation of ave foring and a roller model varying on the time-sale of ave groups. A series of validation studies should be arried out to assess the appliability of the model to general oastal engineering problems, both on a relatively small sale and for areas the size of a tidal inlet. Aknoledgements The present ork is undertaken as part of the SASME-projet under ontrat number MAS-CT and the LWI-projet Kustmorfologishe Veldmodellen. Additional funding as provided by the National Institute for Coastal and Marine Management (RIKZ) under projet number Z2899, and. Referenes Dekker S and Jaobs C.E.J. 2000, Sediment Conentration Due To Irregular Waves And Currents. Master s thesis (in print), Delft University of Tehnology Niholson J., Broker I., Roelvink J.A., Prie D., Tanguy J.M., Moreno L. (1997). Interomparison of oastal area morphodynami models, Coastal Engineering (31)1-4 (1997) pp van Rijn L.C. 1987, Mathematial Modelling of Morphologial Proesses in the ase of Suspended Sediment Transport. Dotoral thesis, Delft University of Tehnology. van Rijn L.C. 1993, Priniples of Sediment Transport in Rivers, Estuaries and Coastal Seas. Aqua Publiations, Amsterdam. Walstra D.J.R, Roelvink J.A. and J. Groeneeg (2000), Calulation of ave driven urrents in a 3D meanflo model.. International Conferene on Coastal Engineering, Sydney, July 2000 (to appear); also SASME final abstrat, this volume. 4

5 5