Nonlinear Wave Dynamics in Fluid Flows

提案ID：0604416PI：Triantassillos R Akylas机构：麻省理工学院标题：流体流动中的非线性波动力学摘要将用渐近和数值方法研究流体介质中非线性波传播的两个问题：完全定域自由面和界面孤立波的非定常动力学，通常称为“块”；以及密度分层流体中内重力波包与高模长波的共振非线性相互作用。最近的理论工作提出了一种新的重力-毛细管团块，有实验证据表明，这些团块可以由吹过水面的风驱动。虽然以前的研究集中在稳定团块的存在上，但本次调查将解决这样的团块如何由一般初始条件和外部强迫产生的问题。第二个要解决的问题是共振机制，通过这种机制，三维内重力波包可以将能量转移到斜向传播的高模长波，从而有助于产生更小的垂直尺度，并增强背景平均流场的精细垂直结构(密度、速度等)。重力-毛细管团可能对海洋表面的小尺度粗糙度有很大贡献。因此，了解它们的动力学可能有助于解释海洋表面的卫星图像。此外，由于负载在冰面上移动，预计漂浮的冰盖上也会出现类似的结块，这在几个应用中都是一个问题，包括在漂浮的冰上使用车辆。另一方面，揭示分层流体中的内部重力波如何有助于背景流的精细垂直结构，是理解海洋中如何发生混合的一个重要问题，而混合又被认为会影响气候动态、生物生产力和废物处理。

Proposal ID: 0604416PI: Triantaphyllos R AkylasInstitution: Massachusetts Institute of TechnologyTitle: Nonlinear Wave Dynamics in Fluid FlowsABSTRACTTwo problems of nonlinear wave propagation in fluid media will be studied by asymptotic and numerical methods: the unsteady dynamics of fully localized free-surface and interfacial solitary waves, often referred to as "lumps"; and resonant nonlinear interactions of internal gravity wavepackets with higher-mode long waves in a density-stratified fluid. Recent theoretical work has brought out a new class of gravity-capillary lumps, and there is experimental evidence that these lumps can be driven by wind blowing over water. While previous studies have focused on the existence of steady lumps, the present investigation will tackle the question of how such lumps may arise from general initial conditions and by external forcing. The second problem to be addressed is a resonance mechanism by which three-dimensional internal gravity wavepackets can transfer energy to higher-mode obliquely propagating long waves, thus contributing to the generation of smaller vertical scales and enhancing the fine vertical structure of the background mean flow fields (density, velocity, etc).Gravity-capillary lumps are likely to contribute significantly to the small-scale roughness of the ocean surface. Understanding their dynamics may thus prove useful in interpreting satellite images of the ocean surface. Moreover, similar lumps are expected to arise on floating ice sheets due to loads moving on top of the ice, a problem with several applications, including the use of vehicles on floating ice. Shedding light, on the other hand, on how internal gravity waves in a stratified fluid contribute to the fine vertical structure of the background flow is an important issue in understanding how mixing occurs in the ocean, which in turn is believed to affect climate dynamics, biological productivity and waste disposal.