Mathematical modeling of dynamical processes in the sea—land area

Authors: 
V.A. Ivanov, V.V. Fomin
Year: 
2010
Pages: 
286
ISBN: 
978-966-360-158-8
Publication Language: 
English
Publisher: 
PH "Akademperiodyka"
Place Published: 
Kyiv
The dynamics of nearshore wave—current interactions is investigated. A cou­pling model for the description of nearshore currents, storm surges, surface waves, and morphodynamic processes is developed. Economical schemes of time integration and TVD-approximation of advective currents allowing the description of the fields with high spatial gradients are used. The developed model is used to provide the hydrometeorological design of hydrotechnical constructions in the Black and Azov Sea nearshore area.
The monograph is intended for administrative institutions, research and design institutes, and natural departments of the universities.
References: 

1. V.G. Alaev, Yu.N. Ryabtsev, and N.B. Shapiro, "Adaptation calculation of the current velocity on the shelf with the help of a quasiisopycnic model," Morsk. Gidrofiz. Zh., No. 4, 64-79 (1999).

2. D.V. Alekseev, V.A. Ivanov, E.V. Ivancha, et al., "Mathematical modeling of the dynamic processes, spreading of surface emissions of contaminants, and stirring-up of bottom sediments on the northwest shelf of the Black Sea at the passage of a cyclone," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 13, Sevastopol (2005), pp. 259-273.

3. D.V. Alekseev, E.V. Ivancha, V.A. Ivanov, et al., "Modeling of the evolution of wave fields in the region of the northwest shelf of the Black Sea at the passage of a cyclone," Morsk. Gidrofiz. Zh., No. 1, 42-54 (2005). https://doi.org/10.1007/s11110-005-0028-z

4. D.V. Alekseev, V.A. Ivanov, E.V. Ivancha, et al., "A study of the transformation of local domains of contamination in the northwest region of the Black Sea at the motion of a cyclone," Morsk. Gidrofiz. Zh., No. 6, 17-27 (2005). https://doi.org/10.1007/s11110-006-0007-z

5. D.V. Alekseev, V.A. Ivanov, E.V. Ivancha, et al., "A study of the evolution of the three-dimensional structure of an impurity field on the northwest shelf of the Black Sea at the passage of a cyclone," Meteorol. Gidrol., No. 1, 86-94 (2006).

6. D.V. Alekseev, V.A. Ivanov, E.V. Ivancha, et al., "Spreading and transformation of local fields of contaminations in the coastal area of the Odessa-Dnieper region of the Black Sea at the passage of a cyclone," Dopov. Nats. Akad. Nauk Ukrainy, No. 6, 105-110 (2006).

7. D.V. Alekseev, E.V. Ivancha, and V.V. Fomin, "Mathematical modeling of the stirring-up of bottom sediments on the northwest shelf o the Black Sea at the passage of a cyclone," Dopov. Nats. Akad. Nauk Ukrainy, No. 3, 104-110 (2006).

 8. É.N. Al'tman, Water Dynamics of the Kerch Strait and Water Exchange between the Black and Azov Seas under Conditions of Controlled Discharge of Rivers of the Basin [in Russian], Candidate-Degree Thesis Geographic Sciences), Sevastopol Branch of the State Oceanographic Institute, Sevastopol (1980).

9. A.I. Androsovich, É.N. Mikhailova, and N.B. Shapiro, "Numerical model and calculations of water circulation in the northwest part of the Black Sea," Morsk. Gidrofiz. Zh., No. 5, 28-42 (1994). https://doi.org/10.1007/BF02197483

10. A.I. Androsovich, V.A. Ivanov, É.N. Mikhailova, and N.B. Shapiro, "Modeling of wind currents in Lake Donuzlav," Morsk. Gidrofiz. Zh., No. 2, 15-26 (1996). https://doi.org/10.1007/BF02523060

11. S.M. Antsyferov and R.D. Kos'yan, Suspended Sediments in the Upper Part of the Shelf [in Russian], Nauka, Moscow (1986).

 12. V.P. Belov, "Conditions of wind and wind sea on the Sea of Azov," in: Transactions of the GOIN [in Russian], Issue 134 (1978), pp. 48-56.

13. V.P. Belov and Yu.G. Filippov, "Basic features of water dynamics in the Sea of Azov and Kerch Strait," in: Transactions of the GOIN [in Russian], Issue 139 (1978), pp. 11-20.

14. V.P. Belov and Yu.G. Filippov, "Dynamics and vertical structure of the currents of the Sea of Azov," in: Transactions of the GOIN [in Russian], Issue 159 (1980), pp. 127-134.

15. A.S. Blatov and V.A. Ivanov, Hydrology and Hydrodynamics of the Black Sea Shelf Area [in Russian], Naukova Dumka, Kiev (1992).

16. V.S. Bol'shakov, Transformation of River Waters in the Black Sea [in Russian], Naukova Dumka, Kiev (1970).

17. I.A. Brovchenko and V.S. Maderich, "A two-dimensional Lagrangian model of the transfer of multifractional sediments in the coastal area of the sea," Prikl. Gidromekh., 8, No. 2, 9-1 (2006).

18. Hydrometeorology and Hydrochemistry of the Seas of the USSR [in Russian], Vol. 4: Black Sea, Issue 1: Hydrometeorological Conditions, Gidro meteoizdat, St. Petersburg (1991).

19. Hydrometeorological Conditions of the Shelf Area of the Seas of the USSR [in Russian], Vol. III: Sea of Azov, Gidrometeoizdat, Leningrad (1986).

20. S.K. Godunov, "A difference method of the numerical calculation of discontinuous solutions of hydrodynamic equations," Mat. Sb., 47, No. 3, 271-306 (1959).

