Patile dynami la SMS 618 (Emmanuel Bo 11/19/003 Van Rijn TRANSPOR lab: omputation of ediment tanpot in uent and ave dietion Handout: Appendix A in van Rijn 1993 Piniple of ediment tanpot in ive etuaie and oatal ea Aqua Publiation Note: in ti ite-up log i log 10 ile ln i log e Input (ee Fig A1 in appendix fo dietion: -ate dept [m] v - dept-aveaged veloity in main uent dietion [m/] u - time-aveaged and dept-aveaged etun veloity belo ave toug ompenating te ma tanpot beteen ave et and toug [m/] u b - time-aveaged nea-bed veloity due to ave ind o lateal denity gadient [m/] H- ignifiant ave eigt (ignifiant ave eigt H i appoximately equal to te aveage of te iget one-tid of te ave H i alulated uing: H = 40 * qt(m 0 ee m 0 i te vaiane of te ave diplaement time eie aquied duing te ave aquiition peiod Vaiane an alo be alulated uing te nondietional ave petum aoding to te folloing elationip: m 0 = um(s(f*df ee te ummation of petal denity S(f i ove all fequeny band f of te nondietional ave petum and df i te bandidt of ea band Wave analyi ytem typially um ove te ange fom 003 to 040 Hz it fequeny bandidt of 001 Hz (ee ttp://ndbnoaagov/avealtml [m] Tp- Dominant o peak ave peiod (te peiod oeponding to te fequeny band it te maximum value of petal denity in te nondietional ave petum It i te eipoal of te peak fequeny fp: Tp = 1/fp Dominant peiod i epeentative of te ige ave enounteed duing te ave ampling peiod [] φ-angle beteen te dietion of ave popagation and main uent dietion [ ] d 50 - median diamete of bed mateial [m] d 90-90 t peentile diamete of bed mateial [m] d -epeentative diamete of upended mateial (ill be in te ange of (06 1 d 50 [m] k - uent-elated bed ougne eigt (minimum 001m (likely ange 001 1m [m] k - ave-elated bed ougne eigt (minimum 001m (likely ange 001 1m fo eet flo 001m [m] Te- tempeatue of fluid [ C] SA- alinity of fluid [ppt] Aumption: ρ =650kg/m 3 ediment denity κ=04 Von Kaman ontant Geneal paamete omputed: Cloinity: CL=(SA-003/1805 Fluid denity: ρ=1000+1455cl-00065(te-4+04cl [Kg/m 3 ] Kinemati vioity: ν=(4/(0+te10-5 [m /]
Sinking veloity: ( 1 gd 1< d < 100µ m 18ν 3 10ν 001( 1 gd 100 < d < 1000µ m 1+ 1 ; = ρ d ν 1000µ m< d 11 ( 1 gd ρ Sediment aateiti omputed: = ρ /ρ elative denity D * =d 50 [(-1g/ν ] 1/3 - Patile paamete 1 04D* 1< D* < 4 064 014D* 4< D* < 10 01 Sield paamete: θ 004D* 10 < D* < 0 09 0013D 0 < D * * < 150 0055 150 < D* =( ρ -ρgd 50 θ itial ea te u = 575 ( 1 gd θ log 4 d Citial dept-aveaged veloity U ( 50 90 ( 50 p ( 109( 1 gd 50 Tp /3 01( 1 g d T d < 00005m -- Citial peak obital veloity 50 0571 075 00005m< d50 Wave paamete omputed L Dopple ifted avelengt (ange in avelengt due to peene of mean flo: L' gl' π find L te olution of: vr oφ = tan T p π L' T p - Dopple ifted ave peiod: T p Tp ' = 1 o / L' ( vt R p φ Nea-bed peak obital exuion: A = in( π L' Nea-bed peak obital veloity: π H U = T' in π L' p H ( Wave-bounday laye tikne: = 007A ( A k 05
