确定性联合模拟的优化方法

本书在介绍波浪数学模型与物理模型确定性联合模拟方法的应用中，考虑到数学模型的准确性及计算的耗费，选取丹麦DHI开发的MIKE 21 BW数值模型（模型简介参见附录A及Madsen和Sørensen的文献[6]）用于远区的数值波浪计算。该模型属于Boussinesq方程模型。它是目前波浪数学模型中世界范围内应用最多、最广的商业模型之一。波浪数学模型及物理模型之间的数据传递是基于确定性联合模拟方法，将造波板处数学模型的包括时间、空间的详细波浪信息传递至物理模型。推板式造波机及其具有主动式吸收的控制系统提供了波浪数学模型及物理模型间的接口。该确定性联合模拟方法实现了单一方向的联合，即波浪从数学模拟区域传递至物理模型区域，没有考虑物理模型中被造波板吸收的反射波对数学模型的反馈。物理模型试验在丹麦DHI水力实验室的波浪水槽及波浪水池中完成。水槽及水池中的二维及三维推板式造波机分别由主动式吸收造波控制系统DHI AWACS以及DHI 3D AWACS[45-47]进行控制，在生成波浪的同时可以实现主动式波浪吸收。将全色散线性造波理论和一般的非线性浅水波造波方法相结合的特定统一造波理论为波浪数学模型和物理模型之间的连接提供了确定性的连接方式。

在波浪物理模型实验进行期间，DHI（3D）AWACS的造波机控制系统能够提供三种不同的控制方式。第一种为定位模式（position mode），其控制信号为造波板运动位移的时间序列。该模式与常用的非线性波造波方法兼容，但不包含主动式波浪吸收。第二种为单信号模式（single mode）。该模式是一种传统的主动式波浪吸收方法，其控制信号为入射行进波的波面高程时间序列，其缺点是不适用于非线性波浪的生成。第三种方式为双信号模式（dual mode）[47]。该模式同时适用于非线性波浪造波和主动式吸收。主动式吸收是通过在非线性波浪造波之上的线性扰动来实现的。双信号模式的控制信号有两个，一个是造波板运动位移的时间序列，另一个是对应的运动造波板处的波面高程时间序列。这两种控制信号可通过特定统一造波理论计算获得。

参考文献

[1]Oumeraci H.Strengths and limitations of physical Modelling in coastal Engineeringsynergy effect with numerical modelling and field measurement[C].Proceedings of HYDRALAB-workshop in Hannover.Germany:Forschungszentum Küste，1999.

[2]Boussinesq J.V.Theory of wave and swells propagated in long horizontal rectangular canal and imparting to the liquid contained in this canal[J].Journal de Mathematiques pures et appliquees，1872，17(2):55-108.

[3]Madsen P.A.，Schäffer H.A.A review of Boussinesq-type equations for surface gravity w aves.In:Philip L-F Lin(Ed.)，Advances in Coastal and Ocean Engineering，Vol.5[M].Singapore:World Scientific，1999.

[4]Madsen P.A.，Schäffer H.A.Higher-order Boussinesq-type equations for surface gravity waves:derivation and analysis[J].Philosophical Transactions:Mathematical，Physical and Engineering Sciences，1998，356(1749):3123-3184.

[5]Madsen P.A.，Murray R.，Sørensen O.R.A new form of the Boussinesq equations with improved linear dispersion characteristics[J].Coastal Engineering，1991，15(4):371-188.

[6]Madsen P.A.，Sørensen O.R.A new form of the Boussinesq equations with improved linear dispersion characteristics.Part 2.A slowly-varying bathymetry[J].Coastal Engineering，1992，18(3-4):183-204.

[7]Nwogu O.Alternative form of Boussinesq equations for nearshore wave propagation[J].Journal of Waterway Port Coastal&Ocean Engineering，1993，119(6):618-638.

[8]Schäffer H.A.，Madsen P.A.Further enhancements of Boussinesq-type equations[J].Coastal Engineering，1995，26(1-2):1-14.

[9]Madsen P.A.，Bingham H.B.，Liu H.A new Boussinesq method for fully nonlinear waves from shallow to deep water[J].Journal of Fluid Mechanics，2002，462:1-30.

[10]Dean R.，Dalrymple R.A.Water Wave Mechanics for Engineers and Scientists[M].Singapore:World Scientific，1984.