21. R.G. Grigorkina and V. R. Fuks, Action of Typhoons on the Ocean [in Russian], Gidrometeoizdat, Leningrad (1986).

22. G.A. Grishin, T.M. Bayankina, E.I. Kalinin, and M.M. Lundberg, "On the evolution of south cyclones coming to the Black Sea and territory of Ukraine by the data of satellite and groundbased observations," Issled. Zemli Kosm., No. 3, 89-95 (1991).

23. R.D. Kos'yan, I.S. Podymov, and N.V. Pykhov (editors), Dynamic Processes of the Coastal Area of the Sea [in Russian], Nauchnyi Mir, Moscow (2003).

24. N.N. D'yakov and V.V. Fomin, "Synoptic conditions of the onset of anomalous oscillations of the level in the Sea of Azov," in: Scientific Transactions of the Ukrainian Research Hydrometeorological Institute, Issue 250 (2003), pp. 332-341.

25. V.N. Eremeev, A.V. -4,939Konovalov, Yu.V. Manilyuk, and L.V. Cherkesov, "Modeling of longwaves in the Sea of Azov, induced by the passage of cyclones," Okeanologiya, 40, No. 5, 658- 665 (2000).

26. V.V. Efimov, V.G. Polnikov, and E.N. Sychev, A Spectral Model of the Evolution of Wind Sea and Numerical Experiments Based on It [in Russian], Preprint of the Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol (1986).

27. V.V. Efimov, O.I. Komarovskaya, and M.V. Shokurov, A Numerical Model of Wind Sea in the Black Sea [in Russian], Preprint of the Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol (1998).

 28. V.P. Zenkovich, Dynamics and Morphology of Sea Coasts. Wave Processes [in Russian], Morskoi Transport, Moscow (1946).

29. V.A. Ivanov, Problems and Prospects of the Evaluations of Action on the Environment at the Shelf Development [in Russian], KOSI-Gidrofizika, Sevastopol (2004).

30. V.A. Ivanov, A.N. Ivanova, and Yu.N. Ryabtsev, "Evaluation of the state of the Black Sea ecosystem in the regions of oil and gas production," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 13, Sevastopol (2005), pp. 117-125.

 31. V.A. Ivanov, L.L. Koveshnikov, and A.E. Mikhinov, Anthropogenic Action on the Dynamics of Sediments in the Sea Coastal Area [in Russian], Preprint of the Marine Hydrophysical Institute Ukrainian National Academy of Sciences, Sevastopol (1993).

 32. V.A. Ivanov, A.V. Konovalov, Yu.V. Manilyuk, and L.V. Cherkesov, "Mathematical modeling of surge oscillations in the Black Sea," Meteorol. Gidrol., No. 1, 56-63 (1999).

33. V.A. Ivanov, A.V. Konovalov, and L.V. Cherkesov, "Effect of cyclones on changes in the level тsurface of the Azov and Black Seas," Meteorol. Gidrol., No. 4, 73-80 (2003).

34. V.A. Ivanov, A.I. Kubryakov, and É. N. Mikhailova, "Modeling of the desalinating effect of river discharge during spring overflow on the northwest shelf of the Black Sea," Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana, No. 1, 152-160 (1996).

35. V.A. Ivanov and A.E. Mikhinov, Prediction of the Dynamics of Sediments in the Coastal Area of the Sea (Practical Recommendations and Examples of Calculations) [in Russian], Preprint of the Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol (1991).

36. V.A. Ivanov and N.B. Shapiro, "Modeling of the currents in the Kerch Strait," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 10, Sevastopol (2004), pp. 207-232.

37. S.A. Kitaigorodskii, Physics of Interaction between the Atmosphere and the Ocean [in Russian], тGidrometeoizdat, Leningrad (1970).

38. N.P. Kovrigina and M.S. Nemirovskii, "Hydrochemical characteristic of the waters of Lake Donuzlav by the data of 1990-1997," in: Ecology of the Sea [in Russian], Issue 48 (1999), pp. 10-14.

39. A.V. Konovalov, Yu.V. Manilyuk, and L.V. Cherkesov, "Influence of the Sea of Azov and Kerch Strait on surge oscillations in the Black Sea," Morsk. Gidrofiz. Zh., No. 5, 5-14 (2000).

40. E.B. Kraus, Atmosphere-Ocean Interaction, Clarendon, Oxford (1972).

41. L.A. Krukier, "Mathematical modeling of the hydrodynamics of the Sea of Azov in the realization of projects of the reconstruction of its ecosystem," Mat. Modeling, 3, 3-20 (1991).

42. A.S. Kukushkin, E.A. Agafonov, Z.P. Burlakova, and L.V. Eremeeva, "Variability of the transmittance and content of suspended substance in the surface layer of the northwest part of the Black Sea," Okeanologiya, 44, No. 6, 870-881 (2004).

43. A. G.Kulikovskii, N.V. Pogorelov, and A.Yu. Semenov, Mathematical Problems of the Numerical Solution of Hyperbolic Systems of Equations [in Russian], Fizmatlit, Moscow (2001). https://doi.org/10.1201/9781482273991

44. I.V. Lavrenov, Mathematical Modeling of Wind Sea in Spatially-Inhomogeneous Ocean [in Russian], Gidrometeoizdat, St. Petersburg (1998).

45. P.H. LeBlond and L.A. Mysak, Waves in the Ocean [Russian translation], Vol. 1, Mir, Mosco (1980).

46. P.H. LeBlond and L.A. Mysak, Waves in the Ocean [Russian translation], Vol. 2, Mir, Moscow (1980).

47. I.O. Leont'ev, "On the compensation of wave upward surge in the coastal area of the sea," Okeanologiya, 14, No. 4, 630-635 (1974).

