Process-based modeling of morphodynamics of a tidal inlet system

Acta Oceanol. Sin, 2010, Vol. 29, No. 6, P.51-61DOI: 10.1007/s13131-010-0076-1http://www.hyxb.org.cnE- mail: hyxbe@263.netProcess- based modeling of morphodynamics of a tidalinlet systemXIE Dongfengl-2, GAO Shu2*, PAN Cunhong'1 Zhejiang Institute of Estuaries and Hydraulics, Hangzhou 310020, China2 Ministry of Education Key Laboratory for Coast and Island Development, Nanjing University,Nanjing 210093, ChinaReceived 13 September 2010; accepted 18 October 2010OThe Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2010AbstractThe morphodynamic evolution of an idealized inlet system is investigated using a 2-D depth-averaged process-based model, incorporating the hydrodynamic equations, Englund- Hansen's sed-iment transport formula and the mass conservation equation. The model has a fixed geometry,impermeable boundaries and uniform sediment grain size, and driven by shore-parallel tidal eleva-tions. The results show that the model reproduces major elements of the inlet system, ie, floodand ebb tidal deltas, inlet channel. Equilibrium is reached after several years when the residualtransport gradually decreases and eventually diminishes. At equilibrium, the fow field character-istics and morphological patterns agree with the schematized models proposed by O'Brien (1969)and Hayes (1980). The modeled minimum cross sectional entrance area of the tidal inlet system iscomparable with that calculated with the statistical P-A relationship for tidal inlets along the EastChina Sea coast. The morphological evolution of the inlet system is controlled by a negative feed-back between hydrodynamics, sediment transport and bathymetric changes. The evolution ratesdecrease exponentially with time, ie, the system develops rapidly at an early stage while it slowsdown at later stages. Temporal changes in hydrodynamics occur in the system; for example, theflood velocity decreases while its duration increases, which weakens the flood domination patterns.The formation of the multi-channel system in the tidal basin can be divided into two stages; at thefirst stage the food delta is formed and the water depth is reduced, and at the second stage theflood is dissected by a number of tidal channels in which the water depth increases in response totidal scour.Key words: tidal inlet, morphological evolution, sediment dynamics, numerical modeling1 IntroductionNumerous methods can be found in the literatureA large part of the world's inhabited coastlinesto study the physical processes and the long-term be-is formed by sequences of tidal inlets. A tidal inlethavior of tidal inlets. Empirical relationships showsystem is a long and narrow branch of the open seathat equilibrium exists for different morphological pa-penetrating into land, consisting of a tidal basin, onerameters: inlet cross -sectional area and basin tidalor more entrance channels, and flood and ebb tidalprism (Zhang, 1995a; Gao, 1988; Zhang, 1987; Jarret,deltas (Ren and Zhang, 1985; Bruun, 1978). Through1976; O'Brien, 1969), inlet cross sectional area andthe entrance channels, tidally-induced water and sedi-discharge (Kraus, 1998) and ebb-tidal delta volumement exchange between the tidal basin and the open-and basin tidal prism (Walton and Adams, 1976), andsea occurs. Such channels often serve as a naturalthe ratios of shoal volume to channel volume and tidalnavigation channel, which is important for harbors.amplitude to mean channel depth (Wang et al, 1999).From the viewpoint of morphodynamics, tidal inletsRecently, analytical approaches to defining tidal inletare interesting because their formation and evolutionparameters have shown that morphodynamic behav-are concerned with a nurmber of crucial dynamic pro-cesses.floodi 中国煤化工h fecrs such a_ter discharges andFoundation item: The National Natural Science Foundation of China under conracr o 41Uwww ain rw376023; the Ministry ofTHCNMHGWater Resources' Special Funds for Scientifc Research on Public Causes under contract No.201001072; the Program for InnovativeResearch Team of Zhejiang Province under contract No. 2009F20024.*Corresponding author, E -mail: shugao@nju.edu.cn52XIE Dongfeng et al. Acta Oceanol. Sin, 2010, Vol. 29, No.6, P.51-61sediment transport through the entrance, in addition1980; Brun, 1978). This motivates the present studyto tidal prism (Jia and Gao, 2008; Gao and Collins, to model morphodynamics of tidal inlet systems by1994).considering ebb delta as well 88 the tidal basin, mainQuantitative researches on tidal inlet evolutionschanneland flood deltas. The overall objective of thehave conducted to a large extent in the last decade present study is to improve the knowledge of the phys-(e.g. Bertin et al, 2004; Stive and Wang, 2003;ical mechanisms controlling the morphodynamic de-Vila-Concejo et al, 2003; Zhang et al, 1995; Zhang,velopment of tidal inlets, focusing on tide-dominated1995b). The evolution of of the entrance channels istidal inlets floored with sandy sediments.related with the general characteristics of the tidalinlet system. Further, the hydrodynamics of tidal2 Model descriptioninlets is complex, although their spatial scales areThe process-based model is set up based on therelatively small. Recently, the mid- or small- scale flowstate-of-art Delft3D Online Morphology modeling sys-field around tidal inlets has been