Modelling of the vertical distribution of suspended sediment concentration under waves with a group structure

Transcription

1 9- Modelling of the vertical ditribution of upended ediment concentration under wave with a group tructure Ko yan R.D., Divinkiy B.V., Krylenko M.V., Vincent С.E. Reult of the modelling of the vertical ditribution of upended ediment concentration under the influence of wave with a pronounced group tructure are preented in thi paper. The reliability of the model ha been checked againt laboratory data from the SISTEX 99 experiment. Fluctuation of upended ediment concentration, calculated by the model, correlate very well with the experimental data and reproduce the form, number and duration of concentration peak rather well. Index Term Coatal zone, modelling, ediment, wave A I. INTRODUCTION T preent there are no mathematical model that are ufficiently reliable for the prediction of patial-temporal variability of upended ediment concentration in the hore zone. However the mot intenive upenion and ediment tranport take place in thi zone. Due to difficultie in making meaurement in real marine condition quantitative aement and prediction of upended ediment ditribution in the coatal zone ha been done by mathematical modelling, with the ue of parameter obtained under laboratory condition. To date, many model have been contructed of the ditribution of time-averaged concentration of the upended ediment under the action of wave; a full review of uch model wa undertaken by Antyferov and Akivi []. But a method baed on the ue of time-average value of concentration and water velocity doe not take into conideration temporal fluctuation of upended ediment flow and the reultant calculation may differ from real value by a factor of ten. Earlier field [,,, 8] and laboratory [, ] reearch ha hown that the fluctuation component of ediment upenion i very important to the reultant tranport of Manucript received March 7, 7. The work i carried out under financial upport of the Ruian Foundation of Baicl Reearch, grant -- and grant NATO CLG98/87. R. D. Ko yan i with the Southern Branch of the Intitute of Oceanology, RAS, Gelendzhik, Kranodar region, Ruia (phone: +789; koyan@coatdyn.ru. B. V. Divinkiy i with The Southern Branch of the Intitute of Oceanology, RAS,Gelendzhik, Kranodar region, Ruia. ( divin@bio.coat.ru. M. V. Krylenko i with the Southern Branch of the Intitute of Oceanology, RAS Gelendzhik, Kranodar region, Ruia ( mari@bio.coat.ru. C. E. Vincent i with the School of Environmental Science, Univerity of Eat Anglia, Norwich NR 7TJ, UK ( c.vincent@uea.ac.uk. upended ediment. Many model of patial-temporal fluctuation of upended ediment concentration are baed on the idea of turbulent diffuion priority [, 7] without taking into conideration the mechanim by which ediment i reupended, and thi reult in difference between field and calculated data [,, and ]. In ome model [,, 7] patial-temporal fluctuation of upended ediment concentration in the wave flow are decribed a function of the intantaneou value of Shield parameter. Such model atifactorily correlate with experimental data only for monochromatic wave, howing the correct phae hift of ediment when ediment are moving a a narrow belt, - cm thick, above the flat bed. Field and laboratory experiment have hown the neceity of taking into account an ocillatory motion of water and the phae lag between fluctuation of upended ediment concentration and water velocity at different level from the bottom [,,, ]. It wa revealed that duration and frequency of concentration peak depend on the periodicity of group of high wave and that of the number of wave in certain group []. Modelling of the variability in the vertical ditribution of upended and concentration above the flat bottom under wave with pronounced group tructure i preented in thi paper. The reliability of the model preented here i checked againt the reult of laboratory experiment SISTEX 99. A erie of ynchronou meaurement of upended ediment concentration, component of water velocity and elevation of free urface were elected for modelling and verification of the reult for the cae of wave with a group tructure. II. DESCRIPTION OF THE EXPERIMENT Data for modelling were obtained in the coure of laboratory experiment SISTEX 99 performed in the large wave canal at Hanover Univerity in Germany [7]. The total length of the canal i m, it width i m, depth 7 m. The andy bottom of the canal i compoed of well-orted and with a mean diameter of. mm. Wave in the canal are generated with a ytem of mobile wave plate with dynamic back coupling which decreae the influence of reflected wave. Tet with irregular wave, wave with a clear group tructure and monochromatic wave were carried out during the experiment. A vertical profile of upended ediment concentration, two component of water velocity (vertical and