Nea-bed peak obital veloity in foad dietion: 3π H U + 4 001gTp < 4 Tp ' L' ( in( π L' U f H 1 03 U 001gTp > + Nea-bed peak obital veloity in bakad dietion: 3π H U 4 001gTp < 4 Tp ' L' ( in( π L' U b H 1 03 U 001gTp > 015 gh Retun veloity ma tanpot: u = ( 095 035H U f U b Nea bed ave indued mean veloity: u 005 05 b = U U f U + b Te lat to ae input paamete To ave tem omputed by te pogam inet 9 at te input line Bed paamete omputed: Appaent bed ougne: U ka 10k k exp γ < π ka ( v =08+ -03 R + u γ β β β = φ R 360 oteie 10k Effetive time-aveaged bed-ea tee omputed: log ( 13d90 Effiieny fato fo uent: µ log ( 1k exp 6 + 5 A 3d Effiieny fato fo ave: µ = exp 6 + 5 A k Wave-uent inteation oeffiient: α ( 90 ( 019 019 ( k o ( k ln 90 1+ ln 30 a = 1 ln ( 90 k 1+ ln( 30ka
1 04 Bed ea te due to uent: = ρ ( vr + ur 8 ( log ( 1k 1 exp 6 5 = ρ A k + U 8 Te total ea i te um of te ea: = + Bed ea te due to ave: ( 019 Effetive bed ea veloity uent: = ( u α µ ρ '* Bed ea te paamete omputation: ( α µ + µ Dimenionle bed-ea te fo bed load tanpot: T = Dimenionle bed-ea te fo efeene onentation at z=a: ( α µ + ( 06 / D* Ta = Bot ae zeo if negative Cuent veloity pofile omputation: ( urz vrz ( ur vr ln[ 30z ka] 1+ ln[ 30ka] ( ur vr ln90 [ ka] ln30 [ z k ] 1 ln30 [ k] ln90 [ k ] z 3 z < 3 + a Sediment eddy diffuion pofile omputation: Eddy diffuion due to mean uent: κβu* z( 1 z z < 05 ε ; 05κβu* z 05 ( ( u g u * β + v 1+ < 15 ee: β ; u* = 15 oteie 18log ( 4d90 Eddy diffuion due to ave: εbed = 0004D* U z < ε εmax = 0035 H Tp z 05 ; z εbed + ε max εbed 05 < z< 05 =03 H but =0m & =005m max min Combined uent and ave eddy diffuion: ε = [ ε + ε ] 05
Sediment volume onentation omputation: Refeene level: a=maximum(k k 15 d50 Ta Bed onentation (fo z a: Ca = 0015 03 a D* Fo z a te onentation gadient i give by: 5 ( 1 ( ( dc = dz ε 08 04 ( 1 + / 065 / 065 Obtain C by integation to te ufae fom a (ee onentation i knon to Time aveaged upended load tanpot omputation: ρ vr zcdz uent dietion a q ρ ave dietion ur zcdz a Time aveaged and intantaneou bed load tanpot ate omputation: vrln[ 30 ka] vr 1+ ln[ 30ka] Veloitie ae omputed at =max(3 k : = u Rln[ 30 v ka] ur v 1 + ln[ 30 ka] U = U o ϕ i te pae of te ave Intantaneou ave veloity: ( ϕ Intantaneou veloity along uent: U x U oφ vr ( ub ur Intantaneou veloity ao uent: U y = U inφ + ( ub + ur inφ Intantaneou veloity: U = U + U R x y Intantaneou fition oeffiient: α = v R = + + + oφ v R + U Intantaneou bed ea te: 1 ln( 30k + 04 019 ' 05 05 ( 1 exp 6 5 ( ( b = ρ α α A 3d + + U ln 30 k ( log ( 4d 90 90 R Intantaneou bed-load tanpot:
03 ' b ' b b ' b > b 05γρd50 D* H S qb ρ γ = max 031 b 0 oteie Time aveaged value ae obtained by aveaging ove a ave peiod (eg ove it pae ϕ Bed fom alulation: Ti i beyond te ope of ou la Cla aignment: Ho ave affet te total tanpot Ue te TRANSPOR model it te folloing input (maybe appopiate to te Dok in font of te Daling Maine ente: =1m d 50 =150µm d 90 =400µm d =08 d 50 Te=1 C SA=30pu u = 0 v = 05 m/ k = k = 00 Ho do you expet te tanpot to ange it ave paamete (H Tp and φ ompaed to aving no ave? Wite don you pedition Invetigate o te total tanpot vaie it ange in te ignifiant ave eigt (0 m ave peiod (1 8 and angle (0 90 beteen ave and uent Ho do te eult ompae it pedition? Ho do tey (qualitatively ompae it van-rijn alulation attaed to te andout? Fo one ae vay d fom 06d 50 to d 50 Ho ould you expet te total tanpot to ange? Ho mu ange do you obeve in te total tanpot?