48. I.O. Leont'ev, Dynamics of the Surf Area [in Russian], Izd. Inst. Okeanol. Akad. Nauk, Moscow (1989).

 49. V.V. Longinov, Dynamics of the Coastal Area of Tideless Seas [in Russian], Izd. Akad. Nauk SSSR, Moscow (1963).

 50. G.I. Marchuk, Numerical Solution of the Problems of Dynamics of the Atmosphere and the Ocean [in Russian], Gidrometeoizdat, Leningrad (1974).

51. G.I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1980).

52. É. N. Mikhailova and N.B. Shapiro, "Modeling of the spreading and transformation of river waters on the northwest shelf and in the deep-water part of the Black Sea," Morsk. Gidrofiz. Zh., No. 3, 30-40 (1996).

53. M.S. Nemirovskii and N.P. Kovrigina, "Dynamics of the waters of Lake Donuzlav," in: Ecology of the Sea [in Russian], Issue 51 (2000), pp. 10-13.

 54. V.I. Nikishov, "From the hydraulics of open flows to the hydromechanics of river systems," Prikl. Gidromekh., 8, No. 2-3, 103-121 (2007).

55. S.N. Ovsienko, "Calculation of surge oscillations of the Sea of Azov," in: Transactions of the Hydrometeorological Center of the USSR [in Russian], Issue 126 (1972), pp. 55-58.

56. S.N. Ovsienko, "Calculation of catastrophic upward surge near the southeast coast of the Sea of Azov," in: Transactions of the Hydrometeorological Center of the USSR [in Russian], Issue 127 (1973), pp. 33-37.

57. Instructions on Calculations of the Parameters of Wind Sea [in Russian], Gidrometeoizdat, Leningrad (1969).

58. Yu.N. Ryabtsev and N.B. Shapiro, "Modeling of the seasonal variability of the Black Sea," Morsk. Gidrofiz. Zh., No. 1, 12-24 (1997).

59. A.A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1983).

60. V.G. Simov, Hydrology of the River Mouths of the Sea of Azov [in Russian], Gidrometeoizdat, Moscow (1989).

61. A.I. Sorkina (editor), Handbook on the Climate of the Black Sea [in Russian], Gidrometeoizdat, Moscow (1974).

62. I.N. Davidan (editor), Theoretical Foundations and Methods of Calculation of Wind Sea [in Russian], Gidrometeoizdat, Leningrad (1988).

63. Yu.S. Tuchkovenko, "A numerical mathematical model of water circulation in the Kerch Strait," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 6, Sevastopol (2002), pp. 223-232.

64. O.M. Phillips, The Dynamics of the Upper Ocean [Russian translation], Gidrometeoizdat, Leningrad (1980).

65. V.V. Fomin, "A numerical model of water circulation in the Sea of Azov," in: Scientific Transactions of the Ukrainian Research Hydrometeorological Institute [in Russian], Issue 249 (2002), pp. 246-255.

66. V.V. Fomin and N.N. D'yakov, "Wind sea and sediment transport in the Sea of Azov," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 8, Sevastopol (2003), pp. 175-181.

67. V.V. Fomin, N.N. D'yakov, and S.B. Gorbach, Hydrological Conditions of the Sea of Azov, Final Report on the Scientific-and-Research Work "Investigations of the Present-Day Hydrometeorological Conditions of the Black and Azov Seas and Perfection of the System of Marine Observations and Prediction" [in Russian], Marine Department of the Ukrainian Research Hydrometeorological Institute, Sevastopol (2005).

 68. V.V. Fomin and V.A. Ivanov, "Numerical modeling of wind sea in the region of the Spit Tuzla Island," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 10, Sevastopol (2004), pp. 233-242.

 69. V.V. Fomin and V.A. Ivanov, "Modeling of wind currents and sediment transfer in the coastal area of Evpatoria," in: Ecological Safety of the Coastal and Shelf Areas and Complex Use of the Shelf Resources [in Russian], Issue 13, Sevastopol (2005), pp. 211-226.

70. V.V. Fomin and V.A. Ivanov, "A united numerical model of currents, heaving, and sediment transfer in Lake Donuzlav," Morsk. Gidrofiz. Zh., No. 2, 1-23 (2006). https://doi.org/10.1007/s11110-006-0019-8

71. V. V. Fomin and T. Ya. Shul'ga, "A study of waves and currents formed under the action of wind in the Sea of Azov," Dopov. Nats. Akad. Nauk Ukrainy, No. 12, 110-115 (2006).

72. V.V. Fomin and L.V. Cherkesov, "Modeling of drift currents in a shallow-water basin with regard for changes in the tangential stresses, induced by wind sea," Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana, 42, No. 3, 362-370 (2006). https://doi.org/10.1134/S0001433806030091

73. L.V. Cherkesov, V.A. Ivanov, and S.M. Khartiev, Introduction to the Hydrodynamics and Theory of Waves [in Russian], Gidrometeoizdat, St. Petersburg (1992).

74. A. P. Chernyakova, "Typical wind fields of the Black Sea," in: Transactions of the BGMO ChAM [in Russian], Issue 3 (1965), pp. 79-121.

75. A.L. Chikin, "A three-dimensional problem of calculating the hydrodynamics of the Sea of Azov," Mat. Modeling, 13, No. 2, 87-92 (2001).

76. N.B. Shapiro, "Formation of circulation in the quasiisopycnic model of the Black Sea with regard for the stochastic character of wind stresses," Morsk. Gidrofiz. Zh., No. 6, 26-40 (1998).