[11]Svendsen I.A.Physical modelling of water waves.In:Dolrymple R.A.(Ed.)，Physical Modelling in Coastal Engineering[M].Rotterdam:A.A.Balkema，1985:13-48.

[12]Hughes S.A.Physical Models and Laboratory Techniques in Coastal Engineering[M].Singapore:World Scientific，1993.

[13]Havelock T.H.Forced surface wave on water[J].Philosophical Magazine，1929，7(51):569-576.

[14]Biesel F.，Suquet F.Les Appareils Generateurs de houle en laboratoire[J].La houille blanche，1951，6:152-165.

[15]Biesel F.，Suquet F.Laboratory wave-generating apparatus[R].Minnesota:St.Anthony falls hydraulic laboratory，1954.

[16]Fontanet P.Theorie de la generation de la houle cylindrique par un batteur plan[J].La Huille Blanche，1961，16:3-31(part 1)，174-196(part 2).

[17]Madsen O.S.On the generation of long w aves[J].Journal of Geophysical Research，1971，76(36):8672-8673.

[18]Flick R.E.，Guza R.T.Paddle generated waves in laboratory channels[J].Journal of the Waterway Port Coastal&Ocean Division，1980，106(1):79-97.

[19]Hudspeth R.，Sulisz W.Stokes drift in two dimensional wave flumes[J].Journal of Fluid Mechanics，1991，230:209-139.

[20]Sulisz W.，Hudspeth R.Complete second-order solution for water waves generated in wave flumes[J].Journal of Fluids&Structures，1993，7(3):253-268.

[21]Moubaved W.I.，Williams A.N.Second-order bichromatic waves produced by a generic planar wavemaker in a two-dimensional wave flume[J].Journal of Fluids and Structures，1994，8(1):73-92.

[22]Schäffer H.A.Laboratory wave generation correct to second order[C].Wave kinematics and environmental forces.London，1993.

[23]Schäffer H.A.Second-order wavemaker theory for irregular wave[J].Ocean Engineering，1996，23(1):47-88.

[24]Hammack J.L.，Segur H.The Kd V equation and water waves.Part 2.Comparison with experiment[J].Journal of Fluid mechanics，1974，65(2):289-314.

[25]Goring D.G.Tsunamis-the propagation of long waves onto a shelf[D].California:W.M.Keck laboratory of hydraulics and water resources，1979.

[26]Goring D.G.，Raichlen F.The generation of long waves in the laboratory[C].Pro-ceedings of the 17th International Conference on Coastal Engineering，ASCE，Sydney，1980，1:763-783.

[27]Chappelear J.E.Direct numerical calculation of wave properties[J].Journal of Geophysical Research，1961，66:501-508.

[28]Dean R.G.Stream function representation of nonlinear ocean waves[J].Journal of Geophysical Research，1965，70(18):4561-4572.

[29]Chaplin J.R.Developments of stream function theory[J].Coastal Engineering，1980，3(3):179-206.(www.xing528.com)

[30]Rienecker M.M.，Fenton J.D.A Fourier approximation method for steady water waves[J].Journal of Fluid Mechanics，1981，104:109-137.

[31]Fenton J.D.The numerical solution of steady water wave problems[J].Computers and Geosciences，1988，14(3):357-368.

[32]Zhang H.，Schäffer H.A.Approximate stream function wavemaker theory for highly nonlinear waves in wave flumes[J].Ocean Engineering，2007，34(8-9):1290-1302.

[33]Madsen O.S.A three-dimensional wavemaker，its theory and application[J].Journal of Hydralulics Research，1974，12(2):205-222.

[34]Gilbert G.Generation of oblique waves[R].Technical Report 18，Hydraulic Research Station，Wallingford，England，1976.

[35]Takayama T.Theory of oblique waves generated by serpent-type wavemaker[J].Coastal Engineering in Japan，1984，27:1-19.

[36]Takayama T.，Hiraishi T.Fundamental characteristics of oblique regular waves and diretional random waves generated by a serpent-type wave generator[R].Report of Port and Harbor Research Institute，Japan，1987.

[37]Dalrymple R.A.，Greenberg M.Directional wave makers[M]//Dalrymple，R.A.Physical Modelling in Coastal Engineering.Rotterdam:A.A.Balkema，1985:67-81.

[38]Suh K.，Dalrymple R.Directional wavemaker theory:a special approach[C].Proceedings of 22th IAHR conference，Lausanne，Switzerland，1987:389-395.

