COMPENSATORY REVERSE FLOW OF PROGRESSIVE WAVES WITH FINITE AMPLITUDE
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Keywords

Stokes waves
cnoidal waives
Stokes drift
reverse flow

How to Cite

Shakhin, V. M., & Shakhina, T. V. (2017). COMPENSATORY REVERSE FLOW OF PROGRESSIVE WAVES WITH FINITE AMPLITUDE. Coastal Engineering Proceedings, 1(35), waves.9. https://doi.org/10.9753/icce.v35.waves.9

Abstract

This paper is devoted to problem of mass transport of fluid for the surface progressive waves. Both Stokes and cnoidal waves are considered. New solutions for the transitional current are obtained. It is discovered that the mass transport of fluid in the direction of wave propagation exists only in the top layer. In the underlying layers a compensatory reverse flow is formed. The existence of a compensatory flow was verified experimentally. It is revealed that theoretical results duly conform to experimental data.
https://doi.org/10.9753/icce.v35.waves.9
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References

Chen Y-Y., Hsu H-C. and Chen G-Y. 2010. Lagrangian experiment and solution for irrotational finite- amplitude progressive gravity waves at uniform depth, Fluid Dynamics Research, v.42, 4, 1-34.

Fenton J.D. 1979. A high -order cnoidal wave theory, Fluid Mechanics, 94, 129-161.

Fenton J.D. 1985. A fifth-order Stokes theory for steady waves, Journal of Waterway, Port, Coastal and Ocean Eng., ASCE, v. 111, 2, 216-234.

Friedrichs K.O., Hyers D.H. 1954. The existence of solitary waves, Comm. Pure Appl. Math., v. 7, 517-550.

Keller J.B. 1948. The solitary wave and periodic waves in shallow water, Comm. On Appl. Math., v. 1, 4, 323-340.

Kohin N.E. 1927. Determination regoureuse des ondes permanentes d'ampleur finite a la surface de separation de deux liquides de profondeur finie, Math. Ann., v. 98, 3-4, 582-615.

Lamb H. 1932. Hydrodynamics, Cambridge University, Press.

Lavrentyev M.A. 1946. Long waves theory, Works Inst. Mathem. AS URSR, 8, 13-69, (in Ukrain).

Levi-Civita T. 1925. Determination regoureuse des ondes permanentes d' amleur finite, Math. Ann., 23, 264-313.

Lighthill J. 1978. Waves in fluids, Cambridge University, Press.

Littman W. 1957. On the existence of periodic waves near critical speed, Comm., Pure Appl. Math., 10, 241-269.

Madsen P.A. and Sorensen O.R. 1992. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly - varying bathymetry, Coastal Engineering, 18, 183-204.

Ovsyannikov L.V. 1983. Parameters of cnoidal waves, The book: Problems of mathematics and mechanics. Novosibirsk: Science, 150 - 166 (in Russsian).

Peregrine D.H. 1967. Long waves on the beach, Fluid Mechanics, v. 27, 4, 815-827.

Shakhin V.М. 2001. Progressive waves of finite amplitude, Physics of the atmosphere and the ocean,

v. 37, 2, 245-248 (in Russsian).

Shakhin V.M., Atavin A.A. 2004. About calculation of the parameters of cnoidal waves. Proceedings of 6-th Conference on Dynamics and thermal of rivers, reservoirs and coastal zone, IWP RAS, M.:, 270-272 (in Russsian).

Shakhin V.М., Shakhina Т.V. 2009. Waves of high amplitude on the fluid surface, Materials of international conference on Lithodynamics of the bottom contact zone of the ocean, Moscow GEOS., 44-46 (in Russsian).

Shakhin V.М., Shakhina Т.V. 2015. Waves on the Water Surface - Mathematical Models - Part 1, Int. J. of Ocean and Climate Systems, 6, 3, 113-135.

Stoker J.J. 1957. Water waves. Interscience.

Stokes G.G. 1847. On the theory of oscillatory waves, Camb. Trans., 8, 441-473.

Struik D.J. 1926. Determination regoureuse des ondes irrotationelles periodiques dans un canal a profondeur finie, Math. Ann., 95, 595-634.

Whitham G. 1974. Linear and nonlinear waves, Wiley, Interscience.

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