Abstract
A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wavccurrent field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does so by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.
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References
Wang, T., Li, J. C.. Application of conservation law of wave action flux to wave-current interaction.Acta Mech.Sinica (in Chinese), 1996, 28(3):281.
Bea, R. G., Lai, N. W., Hydrodynamic loadings on offshore platforms, inProc. 10th Offsh. Tech. Conf., Houston: OTC, 1978, 155.
Toumazis, A. D., Ahilan, R. V., Review of recent analytical and approximate solutions of wave-current interaction, inEnvir. Forces on Off sh. Struct. &Their Predict., Netherlands: Kluwer Acad. Pub., 1990, 61.
Li, J. C., Chwang, T. A., Effect of non- uniform current on wave fields, inProc. 4th Int. Offsh. &Polar Eng. Conf., 1994, 3:125.
Osaka: ISOPE, Li, J. C., Lin. M., Wang, T., Flow interaction relevant to water waves, inProc. 1st Int. Conf. on Flow Interact., Hong Kong:Univ. Hong Kong, 1994, 433.
Peregrine, D. H., Interaction of water waves and currents,Adv. in Appl. Mech., 1976, 16:9.
Srokosz, M. A., Models of wave-current interaction, inModelling the Offsh. Envir., Netherlands: Kluwer Acad. Pub., 1987, 313.
Cummims, I., Swan, C.. Nonlinear wave current interaction, inWave Kinemat. &Envir. Forces, Netherlands: Kluwer Acad. Pub., 1993. 35.
Skyner, D. J., Easson, W. J., Wave kinematics on sheared currents, inWave Kinemat. &Envir. Forces, Netherlands: Kluwer Acad. Pub., 1993, 101.
Hui,W. H., Tenti, G., A new approach to steady flows with free surfaces,J. Appl. Math. &Phys., 1982, 33:569.
Drennan, W. M., Hui, W. H., Tenti, G., Accurate calculation of Stokes water waves of large amplitude,J. Appl. Math. &Phys., 1992, 43:367.
Chaplin, J. R., Computation of steep waves on a current with strong shear near to the surface, inWater Wave Kinemat., Netherlands: Kluwer Acad. Pub., 1990, 429.
Kirby, J. T., Chen, T. M., Surface waves on vertically sheared flows: approximate dispersion relations.J. Geoph. Res., 1989, 94:1013.
Phillips, O. M.,The Dynamics of the Upper Ocean, New York: Cambridge Univ. Press, 1977, 33.
Gudmestad, O. T., Karunakaran, D., Wave-current interaction, inEnvir. Forces on Offsh. Struch. &Their Predict., Netherlands: Kluwer Acad. Pub., 1990, 81.
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Project supported by the Chinese Academy of Sciences.
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Wang, T., Li, J. Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces. Sci. China Ser. A-Math. 40, 622–632 (1997). https://doi.org/10.1007/BF02876066
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DOI: https://doi.org/10.1007/BF02876066