77. G.I. Shapiro, T.M. Akivis, N.V. Pykhov, and S.M. Antsyferov, "Transfer of fine-dispersed sediment material by mesoscale currents in the shelf-slope area of the sea," Okeanologiya, 40, No. 3, 333-339 (2000).

78. F. Anctil and M.A. Donelan, "Air-water momentum flux observations over shoaling waves," J. Phys. Oceanogr., 26, 1344-1353 (1996). https://doi.org/10.1175/1520-0485(1996)026<1344:AMFOOS>2.0.CO;2

79. D.G. Andrews and M.E. McIntyre, "An exact theory of nonlinear waves on a Lagrange-mean flow," J. Fluid Mech., 89, 609-646 (1978). https://doi.org/10.1017/S0022112078002773

80. D.G. Andrews and M.E. McIntyre, "On wave action and its relatives," J. Fluid Mech., 89, 647-664 (1978). https://doi.org/10.1017/S0022112078002785

81. F. Ardhuin, N. Rascle, and K. Belibassakis, Explicit Wave-Averaged Primitive Equations Using a Generalized Lagrangian Mean, Preprint, Elsevier (2007). https://doi.org/10.1016/j.ocemod.2007.07.001

82. A.F. Blumberg, A Primer for ECOMSED, Version 1.3, HydroQual, Inc., Mahwah, NJ (2002).

83. A.F. Blumberg and L.H. Kantha, "Open boundary condition for circulation models," J. Hydraulic Eng., 111, 273-285 (1985). https://doi.org/10.1061/(ASCE)0733-9429(1985)111:2(237)

84. A.F. Blumberg and G.L. Mellor, "A description of three dimensional coastal ocean circulation model," in: Three-Dimensional Coast Ocean Models, Vol. 4 (1987), pp. 1-16. https://doi.org/10.1029/CO004p0001

 85. J.P. Boris and D.L. Book, "Flux corrected transport. I: SHASTA a fluid transport algorithm that works," J. Comput. Phys., 11, 38-69 (1976). https://doi.org/10.1016/0021-9991(73)90147-2

 86. H. Burchard, Applied Turbulence Modeling in Marine Waters, Lecture Notes in Earth Sciences, Vol. 100, Springer, Berlin (2002).

87. H. Burchard and H. Baumert, "The formation of estuarine turbidity maxima due to density effects in the salt wedge. A hydrodynamic process study," J. Phys. Oceanogr., 28, 309-321(1998). https://doi.org/10.1175/1520-0485(1998)028<0309:TFOETM>2.0.CO;2

88. H. Burchard, K. Bolding, and M.R. Villareal, "Three-dimensional modeling of estuarine turbidity maxima in a tidal estuary," Ocean Dynamics, 54, No. 2, 250-265 (2004). https://doi.org/10.1007/s10236-003-0073-4

89. S.Y. Chao, "River-forced estuarine plumes," J. Phys. Oceanogr., 18, 72-88 (1988). https://doi.org/10.1175/1520-0485(1988)018<0072:RFEP>2.0.CO;2

90. H. Charnock, "Wind stress on a water surface," Quart. J. Roy. Meteorol. Soc., 81, 639-640 (1955). https://doi.org/10.1002/qj.49708135027

91. B.Q. Chen, J.T. Kirby, and R.A. Dalymple, "Boussinesq modeling of wave transformation, breaking and run-up," J. Waterway, Port, Coastal Ocean Eng., 126, No. 1, 48-56 (2000). https://doi.org/10.1061/(ASCE)0733-950X(2000)126:1(48)

92. Y.S. Cho and P.L. Liu, "Crest length effect in nearshore tsunami run-up around island," J. Geophys. Res., 104, 7907-7913 (1999).

93. P.C. Chu and C. Fan, "Sixth-order difference scheme for sigma coordinate ocean models," J. Phys. Oceanogr., 27, No. 9, 2064-2071 (1997). https://doi.org/10.1175/1520-0485(1997)027<2064:SODSFS>2.0.CO;2

94. M. Cobb and C.A. Blain, "A coupled hydrodynamic-wave model for simulating wave and tidally- driven 2D circulation in inlets," in: M. Spaulding (editor), Estuarine and Coastal Modeling: Proceedings of the 7th International Conference, ASCE, Reston, VA (2002), pp. 725-744. https://doi.org/10.1061/40628(268)47

95. Ph. Colella and P.R. Woodward, "The piecewise parabolic method (PPM) for gasdynamical simulations," J. Comput. Phys., 54, No. 1, 174-201 (1984). https://doi.org/10.1016/0021-9991(84)90143-8

96. P.D. Craig and M.L. Banner, "Modeling wave-enhanced turbulence in the ocean surface layer," J. Phys. Oceanogr., 24, 2546-2559 (1994). https://doi.org/10.1175/1520-0485(1994)024<2546:MWETIT>2.0.CO;2

97. A. Craik and S. Leibovich, "A rational model for Langmuir circulations," J. Fluid Mech., 73, 401-426 (1976). https://doi.org/10.1017/S0022112076001420

98. Delft3D-MOR User Manual, WL Delft Hydraulics, Netherlands (2003).

99. H.J. De Vriend and M.J.F. Stive, "Quasi 3-D modelling of nearshore currents," Coastal Eng., 11, 565-601 (1987). https://doi.org/10.1016/0378-3839(87)90027-5

 100. L.F. Dolata and W. Rosental, "Wave setup and wave-induced currents in coastal areas," J. Geophys. Res., 89, 1973-1982 (1984). https://doi.org/10.1029/JC089iC02p01973

