A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas

Feng Shizuo

doi:10.1007/BF02851489

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A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas

OriginalPaper | Updated：2023-05-16

- A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas
- A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas
- 海洋湖沼学报（英文） 1984年2卷第2期页码：177-187
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  This paper was presented at the Joint Oceanographic Assembly (J.O.A.) held at Halifax, Canada, August 2–13, 1982, and included in “Poster Abstract” Vol. I.
- DOI：10.1007/BF02851489
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- 纸质出版：1984
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A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas[J]. 海洋湖沼学报（英文）, 1984,2(2):177-187.

Shizuo, F. A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas., Chin. J. Ocean. Limnol. 2, 177–187 (1984). https://doi.org/10.1007/BF02851489
A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas[J]. 海洋湖沼学报（英文）, 1984,2(2):177-187. DOI： 10.1007/BF02851489.

Shizuo, F. A three-dimensional nonlinear hydrodynamic model with variable eddy viscosity in shallow seas., Chin. J. Ocean. Limnol. 2, 177–187 (1984). https://doi.org/10.1007/BF02851489 DOI：

摘要

Abstract

Considerable scientific and practical interest exists in ascertaining the dynamic processes in shallow seas. This is especially true for China having a vast area of shallow seas. To simulate the observed data and study the dynamical mechanism of waves and currents in shallow seas a numerical model is developed in this paper. In view of the notable nonlinearity of shallow sea waves and currents

and in order to solve the current distribution in the vertical direction

and to examine the effect of variable eddy viscosity

the model proposed is a three-dimensional nonlinear one with variable eddy viscosity. The eddy viscosity can be considered as a physically acceptable arbitrary function of depth

which is realized in terms of a Sturm-Liouville System. The currents are expressed by using the eigenfunctions satisfying the Sturm-Liouville System just mentioned. A boundary-value problem (or an initio-boundary-value problem) of free surface elevation is derived. And then

the application of the proposed shallow sea model to nonlinear tides

ultra-shallow water storm surges and steady circulation is given

respectively. Finally

a generalized linear law between the bottom friction and the transport is derived.

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references

Chin Tsenghao and Feng Shihzao (Feng Shizuo), 1975. A preliminary study on the mechanism of shallow water storm surges.Scientia Sinica XVIII (2): 242–261.

Feng Shihzao (Feng Shizuo), 1977. A three-dimensional nonlinear model of tides.Scientia Sinica XX (4): 436–446.

Feng Shizuo and Shi Ping, 1980. An ultra-shallow water storm surge model with variable eddy viscosity.Acta Oceanologia Sinica 2 (3): 1–11. (in Chinese with English abstract)

Feng Shizuo and Sun Wenxin, 1983. A tidal three-dimensional nonlinear model with variable eddy viscosity (I),Chin. J. Ocean. Limn. 1 (2): 166–170.

Feng Shizuo, Zhang Shuzhen and Xi Pangen, 1981. Mathematical modeling of circulation in the East China Sea (II).J. Shandong College Ocean. 11 (2): 8–26. (in Chinese with English abstract)

Feng Shizuo, 1982. On thef-and β-coordinates,J. Shandong College Ocean. 12 (3): 1–10 (in Chinese with English abstract)

Feng Shizuo, 1982. An Introduction to Storm Surger, Springer-Verlag, Beijing, pp. 241. (in Chinese)

Hansen, W., 1952. Gezeiten und Gezeitenströme der halbtaqiqen Hauptmondtide M2 in der Nordsee-Deut. Hydrog. Z. Ergänzungsheft 1.

Heaps, N. S., 1971. On the numerical solution of the three-dimensional hydrodynamical equations for tides and storm surges.Mém. Soc. r. Sci. Liégo 6 (2): 143–180.

Qin Zenghao, 1981. A simple air-sea planetary boundary layer model with special reference to Ekman currents.Ocean. Limn. Sin. 12 (1): 9–24. (in Chinese with English abstract)

Sgibnewa, L. and A. Felsenbaum, 1965. Theory on tides in water with friction.Doklady Akad. Nauk S.S.S.R. 164 (2): 315–318. (in Russian)

Sun Wenxin, Chen Zongyong and Feng Shizuo, 1981. Numerical simulation of the three-dimensional nonlinear tidal waves (I)—A numerical study for M4 and MS4 waves in the Bohai Sea.J. Shandong College Ocean. 11 (1): 23–31. (in Chinese with English abstract)

Sun Wenxin, Feng Shizuo and Qin Zenghao, 1979. Numerical modeling of an ultra-shallow water storm surge (I).Acta Oceanologia Sinica 1 (2): 193–211. (in Chinese with English abstract)

Sun Wenxin, Qin Zenghao and Feng Shizuo, 1980. Numerical modeling of an ultra-shallow water storm surge (II).J. Shandong College Ocean. 10 (2): 7–19. (in Chinese with English abstract)

Xi Pangen, Zhang Shuzhen and Feng Shizuo, 1980. Mathematical modeling of circulation in the East China Sea (I).J. Shandong College Ocean. 10 (3): 13–25. (in Chinese with English abstract)

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