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适合复杂地形的高阶Boussinesq水波方程 总被引：17，自引：4，他引：17
针对海底坡度较大(量阶为O(1))或海底曲率较大的复杂地形,建立了一个新型高阶Boussinesq水波方程.该方程可用于研究海底存在若干相互平行沙坝引起的Bragg反射问题.方程的水平速度沿水深的分布为四次多项式,色散性和变浅作用性能的精度比经典Boussinesq方程高了一阶.方程在浅水水域可以是完全非线性的. 相似文献
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建立基于四阶完全非线性Boussinesq水波方程的二维波浪传播数值模型。采用Kennedy等提出的涡粘方法模拟波浪破碎。在矩形网格上对控制方程进行离散,采用高精度的数值格式对离散方程进行数值求解。对规则波在具有三维特征地形上的传播过程进行了数值模拟,通过数值模拟结果与实验结果的对比,对所建立的波浪传播模型进行了验证。同时,为了考察非线性对波浪传播的影响,给出和上述模型具有同阶色散性、变浅作用性能但仅具有二阶完全非线性特征的波浪模型的数值结果。通过对比两个模型的数值结果以及实验数据,讨论非线性在波浪传播过程中的作用。研究结果表明,所建立的Boussinesq水波方程在深水范围内不但具有较精确的色散性和变浅作用性能,而且具有四阶完全非线性特征,适合模拟波浪在近岸水域的非线性运动。 相似文献
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Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。 相似文献
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通过改进二阶全非线性 Boussinesq 波浪方程中的色散项,得到了一组没有改变原方程的数学形式但适用于更大变化水深的新方程,其色散性能和变浅性能都比原方程有了很大改进,所适用的水深范围更大,能更好地描述从深水到近岸浅水处的波浪传播;并基于新方程建立了波浪数值模型,通过模拟波浪从浅水到深水的传播变形来验证新方程的有效性. 相似文献
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基于改进缓坡方程的波浪传播数值模拟 总被引：1，自引：1，他引：0
用变分原理导出考虑底坡一阶导数平方项和二阶曲率项影响的缓坡方程,对传统缓坡方程作了改进,提高波浪在海底地形变化剧烈、水深较浅时数值模拟精度。数值计算与已有实验室试验资料比较表明,该模型可以较好地模拟有剧烈变化的海底地形的波浪传播,比传统缓坡方程模型计算结果在精度上有明显提高。 相似文献
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海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究 总被引：3，自引：2，他引：1
浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。 相似文献
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利用Boussinesq方程,采用线性摄动展开法,求解波浪正向通过有限沙坝地形的一阶反射波解,研究比较Boussinesq类方程描述沙坝地形对波浪的反射作用的性能。通过研究反射系数并与势流理论结果及实验结果对比,发现:邹志利的高阶方程、张永刚及Madsen的方程适用的水深范围较广,而Nwogu和Peregrine的方程仅在共振点附近有效;当入射波的波长为沙坝波长两倍时,反射波产生共振效应(即Bragg反射),反射系数与沙坝振幅和水深的比值以及地形中沙坝的条数成正比;相对势流理论的共振时的反射系数,以张永刚为代表的一系列Boussinesq方程色散精度越高,适用水深范围越广,而高阶方程适用的水深很浅。 相似文献
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For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given. 相似文献
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An explicit finite difference model for simulating weakly nonlinear and weakly dispersive waves over slowly varying water depth 总被引：2，自引：0，他引：2
In this paper, a modified leap-frog finite difference (FD) scheme is developed to solve Non linear Shallow Water Equations (NSWE). By adjusting the FD mesh system and modifying the leap-frog algorithm, numerical dispersion is manipulated to mimic physical frequency dispersion for water wave propagation. The resulting numerical scheme is suitable for weakly nonlinear and weakly dispersive waves propagating over a slowly varying water depth. Numerical studies demonstrate that the results of the new numerical scheme agree well with those obtained by directly solving Boussinesq-type models for both long distance propagation, shoaling and re-fraction over a slowly varying bathymetry. Most importantly, the new algorithm is much more computationally efficient than existing Boussinesq-type models, making it an excellent alternative tool for simulating tsunami waves when the frequency dispersion needs to be considered. 相似文献
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V. A. Kalmykov 《Physical Oceanography》1998,9(2):121-127
Dispersion relations and phase velocities of surface gravity waves, with their non-linearity being considered, have been derived
numerically from an equation for a nonvortical incompressible fluid of finite depth. For all the depths being considered,
the dispersion relations are readily realized for the wavenumbers smaller than the wavenumber of the basic harmonic. Then
the acquired relations tend to increasingly deviate from the linear dispersion relations. This is the case for all the depths
and wave steepnesses under discussion. When the depth of the sea diminishes, the deviations dramatically increase in both
cases, when waves grow steeper and when the form of the wave spectrum changes from wide to narrow. This also holds for the
phase velocity of waves.