2 9- along the axi of the flow and elevation of free urface were meaured in every tet. Intrument for meauring the upended ediment concentration and component of water velocity were intalled on frame cantilevered out from the wall of the canal. Meaurement of water velocity were made at a ditance of - cm above the bottom with the help of Doppler acoutic meaurer (ADV. Wave-wire, which recorded the location of the water urface, were mounted along the canal wall. Supended ediment concentration wa meaured with the help of high-frequency (,,, MHz acoutic backcatter enor (ABS [], which wa intalled at the ditance of - cm from the bottom. Concentration of upended ediment wa meaured in point along the vertical line in every mm with the frequency of. Hz. Synchronou meaurement of upended and concentration, component of water velocity and elevation of free urface were done in burt, each of which ha reading. III. MODEL OF SUSPENDED SEDIMENTS The model i baed on the diffuion equation for upended ediment concentration: C C C = w + ε, t z z z where C(z,t i upended ediment concentration, ε i a coefficient of turbulent diffuion of upended particle, w i a rate of and ettling velocity, t i time and z the vertical coordinate. According to thi equation a change of concentration in time at any horizon from the bottom i defined by the change oin the balance between the vertical upended ediment flux due to particle ettling (the firt term of the r.h. of the equation, and the ediment re-upended from the bottom (the econd term on the r.h.. A. Determination of diffuion coefficient The generalized diffuion coefficient of ediment i conidered to be variable in vertical direction and i given by [9]: ε(z=ε (z+ε (z+ε (z. Here ε (z i the contribution of the orbital motion, πh inh kz ε ( z =, T inh kh ε (z i the contribution of the wave flow, πχ H inh kz ε ( z =, T inh kh coh kz ε (z i the contribution of diffuion in near bottom layer, z b( u g w ε ( δ, z = z z +. exp( δ δ where coefficient b i defined a ρ ν b =. ρ ρ g u g i the maximum value of bottom orbital velocity with component δ + h coh(π HTg λ, U = λ h coh(π λ δ + h inh(π HTg λ. W = λ h coh(π λ δ i the thickne of boundary layer from Johnon equation [8]: δ δ H lg. z = z, D inh kh where z i the roughne parameter, z =, z N i the effective roughne of the bed, which for a mooth andy bottom i equal to the z N =.d where d i the mean diameter of andy particle on the bottom. H, T, λ are the height, period and length of the wave, and h i water depth. B. Boundary condition At the free water urface upended ediment flow i conidered to be equal to zero: C ε + w C = z At the bottom boundary upended ediment concentration i decribed by С(,t=A p(t, where p(t i a function of local ejection of upended ediment (pick-up function [], defined by....8 θ ( t θ cr ( g d p( t =.. θ, where cr ν i the relative denity of ediment. ρ = ρ When individual wave are paing ediment upendion take place not during the whole period but a a quick ejection of a cloud of upended ediment. The analyi of experimental data ha hown that one ejection happen during the phae decreae from maximum to zero of the horizontal component of velocity. Group tructure of wave greatly influence the proce of vertical profile formation under certain wave within the group. Intenification of ediment upenion under wave group tend to occur after the paage of maximum wave in the group and then gradually decay toward the trough of the geometric envelop of wave group []. Thee fact are taken into conideration by coefficient A, that change from A, and i equal to during the upenion phae and to zero at other time. It applie both to ingle wave and group of wave in term of their envelop. The intantaneou value of Shield parameter how a balance between hearing and confining force: θ u* ( t ( t =, (( ρ ρ / ρ g d where d i a median diameter of ediment, u * (t maximum hear velocity calculated from the flow velocity U ( t. C. Determination of u * (t z N

