弱非均匀分层的共振和近共振internal wave三元组中的能量转移。第一部分：无界域
Energy transfer in resonant and near-resonant internal wave triads for weakly non-uniform stratifications. Part I: Unbounded domain
摘要：
本文利用多尺度分析方法，导出了一个广义的数学模型，用于计算无界区域内弱非均匀密度层结中弱非线性重力波包组成的共振和近共振三波组的振幅演化和能量交换。这种三元相互作用是高波数内波通过参数次谐波不稳定性导致海洋湍流和混合的机制之一。非均匀层结在垂直波数三波组条件下引入失谐失配，这可能强烈影响能量传输过程。我们详细研究了波包宽度、群速度、非线性耦合系数、失谐量和粘性等因素对弱变化层结中能量传递的影响。我们发现的局限性，著名的“泵波近似”，并推导出一个无量纲的数量，它可以从初始条件进行评估，可以预测的最大能量转移从主波在后期阶段。基于影响近共振波包之间能量转移的各种因素，还定义了两个附加的无量纲数。此外，我们确定了最佳的背景分层在介质中的变化分层的主要波，形成一个三重奏，没有失谐，使能量转移是最大的。最后，我们表明，即使是一个小的变化，在背景分层可以导致显着差异的能量传递过程中的波包时，它们具有相同的数量级的能量。
英文摘要：
In this paper, using multiple scale analysis we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal gravity wave packets in weakly non-uniform density stratifications in an unbounded domain in the presence of viscous and rotational effects. Such triad interactions are one of the mechanisms by which high wavenumber internal waves lead to ocean turbulence and mixing via parametric subharmonic instability. Non-uniform stratification introduces detuning - mismatch in the vertical wavenumber triad condition, which may strongly affect the energy transfer process. We investigate in detail how factors like wave-packets' width, group speeds, nonlinear coupling coefficients, detuning, and viscosity affect energy transfer in weakly varying stratification. We find limitations of the well-known 'pump-wave approximation' and derive a non-dimensional number, which can be evaluated from initial conditions, that can predict the maximum energy transferred from the primary wave during the later stages. Two additional non-dimensional numbers, based on various factors affecting energy transfer between near-resonant wave-packets have also been defined. Moreover, we identify the optimal background stratification in a medium of varying stratification for the primary wave to form a triad with no detuning so that the energy transfer is maximum. Finally, we show that even a small change in the background stratification can cause a significant difference in the energy transfer process between the wave-packets when they have the same order of magnitude of energy.
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