Nonlinear Wave Dynamics in Fluid Flows

提案ID：0604416 PI：Triantaphyllos R Akylas研究机构：马萨诸塞州理工学院题目：流体中的非线性波动力学摘要本文将用渐近和数值方法研究流体介质中的两个非线性波动问题：完全局部化的自由表面和界面孤立波的非定常动力学，通常被称为“块”;以及密度分层流体中重力内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类新的重力毛细管块，有实验证据表明，这些块可以由风吹过水面驱动。虽然以前的研究都集中在稳定的肿块的存在，目前的调查将解决这样的肿块可能会出现一般的初始条件和外部强迫的问题。要解决的第二个问题是一个共振机制，三维内部重力波包可以传递能量的高模式斜向传播的长波，从而有助于产生较小的垂直尺度和增强精细的垂直结构的背景平均流场（密度，速度等）。重力毛细管块很可能会显着贡献的小尺度粗糙度的海洋表面。因此，了解它们的动态可能有助于解释海洋表面的卫星图像。此外，由于在冰面上移动的负载，预计在浮冰上也会出现类似的肿块，这是几种应用的问题，包括在浮冰上使用车辆。另一方面，阐明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，是理解海洋中混合如何发生的一个重要问题，这反过来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.