Numerical results are matched up with the experimentally derived data. For calculations, JONSWAP spectra of various width
have been used.
Translated by Vladimir A. Puchkin. 相似文献
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利用多光谱卫星遥感影像反演浅海水深是水深测量的一种重要方式。提出一种基于主成分分析的地理加权回归模型(PCA-GWR),采用WorldView-2多光谱卫星遥感影像数据,对经过数学变换后的波段反射率数据先进行主成分分析,将得到第一主成分量进行地理加权回归分析,并与双波段比值模型、多波段线性模型和地理加权回归模型(GWR)的水深反演结果进行比较。结果显示,各个反演模型反演水深值与实测水深值的相关系数r均大于0.75,其中PCA-GWR模型水深反演结果最好,r为0.96、RMSE为1.56 m、MAE为1.06 m。研究表明,PCA-GWR模型可有效去除数据变换后的冗余信息,降低数据空间非平稳性,具有较高的反演精度与可靠性,适用于浅海水深反演。 相似文献
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The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra. 相似文献
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A number of existing models for surface wave phase speeds (linear and non-linear, breaking and non-breaking waves) are reviewed and tested against phase speed data from a large-scale laboratory experiment. The results of these tests are utilized in the context of assessing the potential improvement gained by incorporating wave non-linearity in phase speed based depth inversions. The analysis is focused on the surf zone, where depth inversion accuracies are known to degrade significantly. The collected data includes very high-resolution remote sensing video and surface elevation records from fixed, in-situ wave gages. Wave phase speeds are extracted from the remote sensing data using a feature tracking technique, and local wave amplitudes are determined from the wave gage records and used for comparisons to non-linear phase speed models and for non-linear depth inversions. A series of five different regular wave conditions with a range of non-linearity and dispersion characteristics are analyzed and results show that a composite dispersion relation, which includes both non-linearity and dispersion effects, best matches the observed phase speeds across the domain and hence, improves surf zone depth estimation via depth inversions. Incorporating non-linearity into the phase speed model reduces errors to O(10%), which is a level previously found for depth inversions with small amplitude waves in intermediate water depths using linear dispersion. Considering the controlled conditions and extensive ground truth, this appears to be a practical limit for phase speed-based depth inversions. Finally, a phase speed sensitivity analysis is performed that indicates that typical nearshore sand bars should be resolvable using phase speed depth inversions. However, increasing wave steepness degrades the sensitivity of this inversion method. 相似文献
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Based on the classical Boussinesq model by Peregrine [Peregrine, D.H., 1967. Long waves on a beach. J. Fluid Mech. 27 (4), 815–827], two parameters are introduced to improve dispersion and linear shoaling characteristics. The higher order non-linear terms are added to the modified Boussinesq equations. The non-linearity of the Boussinesq model is analyzed. A parameter related to h/L0 is used to improve the quadratic transfer function in relatively deep water. Since the dispersion characteristic of the modified Boussinesq equations with two parameters is only equal to the second-order Padé expansion of the linear dispersion relation, further improvement is done by introducing a new velocity vector to replace the depth-averaged one in the modified Boussinesq equations. The dispersion characteristic of the further modified Boussinesq equations is accurate to the fourth-order Padé approximation of the linear dispersion relation. Compared to the modified Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling characteristic of the equations has higher accuracy from shallow water to deep water. 相似文献
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Practical modified scheme of linear shallow-water equations for distant propagation of tsunamis 总被引：2，自引：0，他引：2
A simple but practical numerical model describing a distant propagation of tsunamis is newly proposed by introducing an additional term to the existing modified scheme. The numerical dispersion of the proposed model is manipulated to replace the physical dispersion of the linear Boussinesq equations without any limitation. The new model developed in this study is applied to propagation of a Gaussian hump over a constant water depth and the predicted free surface displacements are compared with available analytical solutions. A very reasonable agreement is observed. 相似文献