计算有限深度剪切流和涡度水波傅里叶系数和特性的数值方法

JangRyong Shin
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摘要

:自 1961 年以来,已开发出许多数值方法,但仍有一些问题尚未解决。本研究开发了一种数值方法来解决这些问题,并确定有限水深中带有剪切流的旋转波的系数和特性。通过引入与波长无关的坐标系,大大减少了未知常数的数量。参考深度是通过拍摄法独立计算得出的。因此,无需对波长和参考深度进行偏导数计算,从而简化了数值计算。这种方法的未知常数不到其他方法的一半,因为牛顿方法只确定系数。计算了断裂极限进行验证,结果与米歇尔公式一致。计算了水颗粒速度,结果与实验数据一致。计算了分散关系,结果与其他数值结果一致。研究了该方法的收敛性。虽然所需的序列阶数大大减少,但总误差较小,收敛速度较快。
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Numerical Method for Calculating Fourier Coefficients and Properties of Water Waves with Shear Current and Vorticity in Finite Depth
: 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.
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