101. M.A. Donelan, F.W. Dobson, S.D. Smith, and R.J. Anderson, "On the dependence of sea surface roughness on wave development," J. Phys. Oceanogr., 23, 2143-2149 (1993). https://doi.org/10.1175/1520-0485(1993)023<2143:OTDOSS>2.0.CO;2

102. M.A. Donelan, W.M. Drennan, and K.B. Katsaros, "The air-sea momentum flux in conditions of wind sea and swell," J. Phys. Oceanogr., 27, 2087-2099 (1997). https://doi.org/10.1175/1520-0485(1997)027<2087:TASMFI>2.0.CO;2

103. W.M. Drennan, H.C. Graber, and M.A. Donelan, "Evidence for the effects of swell and unsteady winds on marine wind stress," J. Phys. Oceanogr., 29, 1853-1864 (1999). https://doi.org/10.1175/1520-0485(1999)029<1853:EFTEOS>2.0.CO;2

104. R.A. Flather, "A tidal model of Northeast Pacific," Atmosphere-Ocean, 25, 22-45 (1987). https://doi.org/10.1080/07055900.1987.9649262

105. D.A. Fong and W.R. Geyer, "The alongshore transport of freshwater in a surface-trapped river plume," J. Phys. Oceanogr., 32, 957-972 (2002). https://doi.org/10.1175/1520-0485(2002)032<0957:TATOFI>2.0.CO;2

106. A.D. Fox and S.J. Maskell, "Two-way interactive nesting of primitive equation ocean models with topography," J. Phys. Oceanogr., 25, 2977-2996 (1995). https://doi.org/10.1175/1520-0485(1995)025<2977:TWINOP>2.0.CO;2

107. R.W. Gi ths and P.F. Linden, "The stability of vortices in a rotating, stratified fluid," J. Fluid Mech., 105, 283-316 (1981). https://doi.org/10.1017/S0022112081003212

108. W.D. Grant and O.S. Madsen, "Combined wave and current interaction with a rough bottom," J. Geophys. Res., 84, 1797-1808 (1979). https://doi.org/10.1029/JC084iC04p01797

109. J. Groeneweg and G. Klopman, "Changes in the mean velocity profiles in the combined wavecurrent motion described in GLM formulation," J. Fluid Mech., 370, 271-296 (1998). https://doi.org/10.1017/S0022112098002018

110. H. Gunther, S. Hasselmann, and P.A.E.M. Janssen, The WAM Model Cycle 4, Technical Report Deutsches KlimaRechenZentrum, Hamburg, Germany (1992).

111. K. A. Haas, I. A. Svendsen, M. C. Haller, and Q. Zhao, "Quasi three-dimensional modelling of rip current systems," J. Geophys. Res., 108, No. С7, 3217-3238 (2003). https://doi.org/10.1029/2002JC001355

112. R. L. Haney, "On the pressure gradient force over steep topography in sigma coordinate ocean models," J. Phys. Oceanogr., 21, 610-618 (1991). https://doi.org/10.1175/1520-0485(1991)021<0610:OTPGFO>2.0.CO;2

113. A. Harten, "High resolution schemes for hyperbolic conservation laws," J. Comput. Phys., 49, 371-393 (1983). https://doi.org/10.1016/0021-9991(83)90136-5

114. A. Harten, "On a class of high resolution total-variation-stable finite-difference schemes," J. Numer. Phys., 24, 1-23 (1984). https://doi.org/10.1137/0721001

115. K. Hasselmann, "On the mass and moment transfer between short gravity waves and largerscale motions," J. Fluid Mech., 50, 189-201 (1971). https://doi.org/10.1017/S0022112071002520

116. S. Hasselmann, K. Hasselmann, E. Buer, et al., "The WAM model - a third generation ocean wave prediction model," J. Phys. Oceanogr., 18, 1775-1810 (1988). https://doi.org/10.1175/1520 0485(1988)018<1775:TWMTGO>2.0.CO;2

117. S.A. Hsu, "A dynamic roughness equation and its application to wind stress determination at the air-sea interface, " J. Phys. Oceanogr., 4, 116-120 (1974). https://doi.org/10.1175/1520-0485(1974)004<0116:ADREAI>2.0.CO;2

118. S.A. Hsu, "A mechanism for the increase of wind stress coefficient with wind speed over water surface: A parametric model," J. Phys. Oceanogr., 16, 144-150 (1986). https://doi.org/10.1175/1520-0485(1986)016<0144:AMFTIO>2.0.CO;2

119. P.A.E.M. Janssen, "Quasi-linear theory of wind wave generation applied to wave forecasting," J. Phys. Oceanogr., 21, 1631-1642 (1991). https://doi.org/10.1175/1520-0485(1991)021<1631:QLTOWW>2.0.CO;2

120. T.G. Jensen, "Open boundary conditions in stratified ocean models," J. Marine Syst., 16, 297- 322 (1998). https://doi.org/10.1016/S0924-7963(97)00023-7

121. I.G. Jonsson and N.A. Carlsen, "Experimental and theoretical investigations in an oscillatory turbulent boundary layer," J. Hydraulic Res., 14, 45-60 (1973). https://doi.org/10.1080/00221687609499687

122. L.H. Kantha and C.A. Clayson, "An improved mixed layer model for geophysical applications," J. Geophys. Res., 99, 25235-25266 (1994). https://doi.org/10.1029/94JC02257

123. L.H. Kantha and C.A. Clayson, "On the effect of surface gravity waves on mixing in an oceanic mixed layer," Ocean Modelling, 6, 101-124 (2003). https://doi.org/10.1016/S1463-5003(02)00062-8

124. J.T. Kirby and T.M. Chen, "Surface waves on vertically sheared flows - approximate dispersion relations," J. Geophys. Res., 94, No. C1, 1013-1027 (1989). https://doi.org/10.1029/JC094iC01p01013

125. G.J. Komen, S. Hasselmann, and K. Hasselmann, "On the existence of a fully developed wind-sea spectrum," J. Phys. Oceanogr., 14, 1271-1285 (1984). https://doi.org/10.1175/1520-0485(1984)014<1271:OTEOAF>2.0.CO;2

126. G. Komen, P.A.E.M. Janssen, V. Makin, and W. Oost, "On the sea state dependence of the Charnock parameter," Global Atmos. Ocean Syst., 5, 367- 388 (1998).