3 9- In condition of a trong turbulence of the wave boundary layer k n =D, an iterative condition i fulfilled [9] Abm ( = log (.7 log +. x n n ( n x k + n x where the initial value of x ( =., u(t A bm = and ω = f, where f ω i a factor of wave ω = π. T In thi formula x ω friction. Solution of the equation give a value of the wave ( m factor of friction of x f w = and that of maximum hear velocity fw u* ( t = u( t. An evenly-paced computational grid, in depth and in time, wa ued for calculation, with z=. m and t=.8. The following value of parameter were ued in the model []: ettling velocity w =. m/, critical value of Shield parameter for initiation of ediment motion θ cr =. for and with a mean diameter of. mm, kinematic vicoity of water ν= - m /. Etimation of vertical profile of generalized diffuion coefficient ha hown that contribution of ε (z coefficient i two order le than that of the other component (Fig. and may neglected a a contribution to the diffuion coefficient. Six region of upenion are clearly een in Fig., they correpond to group of wave (number -. Chronogram of horizontal velocity U, experimental (C exp and model (C mod concentration for thee group are given in Fig.. Averaging the vertical profile of concentration for both experimental and model data wa done within every group (Fig.. The profile obtained can be approximated by the following exponential function: C( z a exp( bz, where a and b are parameter controlling the lope and poition of the function. Fig. and Fig. how temporal change of the experimental and model profile of upended and concentration. The predicted and meaured vertical profile of concentration are coincide atifactorily in time. The vertical ditribution of upended ediment concentration change ynchronou from a concave profile to a convex one. The convex hape of the vertical profile of upended ediment concentration i conited with the convective nature of upenion proce. Oberved difference in the abolute value of upended ediment concentration are probably caued by the fact that a thi model doe not take into conideration any advective tranport of upended ediment, fluctuation of granulometric compoition of the and and change of phyical propertie of the flow when upended ediment concentration increae. The reult of pectral analyi of chronogram of horizontal component of flow velocity, elevation of level and upended ediment concentration (experimental and model are given in Fig. 7. All pectra are characterized by pronounced local maxima at the frequency of. and. Hz (Fig. 7.. The phae lag between the experimental C exp and calculated C mod concentration at the ame frequencie i cloe to zero. Fig. 7. demontrate a high coherence between all conidered parameter (U, C exp, C mod both at low frequencie and frequencie of the maximum of pectral denity. Thu, the modelled erie of the upended ediment concentration tatitically agree with experimental one ε (z ε (z ε (z ε(z ε(z, ε (z, ε (z E- E-.E- E-.E- ε (z Fig.. Vertical profile of the diffuion coefficient. experiment model Fig.. Supended ediment concentration at. cm from the bottom.

4 Ñ mod U Fig.. Chronogram of horizontal velocity (U, experimental (C exp and model (C mod concentration under wave group. Ñ exp

5 Ñ mod Fig.. Averaged vertical profile of the experimental (C exp and model (C mod upended ediment concentration under wave group. C, g/l Ñ exp Fig.. High-frequency fluctuation of vertical profile of model upended ediment concentration C, g/l Fig.. High-frequency fluctuation of vertical profile of the experimental upended ediment concentration. Spectral denity.... S u, m S ξ, m E-... Coherence S Cmod, (g/l S Cexp, (g/l... U-C mod U-C exp C mod -C exp... Fig. 7. Reult of the pectrum analyi (C exp experimental and C mod - model upended ediment concentration. IV. CONCLUSION A model ha been decribed for the calculation of the vertical ditribution of upended ediment concentration above a flat bottom under the influence of group of wave. It take into conideration the influence of group tructure of wave and phae of individual wave upon the ediment upenion. Thi i very important for modelling the fluctuation of upended ediment concentration. The model how very well all qualitative peculiaritie of ediment upenion under the given condition. Calculation of profile variability of the upended ediment concentration i neceary for etimation of ediment tranport in the coatal zone. The profile obtained from the model of