[39]Steenberg C.M.，Schäffer H.A.Second-order wave generation in laboratory basins[C].Proceedings of the 27th International Conference on Coastal Engineering，Sydney，Australia，2000.

[40]Schäffer H.A.，Steenberg C.M.Second-order wavemaker theory for multidirectional waves[J].Ocean Engineering，2003，30(10):1203-1231.

[41]Milgram J.H.Active water wave absorbers[J].Journal of Fluid Mechenics，1970，42(4):845-859.

[42]Schäffer H.A.，Klopman G.Review of multidirectional active wave absorption methods[J].Journal of Waterway，Port，Coastal and Ocean Engineering，2000，126(2):88-97.

[43]Schäffer H.A.，Stolborg T.，Hyllested P.Simultaneous generation and active absorption of waves in flumes[C].Proceedings of waves-physical and numerical modelling.University of British Columbia，Vancouver，Canada，1994:90-99.

[44]Schäffer H.A.，Hyllested P.Reflection analysis using an active wave absorption con-trol system[C].Proceedings of the International Conference on Coastal Structures’99，Santander，Spain，1999.

[45]Schäffer H.A.Some design aspects of an absorbing 3D wavemaker[C].Proceedings of the 26th International Conference on Coastal Engineering，Copenhagen，Denmark，1998:1082-1095.

[46]Schäffer H.A.Active wave absorption in flumes and 3D basins[C].Proceedings of Waves 2001，San Francisco，USA，2001.

[47]Schäffer H.A.，Jakobsen K.P.Nonlinear wave generation and active absorption in wave flumes[C].Long Waves Symposium，In parallel withⅩⅩⅩIAHR Congress，Thessaloniki，Greece，2003.

[48]Kamphuis J.W.Composite modelling-an old tool in a new context[C].Proceedings of the 26th Congress of International Association of Hydraulic Research，London，1995，2:230-235.

[49]Kamphuis J.W.Physical modelling of coastal processes.In:Advances in Coastal and Ocean Engineering，Vol.2[M].Singapore:World Scientific，1996.

[50]Kamphuis J.W.Designing with Models[C].Proceedings of the 27th International Conference on Coastal Engineering.Sydney，Australia，2000:19-32.

[51]Watts S.Hybrid hydrodynamic modelling[J].Journal of Offshore Technology，1999，7(1):13-17.

[52]Schäffer H.A.On hybrid modeling in coastal and ocean engineering[C].Proceedings of Hydralab-workshop in Hannover，Germany，1999.

[53]Gierlevsen T.，Vargas B.M.，Pires V.P.L.et al.Numerical and physical modelling of storm waves at Rio de Janeiro yacht club[C].COPEDEC VI，Colombo，Sri Lanka，2003:15-19.

[54]Kofoed-Hansen H.，Sloth P.，Sørensen O.R.et al.Combined numerical and physical modelling of seiching in exposed new marina[C].Proceedings of the 27th International Conference on Coastal Engineering，Sydney，Australia，2000:3601-3614.

[55]Zhang H.，Schäffer H.A.Waves in numerical and physical wave flumes-a deterministic combination[C].Proceedings of the 29th International Conference on Coastal Engineering，Lisbon，Portugal，2004，1:43-55.

[56]Zhang H.，Schäffer H.A.Waves in numerical and physical wave basins-a deterministic combination[C].Proceedings of the 5th International Symposium on Ocean Wave Measurement and Analysis，Madrid，Spain，2005.

[57]Zhang H.，Schäffer H.A.，Jakobsen K.P.Deterministic combination of numerical and physical wave modes[J].Coastal Engineering，2007，54(2):171-186.

[58]Yang Z.，Liu S.，Bingham H.B.et al.Second-order theory for coupling 2D numerical and physical wave tanks:Derivation，evaluation and experimental validation[J].Coastal Engineering，2013，71:37-51.

[59]Yang Z.，Liu S.，Bingham H.B.，Li J.Second-order coupling of numerical and physical wave tanks for 2D irregular waves.Part I:Formulation，implementation and numerical properties[J].Coastal Engineering，2014，92(4):48-60.

[60]Yang Z.，Liu S.，Bingham H.B.，Li J.Second-order coupling of numerical and physical wave tanks for 2D irregular waves.Part II:Experimental validation in twodimensions[J].Coastal Engineering，2014，92(4):61-74.