NUMERICAL SIMULATIONS OF WAVE PROPAGATION COMPARED TO PHYSICAL MODELING

Transcription

1 Numerical Si mulations ofw ave Pro pagation comp ared to Physical Modeling Hydralab 99 NUMERICAL SIMULATIONS OF WAVE PROPAGATION COMPARED TO PHYSICAL MODELING Authors: Stephan Mai Nino Ohle Karl-Friedrich Daemrich Table of Contents 1. Introduction. Physical Modeling 3. Numerical Modeling 4. Comparison of the Results 5. Conclusion and Discussion

2 Introd uction Introduction 1. Introduction Wave propagation within coastal zones is strongly influenced by coastal morphology Predominant processes in the coastal zone are: Investigations: Measurements of the wave propagation along a foreland with and without a submerged dike (summer dike) in the large wave tank of the FZK Numerical simulation of some of the above processes with standard wave models Test of the models by comparing the simulation results with the physical model - Adjustment of the parameters bottom friction and wave breaking Calculation of the transmission coefficients

3 Map and cross-section ofa summe rdike Map and cross-section of a summer dike. Physical Modeling Location and topographical map of a summer dike: Cross-section of a summer dike: seaward side landward side clay 50cm NN+1.7 m 1:7 berm 1:1 1:7 sand NN+3.5m clay 50cm 1:7 NN +1.7 m drainage system NN+0.0m

4 Summerdike i n nature and as model Summer dike in nature and as model Summer dike in nature Due to the grass sods and the flat slope the dike is difficult to be seen. Summer dike in model Concrete coverage replaces clay and grass sods Dipl.-Phys. S. Mai

5 Experi ment set-up an d measuremen ts in the large wave tank Experiment set-up and measurements in the large wave tank wave generator,0 mnn -R c B 3,5 mnn 0,5 mnn waddensea foreland summer dike polder 40 m 3m mnn= meter above German datum wave gauges: 4 1:7 1:7,0 mnn d [m] foreland / wadden sea foreland submerged dike polder x [m] significant wave height H s [m] x [m] 8 mean wave period T m [s] x [m]

6 Calculation ofthe t ransmission coefficient Calculation of the transmission coefficient c T,S [-] 0.8 summer dike Calculation of the transmission coefficient: c T HT = c T : transmission coefficient H H T : transmitted wave height H: incoming wave height transmission coefficient: c = (R /H ) + w T c s classification: w=0.58 (B/H ) (1- e -.59ξ) 0. S measurement: by d'angremond (modified): 0.3 < w < 0.9 w = 0.3 w = < w < 0.36 w = R c /H S [-] d Angremond (1996): 0,075< c T <0,80 - slopes: tanα >(1:4) c T RC = β + β H 1 S B H S β3 β4 ξ ( 1 e ) α ξ: Iribarren-Number, ξ = tan( ) H ( ) 05, L R C : freebord H S : significant wave height B: crest widht H/L: steepness β 1 =0,41 β =0,58 β 3 =0,48 β 4 =,59 Dipl.-Phys. S. Mai

7 Transmission coefficient (measured by diffe rent autho rs) Transmission coefficient (measured by different authors) Dipl.-Phys. S. Mai

8 Theor etical Backgro und of t he Nume rical P rogra ms Theoretical Background of the Numerical Programs 3. Numerical Modeling Standard Wave Models (used): HISWA HIndcast Shallow Water WAves, TU Delft SWAN Simulation WAves Nearshore, TU Delft MIKE 1 EMS Mike 1 Elliptic Mild Slope, Danish Hydraulic Institute Basic Model Equations: HISWA and SWAN Action Balance Equation Wave Breaking by Battjes and Jansen (1978) Bottom Friction by Collins (197) and Madsen (1988) MIKE 1 EMS Wave Breaking by Battjes and Jansen (1978) Bottom Friction by Dingemans (1983)