6 9- the concentration are upportive of the methodology uggeted. Real procee of ediment upenion are more complex than mechanim which are put into the model. It i expected that thi model for the upenion of bottom ediment will be improved with the involvement of additional procee and through further experimental and theoretical invetigation. REFERENCES [] S. M. Antyferov, T. M. Akivi, "Model of tranport of ediment upended by tidal current in the coatal zone", Oceanology,, v. 9,, pp. -. [] R. D. Ko yan, I. S. Podymov, N. V. Pykhov (Ed., Dynamical procee in the coatal zone. Mocow, Nauchnyi Mir,, p. [] E. L. Onichenko, R. D. Ko yan, "About the ue of optical method of determination of upended ediment concentration in natural reervoir", Water Reoure, 989, iue, pp. 9-. [] K. Black, C. E. Vincent, "High-reolution field meaurement and numerical modeling of intra-wave ediment upenion on plane bed under hoaling wave", Coatal Engineering,, vol., pp [] A. G. Davie, Z. Li, "Modeling ediment tranport beneath regular ymmetrical wave above a plane bed", Cont. Shelf. Re., 997, 7 (, pp. -8. [] J. Fredoe, O. H. Anderen, S. Silberg, "Ditribution of upended ediment in large wave", J. Waterway. Port, Coat. and Ocean Eng., 98, vol., pp. -9. [7] K. Hagatun, K. L. Eidvik, "Ocillating turbulent boundary layer with upended ediment", J. Geophy. Re., 988, vol. 9, pp. -. [8] J. G. Jonon, "On the exitence of univeral velocity ditribution in an ocillatory, turbulent boundary layer", Baic Re. Progre Rep., Coatal Eng. Lab. Tech., Univ. of Denmark, 9,. [9] R. Ko yan, "Vertical ditribution of upended ediment concentration eaward of the breaking zone", Coatal Engineering, 98, 9, pp [] R. Ko yan, H. Kunz, S. Kuznetov, N. Pykhov, "Supended ediment tranport in the urf zone of the Nordeney Iland. Hydrodynamic, Theory and Application", Proc. -nd Internal Conference on Hydrodynamic, Rotterdam, A.A.Balkema Publ. 99, pp. 9-. [] R. Ko yan, H. Kunz, S. Kuznetov, N. Pykhov, M. Krylenko, "Sand upenion and intermittence of turbulence in the urf zone" Proc. of the Int. Conference on Coatal Engineering, COASTAL ENGINEERING 9, American Society of Civil engineering. New York, 997, pp. -9. [] S. Kuznetov, N. Pykhov, "Spectral tet of energetic approach for upended and tranport in the urf zone", Proc. of International Conference Coatal Dynamic 97, ASCE, 997, pp. 7-. [] R. L. Soulby, "The Bailard ediment tranport formula: comparion with data and model", MAST 8-M Final Workhop. Gdank, 98, pp [] L. C. Van Rijn, "Principle of ediment tranport in river, etuarine and coatal ea", Aqua Publication, Netherland, 99, 8 p. [] C. Villaret, G. Perrier, "Tranport of fine and by combined wave and current: an experimental tudy", Electricite de France Report HE-/9.8, 99, 8 p. [] C. E. Vincent, M. O. Green, "Field meaurement of the upended and concentration profile, and of the reupenion coefficient over a rippled bed", Journal Geophyical Reearch, 99, 9, pp. 9-. [7] C. E. Vincent, D. Hane, "The accumulation and decay of near-bed upended and concentration due to wave and wave grope", Continental helf reearch, V.. [8] C. E Vincent., S. V. Marh, M. P. Webb, P. D. Oborne, "Spatial and temporal tructure of upenion and tranport over megaripple on the hore face", J. Geophyical Reearch, 999, V., pp. -. [9] T. Walton (editor, Coatal Engineering Manual, Part III, Coatal Sediment Procee, Chapter III-, Engineer Manual --,, U.S. Army Corp of Engineer, Wahington, DC. [] S. Zou, R. Dalrymple, F. Ace, B. Roger, "Smoothed particle hydrodynamic imulation on ediment upenion under breaking wave", Ocean wave meaurement and analyi, Fifth Inter. Sympoium Wave, Madrid, Spain,, paper number: 8. [] R. D. Ko'yan, M. V. Krylenko, C. E. Vincent, Fluctuation of intantaneou vertical ditribution of upended ediment in the urf zone, Proc. of the th International Conference on Coatal Engineering (ICCE, 7.