Preview

Fundamental and Applied Hydrophysics

Advanced search

The structure of surface layer above sea

https://doi.org/10.7868/S2073667319020072

Abstract

The one-dimensional model of boundary layer above sea waves is suggested. The model is based on results obtained before with two-dimensional coupled model of wind and waves. The boundary layer above waves is different of model above flat surface by appearance of additional momentum flux created directly by curvilinear and moving interface. The one-dimensional equations of wave boundary layer can be derived in curvilinear surface-following coordinate system. In this case the equations contain explicitly the specifics of wave boundary layer. The momentum exchange between wind and waves is calculated in spectral space as a sum of separate fluxes, produced by wave modes. It is traditionally suggested that momentum flux is proportional to spectral density of wave energy with coefficient depending on wave age of each mode. The calculations illustrating the specific features of wave boundary layer: velocity and energy of turbulence profiles, wave and turbulent fluxes of momentum. The ratio of external (at upper level of boundary layer) and internal (at surface) roughness parameters is discussed. It is shown that external drag coefficient depends not only on wind velocity but also on shape of wave spectrum, what explains the large scatter of experimental data. Further development of suggested approach for problems of geophysical fluid mechanics is discussed. Such models are intended for coupling of atmosphere and ocean models with wave forecasting models.

About the Authors

D. V. Chalikov
Shirshov Institute of Oceanology of Russian Academy of Sciences
Russian Federation

Moscow



K. Yu. Bulgakov
University of Melbourne
Australia


References

1. Charnock H. Wind stress on a water surface. Quart. J. Roy. Meteorol. Soc. 1955, 81, 639–640.

2. Chalikov D.V. A mathematical model of wind-induced waves. Doklady Acad Sci USSR. 1976, 229, 121–126.

3. Chalikov D.V. Numerical simulation of wind-wave interaction. J.Fluid Mech. 1978, 87, 561–582.

4. Chalikov D.V. Mathematical modeling of wind-induced waves. News and problems of sciences series. Gidrometeoizdat, 1980, 50 p. (in Russian).

5. Chalikov D.V. Numerical simulation of the boundary layer above waves. Bound Layer Met. 1986, 34, 63–98.

6. Chalikov D. The parameterization of the wave boundary layer. J. Phys. Oceanogr. 1995, 25, 1335–1349.

7. Chalikov D., Belevich M. One-dimensional theory of the wave boundary layer. Bound-Lay Meteorol. 1993, 63, 65–96.

8. Monin A.S., Yaglom A.M. Statistical fluid mechanics: mechanics of turbulence. Vol. 1. Cambridge, M.I.T. Press, 1971. 770 p.

9. Chalikov D. Interactive modeling of surface waves and boundary layer. Proceeding of the third international symposium WAVES97. 1998, 1525–1540.

10. Chalikov D., Rainchik S. Coupled numerical modelling of wind and waves and the theory of the wave boundary layer. Boundary-Layer Meteorol. 2010, 138, 1, 1–41. doi:10.1007/s10546-010-9543-7

11. Chalikov D. Numerical modeling of sea waves. Springer, 2016. 330 p.

12. Miles J.W. On the generation of surface waves by shearflows. J. Fluid Mech. 1957, 3, 2, 185–204.

13. Donelan M.A., Babanin A.V., Young I.R., Banner M.L., McCormick C. Wave follower field measurements of the wind input spectral function Part I. Measurements and calibrations. J. Atmos. Oceanic Tech. 2005, 22, 799–813.

14. Donelan M.A., Babanin A.V., Young I.R., Banner M.L. Wave follower field measurements of the wind input spectral function. Part II. Parameterization of the wind input. J. Phys Oceanogr. 2006, 36, 1672–1688.

15. Launder B.E., Spalding D.B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 1974, 3, 269–289.

16. Hasselmann K., Barnett R.P., Bouws E. et al. Measurements of wind-wave growth and swell decay during the Joint Sea Wave Project (JONSWAP). Deutsches Hydrogr. Inst. 1973, 95 p.

17. Babanin A.V., Soloviev Yu.P. Parameterization of width of directional energy distributions of wind-generated waves at limited fetches. Izv. RAS, Atmospheric and Oceanic Physics. 1987, 23, 645–651.

18. Pierson W.J., Moscowitz L. A proposed spectral form for fully developed wind seas based on the similarity theory of S.A. Kitaigorodskii. J. Geophys. Res. 1964, 69, 24, 5181–5190.

19. Donelan M.A. Air-sea interaction. The sea. 1990, 9, 239–292.

20. Thomas L.H. Elliptic problems in linear differential equations over a network. New York, Columbia University, 1949.

21. Smedman A.S., Larsen X.G., Höström U. Is the logarithmic wind law valid over the sea? Wind over waves II: forecasting and fundamentals of applications. 2003, 23–33.

22. Tolman H., Chalikov D. On the source terms in a third-generation wind wave model. J. Phys. Oceanogr. 1996, 11, 2497–2518.


Review

For citations:


Chalikov D.V., Bulgakov K.Yu. The structure of surface layer above sea. Fundamental and Applied Hydrophysics. 2019;12(2):50-65. (In Russ.) https://doi.org/10.7868/S2073667319020072

Views: 112


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2073-6673 (Print)
ISSN 2782-5221 (Online)