studied by many reem (edition 3.28), in which hydrodynamics and sed-searchers (e.g. Gong et al, 2009; Guyondet and Kouti-iment transport processes are included and for eachtonsky, 2008; Gong et al., 2008; Eguiluz and Wong,time step the bathymetry is updated using sediment2005; Li, 202; Van Leeuwen and De Swart, 2002),mass balance (Roelvink and Van Banning, 1994). Theproviding abundant information on spatial distribu-principal constituents of the morphodynamic modeltions of current velocities, residual currents and theare the flow, sediment transport and bottom changestructure of circulation patterns within the channels.modules, as described below.However, most studies treated the bathymetry of tidal2.1 Flowinlets as unchangeable boundary conditions; and fewfocused on the feedback processes between hydrody-The fow module computes unsteady flow result-namics and bathymetry.ing from tidal and meteorological forcing, based onEven there is a lack of long-term (i.e, years to the 2-D depth-averaged shallow water equations. Thedecades, the typical timesceale of coastal morpholog equations for conservation of momentum areical changes) data, developing a process-based mor-8Oua. fu+;gulUlphodynamic model would be an important attempt8x'yt9TxC2(d+η)to understanding the physical processes around tidal02u, 82u)= 0,(1)inlets. With the development of computer capacity,0x2T 0process-based models have been increasingly employed)u,8u. fu+gu|U Ifor coastal morphodynamic studies, such as estuar-8t 8xFy t 9可yies, embayment and tidal channels (e.g. Xie et al,82u, 820、)=0(2)2009; Xie et al, 2008; Hibma et al, 2004; Lanzoni and)x2十 Fy2Seminara, 2002; Ranashinghe and Pattiaratchi, 1999;and the continuity equation isWang et al, 1995). These models are based on phys-ical principles, capable of simulating various morpho四。8(d+n)u + 8(d+n)二o.(3)dynamic processes of hydrodynamics, sediment trans-8xayport and seabed evolution by solving mathematicalwhere C is Chezy's friction cofficient, defined by早equations (De Vriend et al., 1993). Several idealized(m1/2/s), in which n is Manning's coefficient (s/m1/3)models have been used to simulate the formation andd is water depth (m), η is water level (m), U is mag-equilibrium of ebb-tidal deltas (Van der Vegt et al.,nitude of total velocity (m/s),U= V(w2+ 2), u and2006; Van Leeuwen et al., 2003) and the influence ofV are depth-averaged velocities in the r- and y- di-tidal currents on the asymmetry of tidal- dominatedrections (m/s), 9 is gravitational acceleration (m2/s),ebb-tidal deltas (Van der Vegt et al, 2009)，improv-Uw is difusion cofficient (m2/s), f is Coriolis factoring the understanding of underlying physical mecha-(1/s).中国煤化工)oundaries by wet-nisms responding for the ebb tidal deltas evolutions.ting/<204).The components of tidal inlet systems, such as tidal.2YHCNMHGbasin, entrance channel and flood and ebb deltas, in-teract with each other and respond to inherent orVarious formulae are available for sediment trans-external forcing (e.g. Kragtwijk et al, 2004; Hayes, port calculation in literature. Hibma et al. (2004)XIE Dongfeng et al. Acta Oceanol. Sin, 2010, Vol. 29, No.6, P. 51-6153tested the sensitivity of estuarine morphodynamics timescale that is typically one to two orders of magni-for different sediment transport formulae, e.g. the tude smaller than the morphological timescale (Wangtotal-load transport formula of Engelund and Hansen et al., 1995). In terms of numerical modeling this im-(1976) and the transport formula of Van Rijn (1984) plies that many hydrodynamic calculations need to bewhich calculated bed load transport and the equilib- performed that have only limited efect on the mor-rium suspended sediment transport rate. Their re-phology. Morphodynamic calculations would thereforesults show that the estuarine morphodynamic devel- require long and infficient bydrodynamic calculationopment is largely analogous, with few local differ- time. In order to increase the efficiency of processences. Furthermore, Lanzoni and Seminara (2002) based morphodynamic models, Roelvink (2006) pro-analyzed dominant sediment transport processes in posed the“online morphology" approach to acceleratetidal environments, with the situations of the presence bed level changes. In this approach the bed level isof multiple sediment fractions, tidally-induced time updated at each computational time step by multiply-velocity asymmetry, continuously changing suspended ing the erosion and deposition fuxes from the bed tosediment concentration profiles, and erosion and set- the flow and vice versa by a constant factor“Morpho-tling lags around slack tide. Their analysis shows that logical Factor”the formulae for the bed and suspended load trans-ports based on local and instantaneous flow conditionsOtmorphology = fMor Othydrodynamics.are applicable.The morphodynamics update scheme is presentedLanzoni and Seminara (2002) suggested that a rel-in Fig.1.atively simple transport equation without making dis-tinction between suspended load and bed load be usedInitial conditionsso that the results can be analyzed in a more straight-forward way. This method is adopted in the presentHydrodynamicsstudy.The instantaneous total sediment transportformula developed by Engelund and Hansen (1967)Sediment transportthat relates velocity directly and locally to a sediment< Bathymetry update>transport is used: