Numerical Method for Calculating Fourier Coefficients and Properties of Water Waves with Shear Current and Vorticity in Finite Depth
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.
Abstract
Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.
참고문헌 (16)
- Baddour, R. E., "The rotational flow of finite amplitude periodic water waves on shear currents", Applied Ocean Research, 20(3), pp.163~171 (1988)[DOI]
- Chaplin, J. R., "Developments of stream-function wave theory", Coastal Engineering, 3, pp.179~205 (1979)[DOI]
- Chappelear, J. E., "Direct numerical calculation of wave properties", Journal of Geophysical Research, 66(2), pp.501~508 (1961)[DOI]
- Cokelet, E. D., "Steep gravity waves in water of arbitrary uniform depth. Philosophical Transaction of the Royal Society of London. Series A", Mathematical and Physical Sciences, 286(1335), pp.183~230 (1977)[DOI]
- Dean, R. G., "Stream function representation of nonlinear ocean waves", Journal of Geophysical Research, 70(18), pp.4561~4572 (1965)[DOI]
- Dean, R. G., "Water wave mechanics for engineers and scientists", pp.368~ (1984), Prentice-Hall, Inc
- Fenton, J. D., "The numerical solution of steady water wave problems", Computers & Geosciences, 14(3), pp.357~368 (1988)
- Fenton, J. D., "The Sea, Vol. 9: Ocean Engineering Science, Part A" (1990), Wiley
- Le Méhauté, B, "Shallow water waves:A comparison of theories and experiment", Proceedings of 11th Conference Coastal Engineering, 1, pp.86~107 (1968), ASCE
- Rienecker, M. M., "A fourier approximation method for steady water waves", Journal of Fluid Mechanics, 104, pp.119~137 (1981)[DOI]
- Shin, J., "An analytical approximation and a numerical method to progressing periodic water waves on irrotational flow over a horizontal bed", The 28th ISOPE Conference (2018)
- Shin, J., "A regression analysis result for water waves on irrotational flow over a horizontal bed", International Journal of Offshore and Polar Engineering, 29(4), pp.461~466 (2019)[DOI]
- Shin, J, "Solution for water waves with a shear current and vorticity over a flat bed", International Journal of Offshore and Polar Engineering, 32(4), pp.418~423 (2022)[DOI]
- 신장용, "Newton's Method to Determine Fourier Coefficients and Wave Properties for Deep Water Waves", 한국해양공학회지, 37(2), pp.49~57 (2023), 한국해양공학회[DOI]
- Tao, L., "Nonlinear progressive waves in water of finite depth-an analytic approximation", Coastal Engineering, 54(11), pp.825~834 (2007)[DOI]
- Vanden-Broeck J. M., "Numerical computation of steep gravity waves in shallow water", Physic and Fluids, 22(10), pp.1868~1871 (1979)[DOI]