CUADRO DE CONTINGENCIA N°
D. Dimensión: Decir no y cortar interacciones CUADRO N°
Figu re A 31: Peak valu e analysis for m easu rem ents, m od el settings L1 (k=0.1m ) and m od el settings L2 (k=0.05m ).
Table A 7: L2- m od el stage 1 calibration resu lts.
Measurement location RMSE calibration RMSE validation
WL-Cromer 0.48 m 0.01 m WL-Low erstoft 0.25 m 0.04 m VEL-Zeepipe 8 U-com p V-com p 0.054 m / s 0.18 m / s 0.03 m / s 0.04 m / s VEL-Zeepipe 9 U-com p V-com p 0.056 m / s 0.12 m / s 0.02 m / s 0.05 m / s
VEL-Sandw ave area U-com p V-com p - - 0.0153 m / s 0.0195 m / s S tag e I: V al i d ati o n
The valid ation of the L2-m od el is p erform ed by com p aring the new L2-m od el to the existing L1-m od el on corresp ond ing locations. Becau se the L2-m od el is valid ated based the L1-m od el resu lts, this is m erely a check w hether the m od el d oes not show anom alou s valu es. The locations are the sam e as the calibration locations, ad d ed w ith a site w ithin the area KP 183-191. These locations are show n in Table A 6 and Figu re A 30.
Looking at the RMSE valu es in Table A 7 the m od el show s no u nexp ected behaviou r , regard ing d ifferences u p to 0.04 m / s m axim u m . These d ifferences are to be exp ected as the rou ghness valu e is changed . Still the m od elled valu es for the L2-m od el are close to the valu e of the existing L1-m od el. Therefore no bou nd ary effects d u e to the nesting m ethod are visible influ encing the velocity in the sand w ave area (KP 183-191).
S tag e II: Cal i b rati o n
The calibration in stage 2 (d om ain d ecom p osition) is p erform ed by looking at the resu lts of the sensitivity analysis and com p are them to the L2-m od el level 0 (2DH ), the m od el w hich is valid ated by m easu rem ents in stage 1. Moreover, it is looked into w hat p aram eters seem realistic for the id ealized w ind scenarios. The m od el settings as ch osen are given in Table A 8, follow ed by a m otivation.
Table A 8: Chosen valu es d u ring calibration .
Parameter Unit L2-model
level 0 L2-model level 1 L2-model level 2 L2-model level 3 Horizontal viscosity (m2/ s) 1 1 1 1
Grid cell size - (m ) 1000 300 100 30
Vertical viscosity (m2/ s) (-) 0.05
The horizontal viscosity is p u t on one. The influ ence w as noticeable in the sensitivity analysis w hen taking a really high valu e. H ow ever, for each valu e no strange circu lations seem to occu r. Therefore the d efau lt valu e in Delft 3D-FLOW of 1 m2
/ s is ap p lied .
The grid cells increase from 1000 to 30 m eter. It is investigated if taking a larger m od el d om ain for the 100 x 100 m eter and 30 x 30 m eter cell d om ain changes the resu lts for the tid e averaged cu rrent, since the cell size tu rned ou t to be sensible. This is not the case.
For the vertical viscosity both the m od el and constant valu e of 0.05 m2
/ s are ap p lied . For L2-m od el level 1 a constant valu e of 0.05 m2
/ s is ap p lied , since this m od el w ith only three layers is sensitive for high elevation ch anges for the bottom layer of the m od el in com bination w ith the m od e. This cau ses a resid u al cu rrent w hich is overestim ated in the sou thern p art of the m od el com p ared to the L2-m od el level 0 (com p are box ‘A’ in Figu re A 28 w ith box ‘B’ in Figu re A 29). The valu e 0.05 is ch osen since valu es close to 0.05 are m ore often u sed (Cam p m ans et al., 2017), and the resu lts corresp ond w ell w ith the L2-m od el level 0. The L2- m od el level 2 and 3 u se the m od el to sim u late the w ind correct in the fine d om ain.
S tag e II: V al i d ati o n
The valid ation is p erform ed for the p aram eters settings as d efined in the calibration, and cond u cted by looking at the p hysical p rocesses that m ay p lay a role for the m igrat ion of the sand w aves. The best valid ation p ossible for the m od el is the bathym etric d ata (sand w ave m igration). H ow ever, as the m od el has the p u rp ose to check w hether it su p p orts these m igration p atterns, this w ou ld lead to a m od el being valid ated based on inform ation it has to actu ally valid ate itself. Looking at resid u al cu rrents in Figu re A 32, the follow ing notifications are m ad e.