127. W.G. Large and S. Pond, "Open ocean momentum fluxes in moderate to strong winds," J. Phys. Oceanogr., 11, 324-336 (1981). https://doi.org/10.1175/1520-0485(1981)011<0324:OOMFMI>2.0.CO;2

128. S. Leibovich, "On the evolution of the system of wind drift currents and Langmuir circulation in the ocean. Part 1. Theory and averaged current," J. Fluid Mech., 79, 715-743 (1977). https://doi.org/10.1017/S002211207700041X

129. S. Leibovich, "On wave-current interaction theory of Langmuir circulations," J. Fluid Mech., 82, 715-724 (1980). https://doi.org/10.1017/S0022112080000857

130. B.Li, D.E. Reeve, and C. A. Fleming, "An investigation of inshore wave conditions using satellite data," Water Maritime Eng., 154, Issue 4, 275-283 (2002). https://doi.org/10.1680/wame.2002.154.4.275

131. Z. Li and B. Johns, "A three-dimensional numerical model of surface waves in the surf area and longshore current generation over a plane beach," Estuarine, Coastal Shelf Sci., 47, 395-413 (1998). https://doi.org/10.1006/ecss.1998.0382

132. Q. Liang, A.G.L. Borthwick, and G. Stelling, "Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids," Int. J. Numer. Methods Fluids, 46, 127-162 (2004). https://doi.org/10.1002/fld.748

 133. P.L. Liu, Y.S. Cho, M.J. Briggs, et al., "Run-up of solitary wave on a circular island," J. Fluid Mech., 302, 259-285 (1995). https://doi.org/10.1017/S0022112095004095

134. M.S. Longuet-Higgins, "Longshore currents generated by obliquely incident sea waves. 1," J. Geophys. Res., 75, No. 33, 6678-6789 (1970). https://doi.org/10.1029/JC075i033p06778

135. M.S. Longuet-Higgins, "Longshore currents generated by obliquely incident sea waves. 2," J. Geophys. Res., 75, No. 33, 6690-6801 (1970). https://doi.org/10.1029/JC075i033p06790

136. M.S. Longuet-Higgins and R.W. Stewart, "Radiation stress and mass transport in gravity waves with applications to surf beats," J. Fluid Mech., 13, 481-504 (1963). https://doi.org/10.1017/S0022112062000877

137. M.S. Longuet-Higgins and R.W. Stewart, "Radiation stresses in water waves: a physical discussion, with applications," Deep-Sea Res., 11, 529-562 (1964). https://doi.org/10.1016/0011-7471(64)90001-4

138. P.J. Lynett, A Multi-Layer Approach to Modeling Generation, Propagation, and Interaction of Water Waves, PhD Thesis, Cornell University, USA (2002).

139. R.V. Madala and S.A. Piacsek, "A semi-implicit numerical model for baroclinic oceans," J. Comput. Phys., 23, 167-178 (1977). https://doi.org/10.1016/0021-9991(77)90119-X

140. P. Marchesiello, J.C. McWilliams, and A.F. Shepetkin, "Open boundary conditions for longterm integration of regional oceanic models," Ocean Modeling, 3, 1-20 (2001). https://doi.org/10.1016/S1463-5003(00)00013-5

141. J.D. McCalpin, "A comparison of second-order and fourth-order pressure gradient algorithms in a -coordinate ocean model," Int. J. Numer. Methods Fluids, 18, 361-383 (1994). https://doi.org/10.1002/fld.1650180404

142. J.C. McWillams, J.M. Restpero, and E.M. Lane, "An asymptotic theory for the interaction of waves and currents in coastal waters," J. Fluid Mech., 511, 135-178 (2004). https://doi.org/10.1017/S0022112004009358

143. J.C. McWillams, P.P. Sullivan, and C.H. Moeng, "Langmuir turbulence in the ocean," J. Fluid Mech., 334, 1-30 (1997). https://doi.org/10.1017/S0022112096004375

144. G.L. Mellor, "The three-dimensional current and wave equations," J. Phys. Oceanogr., 33, No. 9, 1978-1989 (2003). https://doi.org/10.1175/1520-0485(2003)033<1978:TTCASW>2.0.CO;2

 145. G.L. Mellor, "Some consequences of the three-dimensional current and surface wave equations," J. Phys. Oceanogr., 35, No. 9, 2291-2298 (2005). https://doi.org/10.1175/JPO2794.1

146. G.L. Mellor and A.F. Blumberg, "Modeling vertical and horizontal diffusivities with the sigma coordinate system," Mon. Weather Rev., 113, 1379-1383 (1985). https://doi.org/10.1175/1520-0493(1985)113<1379:MVAHDW>2.0.CO;2

147. G.L. Mellor and A.F. Blumberg, "Wave breaking and ocean surface layer thermal response," J. Phys. Oceanogr., 34, 693-698 (2004). https://doi.org/10.1175/2517.1