9 Dissipati on o f w av e e ne rgy due to w ave br ea king Dissipation of of Wave-Energy wave energy due to to wave Wave breaking Breaking Numerical formulation of wave breaking - Formula by Battjes and Jansen: D br α 1 Qbr Hrms γ γ 1 = Qbr f ρ g Hmax, =, Hmax = tanh k d 4 ln Qbr Hmax k γ1 D br : mean dissipation rate per area Q br :fractionofbreakingwaves ρ : water density H rms : root mean square H max : maximum wave height α, γ 1, γ : adjustable coefficients Dissipation of wave energy S ds, br due to wave breaking: E( xy,, θ) HISWA: Sds, br( x, y, θ) = Dbr E, where Etot( x, y) = E( x, y, θ) dθ tot( x, y) ( xy,, σθ, ) SWAN: S D E ds, br( x, y, σθ, ) = br E, where Etot( x, y) = E( x, y, σθ, ) dσθ d Dbr MIKE 1 EMS : ebr E. tot( x, y)

10 Dis s ipation of wave ene rgy due to b ottom f riction EXPERIMENTAL EXPERIMENTAL RESEARCH RESEARCH AND AND SYNERGY EFFECTS WITH WITH MATHEMATICAL MODELS MODELS Dissipation of Wave-Energy wave energy due to Bottom bottom friction Friction Dissipation of wave energy S ds, b due to bottom friction: σ 0 HISWA: S θ = C E g sinh ( k d ) ds, b( x, y, ) bot ( x, y, θ) 0 σ SWAN: S σθ = C E g sinh ( k d ) ds, b( x, y,, ) bot ( x, y, σθ, ) k 0.σ 0 : mean wave number and mean wave frequency C bot : friction coefficient. MIKE 1 EMS - Formula by Dingemans fe ω H rms D b = 16 π g sinh( k d), f and e D / E f b 3 e 04., ab / KN < = a b KN ) exp KN, a / b E = ρ g H rms / 8 : energy density of the wave field f e : energy loss factor. Bottom friction coefficient C bot : Collins: Cbot = Cfw g urms g Madsen: C = f u a b bot wr rms = 1 k d E and u 1, 4 f sinh ( ) ( x, y, σθ, ) wr rms = 1 + lg 4 f d σ d θ σ kd E sinh ( ) wr ( x, y, σθ, ) d σ d θ a b mf = + lg KN u rms : orbital velocity at the bottom K N : equivalent Nikuradse bottom roughness a b : representative near-bottom excursion amplitude C fw, f wr,m f : model parameter

11 Simulation ofthe significant wave heightby differentwave mode ls Simulation of the significant wave height by different wave models waterlevel z [m] boundary conditions: waterdepth: d = 4.0 m sig. wave height: Hs= 1.0 m peak period: Tp= 8.0 s foreland summerdike waterlevel polder 0 wave direction x [m]

12 Comparison ofthe results (transmission coefficients ) Simulation Comparison of the significant of the results wave (transmission height by different coefficients) wave models 4. Comparison of the Results Comparison of the transmission coefficients : Boundary conditions of the physical and numerical models No. of test cases : 4 (36) water level : z = 3.5 m up to 4.5 m incoming significant wave height : H = 0.6 m up to 1. m S incoming peak-period: T =3.5supto8.0s P

13 Conclusion and discussion -Calibration parameters Simulation Conclusion of the significant and discussion wave height - Calibration by different parameters wave models 5. Conclusion and Discussion Adjustment of the parameters bottom friction and wave breaking: DISSIPATION NUMERICAL MODEL PROCESS HISWA SWAN MIKE 1 EMS Wave breaking α =0.95 γ 1 =0.85 γ =0.95 α =1.45 γ =0.75 α =1.0 (not adjustable) γ 1 =1.05 γ =0.85 Bottom friction C fw =0.01 K N=0.0 K N =0.03 Summary: All Standard numerical wave models worked well. Still it is necessary to calibrate the models. This can be done with physical models or field data. Advantage of physical models are the well defined boundary conditions. Difficulties of field measurements are costs, extreme and unreliable boundary conditions.