The sand banks in the area show a large influ ence on the resid u al cu rrents. Zoom ing in on the Winterton Rid ge, it is obviou s that on the left sid e of this sand bank the resid u al cu rrents show a northw ard s d irection, and on the right sid e a sou thw ard s d irection. This is in accord ance to w hat Caston (1971) and Robinson (1983) state abou t the resid u al cu rrent near sand banks, being a consequ ence of tid al cu rrents tend ing to bend over the sand banks in a d irection d ep end ing on the flow angle w ith resp ect to the sand banks orientation. Literatu re exp lains this as a consequ ence of vorticity Robinson (1981), also visible for w aves ap p roaching the coast.
The sand bank on the right in Figu re A 32, the Sm iths Knoll, m igrates in a relative high rate to the east (Witteveen+Bos, 2016b). Looking at the asym m etrical shap e, and the tid e resid u al cu rrent to the right, this ind eed m akes sense. The sam e can be seen for the H earty Kn oll.
The resid u al cu rrent on the east sid e of the Sm iths Knoll is d irected northw ard s, agreeing to the fou nd d irection by Sü nd erm ann & Pohlm ann (2011) for this p art of the N orth Sea.
Visible are the tid e resid u al cu rrents d irected to the top of the sand w aves for the L2-m od el level 3 (convergence). The cu rrents are higher at the slop e of the sand w ave than at the crest (box ‘B’ in Figure A 33). Due to the tid e resid u al d irection the m agnitud e is not equ al on both sid es, bu t it d oes ind icate the tid e resid u al cir cu lation near sand w aves (H u lscher, 1996).
Figu re A 32: Dep th average resid u al M2-tid al resid u al cu rrents for p aram eters d efined in calibration.
Figu re A 33: L2-m od el level 3 M2-tid e resid u al cu rrent at the bottom layer (tw o p ercent from the bottom of the w ater colu m n). Location is ind icated in Figu re A 32 by a black box. Box ‘B’ show s resid u al cu rrents going u p - slop e on both sid es of the sand w ave.
Smiths Knoll Winterton Ridge
Hearty Knoll
Li n e ar w av e th e o ry
In ord er to estim ate the influ ence of w aves on the sed im ent transp ort, linear w ave theorem is ap p lied (Borsje, 2015). The extra am p litu d e is cu m u lative to the tid al am p litu d e, and m ay give rise to su sp end ed sed im ent in the low er layers of the w ater colu m n. Linear w ave theory a ssu m es no non - linear effects. Using linear w ave theory, the velocity am p litu d e d u e to w aves can be estim ates over a w ater colu m n, given a w ave height and p eriod . N ote here that an interm ed iate w ater d ep th ap p roxim ation is u sed , as a first estim ation of the w ave length is 80 m eter (TP = 7 sec) u sing both shallow and d eep w ater ap p roxim ations. This gives a valu e of 40 m eter for 0.5xL, being ju st larger than the local w ater d ep th (Borsje, 2015). The basic equ ations u sed are given in eqn. A.16 and eqn. A.17.
eqn. A.16 eqn. A.17
As the interest is in the m axim u m am p litu d e, the tim e d ep end ency and location can be neglected . Therefore the eqns. A.16 and A.17. sim p lify to eqns. A.18 and A.19.
eqn. A.18 eqn. A.19
This set of equ ations can be ap p lied w hen know ing the local w ater d ep th, p eak p eriod and w ave height. H ow ever, the w ave p eriod shou ld be transform ed to w ave length to fill in the equ ation. To d o so the follow ing eqn. A.20. resu lting from linear w ave theory is ap p lied .
eqn. A.20
Using the ratio L0/ h, the valu e for tanh(hk) can be retrieved and next the w ave length L (eqn. A.21).
eqn. A.21
For the estim ation m ad e, there are variou s assu m p tion necessary to sim p lify the case:
The w aves ap p roach d u ring the st orm in only one d irection
Only the significant p eak p eriod and w ave height are taken into accou nt.
The local velocity d ep end s on the local d ep th, interactions/ d eform ations d u e to bathym etrical changes and w ave-cu rrent interaction are therefore not accou nt for.