148. G.L. Mellor and T. Yamada, "Development of a turbulence closure model for geophysical fluid problems," Rev. Geophys. Space Phys., 20, 851-875 (1982). https://doi.org/10.1029/RG020i004p00851

149. I.J. Moon, "Impact of a coupled ocean wave-tide-circulation system on coastal modeling," Ocean Modeling, 8, 203-236 (2005). https://doi.org/10.1016/j.ocemod.2004.02.001

150. B.A. O'Connor, H. Kim, and K.D. Yum, "Modeling siltation at Chukpyon Harbor, in: P. W. Partridge (editor), Coastal Modeling of Seas and Coastal Regions, Elsevier, New York (1992), pp. 397-410. https://doi.org/10.1007/978-94-011-2878-0_29

151. L. Oey, "A wetting and drying scheme for POM," Ocean Modeling, 9, 133-150 (2005). https://doi.org/10.1016/j.ocemod.2004.06.002

152. L. Oey, "An OGCM with movable land-sea boundaries," Ocean Modeling, 13, 176-195 (2006). https://doi.org/10.1016/j.ocemod.2006.01.001

153. L. Oey and P. Chen, "A nested-grid ocean model: with application to the simulation of meanders and eddies in the Norwegian Coastal Current", J. Geophys. Res., 97, No. C12, 20063- 20086 (1992). https://doi.org/10.1029/92JC01991

154. I. Orlanski, "A simple boundary condition for unbounded hyperbolic flows," J. Comput. Phys., 21, 251-269 (1976). https://doi.org/10.1016/0021-9991(76)90023-1

155. A. Papadopoulos, P. Katsafados, G. Kallos, and S. Nickovic, "The weather forecasting system for Poseidon - An overview," Global Atmos. Ocean Syst., 8, No. 2, 219-237 (2002). https://doi.org/10.1080/1023673029000003543

156. J. Pietrzak, "The use of TVD limiters for forward-in-time upstream-biased advection schemes in ocean modeling," Mon. Weather Rev., 126, 812-830 (1998). https://doi.org/10.1175/1520-0493(1998)126<0812:TUOTLF>2.0.CO;2

157. J.A. Polton, D.M. Lewis, and S.E. Belcher, "The role of wave-induced Coriolis-Stokes forcing on the wind-driven mixed layer," J. Phys. Oceanogr., 35, No. 4, 444-457 (2005). https://doi.org/10.1175/JPO2701.1

158. N.H. Rachev, V.M. Roussenov, and E.V. Stanev, "The Black Sea climatological wind stress," Bulg. J. Meteorol. Hydrol., No. 2, 72-79 (1991).

159. R.C. Ris, N. Booji, and L.H. Hothtuijsen, "A third-generation wave model for coastal region. Part II: Verification," J. Geophys. Res., 104, No. C4, 7667-7681 (1999). https://doi.org/10.1029/1998JC900123

160. J. Sheng and L. Tang, "A two-way nested-grid ocean-circulation model for the Meso-American Barrier Reef System," Ocean Dynamics, 54, No. 2, 232-242 (2004). https://doi.org/10.1007/s10236-003-0074-3

161. R.P. Signell, R.C. Beardsley, H. C. Graber, and A. Capotondi, "Effect of wave-current interaction on wind-driven circulation in narrow, shallow embayments," J. Geophys. Res., 95, 9671- 9678 (1990). https://doi.org/10.1029/JC095iC06p09671

162. T.J. Simons, "Verification of numerical models of Lake Ontario. Part I," J. Phys. Oceanogr., 4, 507-523 (1974). https://doi.org/10.1175/1520-0485(1974)004<0507:VONMOL>2.0.CO;2

163. J. Smagorinsky, "General circulation experiments with primitive equations. I. The basic experiment," Mon. Weather Rev., 91, 99-164 (1963). https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

 164. P.K. Smolarkiewicz, "A simple positive definite advection transport scheme with small implicit diffusion," Mon. Weather Rev., 111, 479-486 (1983). https://doi.org/10.1175/1520-0493(1983)111<0479:ASPDAS>2.0.CO;2

165. P.K. Smolarkiewicz, "A fully multidimensional positive definite advection transport algorithm with small implicit diffusion," J. Comput Phys., 54, 325-362 (1984). https://doi.org/10.1016/0021-9991(84)90121-9

166. P.K. Smolarkiewicz and T. L. Clark, "The multidimensional positive definite advection transport algorithm: Further development and applications," J. Comput Phys., 67, 396-438 (1986). https://doi.org/10.1016/0021-9991(86)90270-6

167. C.J. Sonu, "Field observations of nearshore circulation and meandering current," J. Geophys. Res., 77, No. 18, 3232-3247 (1972). https://doi.org/10.1029/JC077i018p03232

168. M.A. Spall and W.R. Holland, "A nested primitive equation model for oceanic applications," J. Phys. Oceanogr., 21, 205-220 (1991). https://doi.org/10.1175/1520-0485(1991)021<0205:ANPEMF>2.0.CO;2

169. L.A. Svendsen and U. Putrevu, "Surf-area modeling," in: International Conference "Coastal Dynamics-95," Gdansk (1995), pp. 11-32.

170. SWAN Cycle III Version 40.11, User Manual, Delft University of Technology, Netherlands (2000) (http://swan.ct.tudeft.nl).

171. SWAN Cycle III Version 40.51, User Manual, Delft University of Technology, Netherlands (2006) ( http://swan.ct.tudeft.nl).

