Effects of the sound speed vertical profile on the evolution of hydroacoustic waves
Effects of the sound speed vertical profile on the evolution of hydroacoustic waves
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DOI：
10.1017/jfm.2019.907
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发表时间：
2019-11
影响因子：
3.7
通讯作者：
Simone Michele;E. Renzi
中科院分区：
文献类型：
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作者：
Simone Michele;E. Renzi
我们提出了一种新的分析模型，其特征在于在弱可压缩流体中的声速剖面的深度变化的水声波的演变。使用微扰展开的声速的小的垂直变化，我们推导出一个新的二阶速度势的表达式，并表明，这种解决方案不存在的情况下，均匀的声速。在三阶，我们推导出一个线性薛定谔方程，该方程控制大长度和时间尺度下波包线的演化，其中包含取决于声速分布的新项。我们表明，广义声速垂直剖面的水声信号的频率可以增加或减少相对于恒定的声速的情况下，取决于配置文件。这对波列包络的速度有实质性的影响。我们的研究结果表明，需要扩展现有的模型，忽略了声速的垂直变化，特别是在海啸预警的应用。
We present a novel analytical model for the evolution of hydroacoustic waves in weakly compressible fluids characterised by depth variations of the sound speed profile. Using a perturbation expansion in terms of the small vertical variation of the sound speed, we derive a novel expression for the second-order velocity potential and show that this solution does not exist in the case of homogeneous sound speed. At the third order, we derive a linear Schrödinger equation governing the evolution of the wave envelope for large length and time scales, which features new terms depending on the sound speed distribution. We show that for generalised sound speed vertical profiles the frequency of the hydroacoustic signal can increase or decrease with respect to the constant sound speed case, depending on the profile. This has substantial implications on the speed of the wavetrain envelope. Our findings suggest the need to extend existing models that neglect the sound speed vertical variation, especially in view of applications to tsunami early warning.