scholarly journals An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit

Wave Motion ◽  
2008 ◽  
Vol 45 (6) ◽  
pp. 835-845 ◽  
Author(s):  
Tae-Hwa Jung ◽  
Kyung-Duck Suh
Keyword(s):  
Analytical Solution ◽  
Long Waves ◽  
Mild Slope Equation

Low-Frequency Oscillations Within the Hambantota Port During the Southwest Monsoon, 2019

2020 ◽  
Author(s):  
Zhenjun Zheng ◽  
Xiaozhou Ma ◽  
Xuezhi Huang ◽  
Yujin Dong ◽  
Guohai Dong
Keyword(s):  
Wind Waves ◽  
Low Frequency ◽  
Southwest Monsoon ◽  
Long Waves ◽  
Frequency Wave ◽  
Low Frequency Oscillations ◽  
Mild Slope Equation ◽  
Spectrum Density ◽  
Forcing Mechanisms ◽  
Low Frequency Waves

Abstract Long waves with periods greater than tens of seconds propagating into a harbor may be trapped and significantly amplified, thereby resulting in detrimental effects on port operations. The water surface elevation in the Hambantota Port, Sri Lanka, was measured to investigate the low-frequency oscillations and their forcing mechanisms. Results show that the port is protected well from short waves with periods less than 30 s; however, the protection against long waves with periods larger than 30 s is inadequate. The spectral analyses identified four dominant periods within the low-frequency wave range. Modal analysis based on the extended mild-slope equation shows that the measured spectrum density for some dominant periods is low because the measurement point is close to the corresponding modal lines. Correlation analysis shows that low-frequency oscillations inside the Hambantota Port are excited directly by the low-frequency waves contained within the incident waves. The low-frequency waves outside the Hambantota Port are generated from the higher-frequency gravity waves (swell and wind waves) due to nonlinear interactions. Empirical formula is adopted to estimate the low-frequency wave height outside the Hambantota Port.

A Series Solution for Wave Scattering by a Circular Island on a Shoal Based on the Mild-Slope Equation

2012 ◽  
Vol 28 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Y.-M. Cheng ◽  
C.-T. Chen ◽  
L.-F. Tu ◽  
J.-F. Lee
Keyword(s):  
Analytical Solution ◽  
Wave Scattering ◽  
Present Method ◽  
Series Solution ◽  
Shallow Water Equation ◽  
Variable Coefficients ◽  
Fourier Cosine ◽  
Mild Slope Equation ◽  
Scattering Field ◽  
Run Up

ABSTRACTA series solution based on the mild-slope equation is produced in this study of wave scattering produced by a circular cylindrical island mounted on an axi-symmetrical shoal. The solution is presumed to be a Fourier cosine expansion with variable coefficients in the radial direction on account of the symmetric scattering field, which translates the original 2-D boundary-value problem to a 1-D one in which an ordinary differential equation is in effect treated. Approximations to the coefficients of the governing equation with the Taylor expansions enable the use of the Frobenius method, and consequently the solution is obtained in a combined Fourier and power series. For verification, the present method is mainly compared with Zhu and Zhang's [1] analytical solution of the linearised shallow water equation for a conical shoal, and with a different analytical solution of the mild-slope equation developed by Liu et al. [2] for a paraboloidal shoal. Fine agreements are achieved. The present method is then used to investigate the variation pattern of the wave run-up when the shoal profile varies from conical to paraboloidal, and some interesting phenomena are observed.

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