172. SWAN Technical Documentation SWAN Cycle III Version 40.51A, Delft, Netherlands (2007).

173. P.K. Sweby, "High resolution schemes using flux limiters for hyperbolic conservation laws," Society for Industrial and Applied Mathematics, J. Numer. Anal., 21, 995-1011 (1984). https://doi.org/10.1137/0721062

174. B. Tartinville, E. Deleersnijder, P. Lazure, et al., "A coastal ocean model intercomparison study for a three-dimensional idealised test case," Appl. Mat. Modeling, 22, 165-182 (1998). https://doi.org/10.1016/S0307-904X(98)00015-8

175. P.K. Taylor and M.J. Yelland, "The dependence of sea surface roughness on the height and steepness of the waves," J. Phys. Oceanogr., 31, No. 2, 572-590 (2001). https://doi.org/10.1175/1520-0485(2001)031<0572:TDOSSR>2.0.CO;2

176. W.C. Thacker, "Some exact solutions of the nonlinear shallow-water equations," J. Fluid Mech., 107, 499-508 (1981). https://doi.org/10.1017/S0022112081001882

177. E.B. Thornton, C. M. Soares, and T.P. Stanton, "Vertical profiles of longshore currents and bed shear stress," in: International Conference «Coastal Dynamics-95,» Gdansk (1995), pp. 449- 459.

178. H.L. Tolman, "A third generation model for wind waves on slowly varying, unsteady, and inhomogeneous depth and currents, "J. Phys. Oceanogr., 21, 782-797 (1991). https://doi.org/10.1175/1520-0485(1991)021<0782:ATGMFW>2.0.CO;2

179. H.L. Tolman and D.V. Chalikov, "Source terms in a third-generation wind wave model," J. Phys. Oceanogr., 26, 2497-2518 (1996). https://doi.org/10.1175/1520-0485(1996)026<2497:STIATG>2.0.CO;2

180. B. Van Leer, "Towards the ultimate conservative finite difference scheme. II: Monotonicity and conservation combined in a second order scheme," J. Comput. Phys., 14, 361-376 (1974). https://doi.org/10.1016/0021-9991(74)90019-9

181. B. Van Leer, "Toward the ultimate conservative difference scheme. IV: A new approach to numerical convection," J. Comput. Phys., 23, 276-299 (1977). https://doi.org/10.1016/0021-9991(77)90095-X

 182. B. Van Leer, "Toward the ultimate conservative difference scheme. V: A second order sequel to Godunov's method," J. Comput. Phys., 32, 101-136 (1979). https://doi.org/10.1016/0021-9991(79)90145-1

183. L.C. Van Rijn, "Sediment transport. Part I: Bed load transport," J. Hydraulic Eng., 110, 1431-1456 (1984). https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431)

184. R. Visser, Morphological Modeling in the Vicinity of Groynes, MSc Thesis, Delft University of Technology, Netherlands (2002).

185. "WAMDI group. The WAM model - a third generation ocean wave prediction model," J. Phys. Oceanogr., 18, 1775-1810 (1988). https://doi.org/10.1175/1520-0485(1988)018<1775:TWMTGO>2.0.CO;2

186. J. Wolf, S.L. Wakelin, and J.T. Holt, "A coupled model of waves and currents in the Irish Sea," in: Proceedings of the Twelfth International Offshore and Polar Engineering Conference (Kitakyushu, Japan, May 26-31, 2002). - Vol. 3 (2002), pp. 108-114.

187. J.Wu, "Wind-stress coefficients over sea surface from breeze to hurricane," J. Geophys. Res., 87, No. C12, 9704-9706 (1982). https://doi.org/10.1029/JC087iC12p09704

188. H. Xia, Z. Xia, and L. Zhu, "Vertical variation in radiation stress and wave-induced current," Coastal Eng., 51, 309-321 (2004). https://doi.org/10.1016/j.coastaleng.2004.03.003

189. L. Xie, K. Wu, L. Pietrafesa, and C. Zhang, "A numerical study of wave current interaction through surface and bottom stress: wind-driven circulation in the South Atlantic Bight under uniform winds," J. Geophys. Res., 106, No. C8, 16841-16855 (2001). https://doi.org/10.1029/2000JC000292

190. L. Xie, L. Pietrafesa, and K. Wu, "A numerical study of wave current interaction through surface and bottom stress: Coastal ocean respond to Hurricane Fran of 1996," J. Geophys. Res., 108, No. C2, 31-1-31-18 (2003). https://doi.org/10.1029/2001JC001078

191. Zh. Yang and I.M. Hamrick, "Variational inverse parameter estimation in a cohesive sediment transport model: An adjoint approach," J. Geophys. Res., 108, No. C2, 37-1-37-10 (2003). https://doi.org/10.1029/2002JC001423

192. H. Yeh, P. Liu, M. Briggs, and C. Synolakis, "Propagation and amplification of tsunamis at coastal boundaries," Nature, Issue 372, 353-355 (1994). https://doi.org/10.1038/372353a0

193. M.J. Yelland, B.I. Moat, P.K. Taylor, R.W. Pascal, "Measurements of the open ocean drag coefficient corrected for air flow disturbance by the ship," J. Phys. Oceanogr., 28, 1511-1526 (1998). https://doi.org/10.1175/1520-0485(1998)028<1511:WSMFTO>2.0.CO;2

194. M.J. Yelland and P.K. Taylor, "Wind stress measurements from the open ocean," J. Phys. Oceanogr., 26, 541-558 (1996). https://doi.org/10.1175/1520-0485(1996)026<0541:WSMFTO>2.0.CO;2

195. S.T. Zalesak, "Fully multidimensional flux-corrected transport algorithms for fluids," J. Comput. Phys., 31, 335-362 (1979). https://doi.org/10.1016/0021-9991(79)90051-2