Freak waves over nonuniform depth with different slopes
Freak waves over nonuniform depth with different slopes
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具有不同斜率的不均匀深度的异常波
DOI：
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发表时间：
2016
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通讯作者：
Shirin Fallahi
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作者：
Shirin Fallahi
以往的实验和数值研究都表明，波浪从深水经过斜坡传播到浅水时存在两种不同的状态。对于浅水和/或深度突变，在底坡浅边附近可能存在极端波的局部最大值，而对于深水和/或轻度深度过渡，则不存在极端波的局部最大值。标准的简化波模型，特别是非线性Schrödinger非均匀深度方程，不能解释这两种状态之间的过渡。在此背景下，本文推导了一个改进的非均匀深度NLS方程，以便更好地表示任意深度的突变水深，希望这可以使NLS模型解释以前的实验观测结果。本文导出的NLS方程以时空演化形式表示，既适用于夜间，也适用于夜间深度。在有限的深度条件下，时空演化方程的稳定性分析表明，当波数k满足kh > 1.363时，均匀深度h上的波列是不稳定的，否则是稳定的。此外，我们在稳定性分析中的研究表明，深水结果的渐近行为再现了深水结果。
Both previous experimental and numerical studies revealed that there are two di erent regimes when waves propagate from deep water over a slope to shallow water. For shallow water and/or abrupt depth transition there can be a local maximum of extreme waves near the shallow edge of the bottom slope, while for deep water and/or mild depth transition no such local maximum of extreme waves is found. Standard simpli ed wave models, in particular nonlinear Schrödinger equations for nonuniform depth, have not been able to account for the transition between these two regimes. With this background, in this thesis we derive a modi ed NLS equation for nonuniform depth in order to better represent abrupt bathymetry of arbitrary depth, in the hope that this may allow NLS models to account for previous experimental observations. The NLS equation derived in this thesis is expressed in space and time evolution forms which can be used for both nite and in nite depth. In the limit of nite depth, the stability analysis for both space and time evolution equations indicates that wave trains on water of uniform depth, h, are unstable if the wavenumber, k, satis es kh > 1.363, but they are otherwise stable. Furthermore, our investigation in stability analysis shows that the asymptotic behavior of the nite-depth results reproduce the deep-water results.