A Study of the M-2 Tide in the Ice-Covered Arctic Ocean

“A Study of the M-2 Tide in the Ice-Covered Arctic Ocean”

Authors: Zygmunt Kowalik,
Affiliation: University of Alaska
Reference: 1981, Vol 2, No 4, pp. 201-223.

Keywords: Hydrodynamics, M2 tide, ice mechanics, numerical methods, Arctic ocean, Barents sea

Abstract: A model to study M2 tide propagation in the Arctic Ocean based on the equation of motion of the water and the pack ice, is considered. The mechanics of the ice floe interaction is described by the non-linear viscous constitutive loaw. Various empirical parameters entering the constitutive law are checked against the tide-induced motion of the pack ice. The distribution of the amplitude, phase, current ellipse in the ice-free and the ice-covered Arctic Ocean is computed and presented in figures. Special attention is given to clarifying the distribution and peculiarities of tide propagation in the Barents Sea. The tide-induced motion of the pack ice has been studied carefully; numerous experiments show that residual (over tidal period) ice drift is observed due to the non-linear ice floe interaction. It is found that both residual ice drift and periodical ice motion may lead to ice redistribution, setting the areas of ice convergence and divergence.

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PDF (1607 Kb) DOI: 10.4173/mic.1981.4.2

DOI forward links to this article:

[1] Z. Kowalik (1984), doi:10.1029/JC089iC06p10570

[2] Florent H. Lyard (1997), doi:10.1029/96JC02596

[3] Igor Polyakov (2001), doi:10.1175/1520-0485(2001)031<2255:AEPBOM>2.0.CO;2

[4] Harold O. Mofjeld (1986), doi:10.1029/JC091iC02p02593

[5] Z. Kowalik and A. Y. Proshutinsky (1993), doi:10.1029/93JC01363

[6] B. A. Kagan, E. V. Sofina and E. H. A. Rashidi (2013), doi:10.1134/S0001433812060059

[7] Jens G. Balchen (2000), doi:10.4173/mic.2000.1.1

[8] IGORV POLYAKOV (1994), doi:10.1111/j.1751-8369.1994.tb00451.x

[9] B. A. Kagan, A. A. Timofeev and E. V. Sofina (2010), doi:10.1134/S0001433810050105

[10] A. Y. Proshutinsky and M. A. Johnson (1997), doi:10.1029/97JC00738

[11] N. E. DMITRIEV, A. YU. PROSHUTINSKY, T. B. LØYNING and T. VINJE (1991), doi:10.1111/j.1751-8369.1991.tb00614.x

[12] B. GJEVIK and T. STRAUME (1989), doi:10.1111/j.1600-0870.1989.tb00367.x

[13] B. A. Kagan, D. A. Romanenkov and E. V. Sofina (2007), doi:10.1134/S0001433807060114

[14] B.A. Kagan, D.A. Romanenkov and E.V. Sofina (2008), doi:10.1016/j.csr.2007.09.004

[15] B.A. Kagan and E.V. Sofina (2010), doi:10.1016/j.csr.2009.05.010

[16] Bernard D. Zetler (1990), doi:10.1029/HG004p0071

[17] B. A. Kagan, D. A. Romanenkov and E. V. Sofina (2008), doi:10.1134/S000143700803003X

[18] Z. Kowalik and A. Y. Proshutinsky (1994), doi:10.1029/GM085p0137

[19] B. A. Kagan and E. V. Sofina (2012), doi:10.1134/S0001433811060077

[20] Bernard D. Zetler (1986), doi:10.1029/EO067i007p00073

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[27] A.Y Proshutinsky and Mark Johnson (2001), doi:10.1016/S0025-326X(00)00234-4

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[37] Amey Vasulkar, Martin Verlaan, Cornelis Slobbe and Lars Kaleschke (2022), doi:10.1007/s10236-022-01516-w

[38] M. G. Hart-Davis, S. L. Howard, R. D. Ray, O. B. Andersen, L. Padman, F. Nilsen and D. Dettmering (2024), doi:10.1038/s41597-024-03012-w

