Abstract
The flow field induced by internal solitary waves (ISWs) is peculiar wherein water motion occurs in the whole water depth, and the strong shear near the pycnocline can be generated due to the opposite flow direction between the upper and lower layers, which is a potential threat to marine risers. In this paper, the flow field of ISWs is obtained with the Korteweg-de Vries (KdV) equation for a two-layer fluid system. Then, a linear analysis is performed for the dynamic response of a riser with its two ends simply supported under the action of ISWs. The explicit expressions of the deflection and the moment of the riser are deduced based on the modal superposition method. The applicable conditions of the theoretical expressions are discussed. Through comparisons with the finite element simulations for nonlinear dynamic responses, it is proved that the theoretical expressions can roughly reveal the nonlinear dynamic response of risers under ISWs when the approximation for the linear analysis is relaxed to some extent.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
APEL, J. R., HOLBROOK, J. R., LIU, A. K., and TSAI, J. J. The Sulu Sea internal soliton experiment. Journal of Physical Oceanography, 15(12), 1625–1651 (1985)
OSBORNE, A. R. and BURCH, T. L. Internal solitons in the Andaman Sea. Science, 208(4443), 451–460 (1980)
BOLE, J. B., EBBESMEYER, C. C., and ROMEA, R. D. Soliton currents in the South China Sea: measurements and theoretical modeling. Offshore Technology Conference, OnePetro, Houston, USA, 2–5 (1994)
CAI, S. Q., LONG, X. M., and GAN, Z. J. A method to estimate the forces exerted by internal solitons on cylindrical piles. Ocean Engineering, 30(5), 673–689 (2003)
CAI, S. Q., WANG, S. G., and LONG, X. M. A simple estimation of the force exerted by internal solitons on cylindrical piles. Ocean Engineering, 33(7), 974–980 (2006)
XIE, J. S., XU, J. X., and CAI, S. Q. A numerical study of the load on cylindrical piles exerted by internal solitary waves. Journal of Fluids & Structures, 27(8), 1252–1261 (2011)
LU, H. B., XIE, J., XU, J., CHEN, Z., LIU, T., and CAI, S. Force and torque exerted by internal solitary waves in background parabolic current on cylindrical tendon leg by numerical simulation. Ocean Engineering, 114, 250–258 (2016)
SONG, Z. J., TENG, B., GOU, Y., LU, L., SHI, Z. M., XIAO, Y., and QU, Y. Comparisons of internal solitary wave and surface wave actions on marine structures and their responses. Applied Ocean Research, 33(2), 120–129 (2011)
GUO, H., ZHANG, L., LI, X., and LOU, M. Dynamic responses of top tensioned riser under combined excitation of internal solitary wave, surface wave and vessel motion. Journal of Ocean University of China, 12(1), 6–12 (2013)
FAN, H., LI, C., WANG, Z., XU, L., WANG, Y., and FENG, X. Dynamic analysis of a hang-off drilling riser considering internal solitary wave and vessel motion. Journal of Natural Gas Science and Engineering, 37, 512–522 (2017)
LOU, M., TONG, B., and WANG, Y. Dynamic response of steel catenary riser in an internal wave field. Journal of Offshore Mechanics & Arctic Engineering, 140(5), 051705 (2018)
HELFRICH, K. R. and MELVILLE, W. K. Long nonlinear internal waves. Annual Review of Fluid Mechanics, 38(1), 395–425 (2006)
MILES, J. W. On internal solitary waves. Tellus, 31(5), 456–462 (1979)
CHOI, W. and CAMASSA, R. Fully nonlinear internal waves in a two-fluid system. Journal of Fluid Mechanics, 396, 1–36 (1999)
MORISON, J. R., JOHNSON, J. W., and SCHAAF, S. A. The force exerted by surface waves on piles. Journal of Petroleum Technology, 2(5), 149–154 (1950)
ZHAO, W., HUANG, X., and TIAN, J. A new method to estimate phase speed and vertical velocity of internal solitary waves in the South China Sea. Journal of Oceanography, 68(5), 761–769 (2012)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest The authors declare no conflict of interest.
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 12132018, 11972352, and 12202455) and the Strategic Priority Research Program of the Chinese Academy of Sciences of China (No. XDA22000000)
Rights and permissions
Open access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Tan, D., Wang, X., Duan, J. et al. Linear analysis of the dynamic response of a riser subject to internal solitary waves. Appl. Math. Mech.-Engl. Ed. 44, 1023–1034 (2023). https://doi.org/10.1007/s10483-023-3006-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-023-3006-9