References:
[1] CAMPBELL, W.J. (1965). The wind-driven circulation of ice and water in a Polar Ocean, Journ. Geoph. Research, 70. 14, 3279-3301 doi:10.1029/JZ070i014p03279
[2] COON, M.D., MAYKUT, G.A., PRITCHARD R.S. ROTHROCK, D.A. THORNDIKE, A.S. (1974). Modeling the pack ice as an elastic-plastic material, AIDJEX bulletin, 24,1-105.
[3] GLEN, J.W. (1970). Thoughts on a viscous: model for sea ice, AIDJEX Bulletin, 2, 18-27.
[4] HANSEN, W. (1962). Hydrodynamical method applied to the oceanographical problems, Proc. Symp. Math.-Hydrodyn, Meth. Phys. Oceanography. Mitt. Inst. Meeresk., Univ. Hamburg 1, 25-34.
[5] HIBLER III, W.D. (1979). A dynamic thermodynamic sea ice model, J. Phys. Oceanogr, 9, 815-846.
[6] HUNKINS, K. (1967). Emerging oscillations of Fletcher´s Ice Island, T-3. J. Geoph. Res., 72, 4, 1165-1174.
[7] JEFFREYS, H. (1921). Tidal friction in shallow seas, Philos. Trans. R. Soc. London.A 221, 239-264 doi:10.1098/rsta.1921.0008
[8] KAGAN, B.A. (1960). Hydrodynamical models of tidal motion in the sea, Gidrometeozdat. Leningrad, pp. 218.
[9] KAGAN, B.A. (1970). On the features of some finite-difference schemes use at numerical integration of tidal dynamics equations, Izv. Atmospheric and Oceanic Physics, 6, 7, 704-717.
[10] KHEYSIN, D.Y., IVCHENKO, V.O. (1973). A numerical model of tidal ice drift with allowance for the interaction between floes, Izv. Atmospheric and Oceanic Physics. 9, 4, 420-429.
[11] KOWALIK, Z. (1979). A note on the co-oscillating M2-tide in the Arctic Ocean, Dt. Hydrogr. Zt., 32, H.3, 100-112.
[12] KOWALIK, Z., BICH HUNG, N. (1977). On a system of hydrodynamic equations for certain oceanographical problems in the region of the earth´s pole and the stability of its solution, Oceanologica, 7, 5-20.
[13] KOWALIK, Z. UNTERSTEINER N. (1978). A study of the M2 tide in the Arctic ocean, Dt. Hydrogr. Zt. 31, H.6, 216-219.
[14] KUZNECOV, D.S. (1951). Hydrodynamics, Gidrometeoizdat. Leningrad, pp. 392.
[15] LEGENKOV, A.P. (1958). On the theory of tidal concentration, dispersion and compaction of ice in open sea, Probl. Arkt. Antarkt., 5, 5-17.
[16] LING, C.H. RASMUSSEN, L.A., CAMPBELL, W.J. (1980). A continuum sea ice model for a global climate model, In Proceedings of the AIDJEX Symposium.University of Washington Press, pp. 187-196.
[17] MARCHUK, G., GORDEV, R., KAGAN, B., et al. (1972). Numerical method to solve tidal dynamics equation and results of its testing, Novosybirsk: Comput. Centre, pp. 78.
[18] MCPHEE, M.G. (1980). An analysis of pack ice drift in summer, In Proceedings of the AIDJEX Symposium.University of Washington Press, pp. 62-75.
[19] NEKRASOV, A.V. (1975). Tidal waves in the adjacent seas, Gidrometeoizdat. Leningrad, pp. 247.
[20] PRITCHARD, R.S., (ed.) (1980). Sea Ice Processes and Models, Proceedings of the AIDJEX Symposium.University of Washington Press, pp. 474.
[21] RAMMING, H-G., KOWALIK, Z. (1980). Numerical modelling of marine hydrodynamics, Elsevier. Amsterdam-New York, pp. 148-154.
[22] ROTHROCK, D.A. (1970). The kinematics and mechanical behaviour of pack ice: the state of subject, AIDJEX Bulletin, 2, 1-10.
[23] ROTHROCK, D.A. (1975). The mechanical behaviour of pack ice, Annual Review of Earth and Planetary Sciences, 3, 317-342.
[24] SGIBNEVA, L.A. (1964). Tides in the Barents Sea, Trudy Okiean. Instituta, 75, 5-19.
[25] SODHI, D.S., HIBLER III, W.D. (1980). Nonsteady ice drift in the Strait of Belle Isle, In Proceedings of the AIDJEX Symposium.University of Washington Press, pp. 177-186.
[26] SÜNDERMANN, J. (1970). The semi-diurnal principal lunar tide M2 in the Bering Sea, Dt. Hydrogr. Zt., 23, H.3, 91-101.
[27] TAYLOR, G.I. (1921). Tidal oscillations in gulf and rectangular basins, Proc. London Math. Soc. Ser. 2, 20, 148-181.
[28] TEE, K.T. (1976). Tide-induced residual current, a 2-D nonlinear numerical tidal model, J. Mar. Res., 4, 603-628.
[29] ZUBOV, N.N. (1955). Selected works on oceanology, Voenoye Izd. Moscow, pp. 266-270.

BibTeX:
@article{MIC-1981-4-2,
  title={{A Study of the M-2 Tide in the Ice-Covered Arctic Ocean}},
  author={Kowalik, Zygmunt},
  journal={Modeling, Identification and Control},
  volume={2},
  number={4},
  pages={201--223},
  year={1981},
  doi={10.4173/mic.1981.4.2},
  publisher={Norwegian Society of Automatic Control}
};

Article

“A Study of the M-2 Tide in the Ice-Covered Arctic Ocean”