Dynamics of Nonlinear Internal Wave Beams in Stratified Flows

Akylas DMS-1107335对非线性内波束在密度分层流体中的传播和相互作用进行了理论研究。这些是来自内部重力波运动的非各向同性的基本时间谐扰动。重点关注以下具体问题：(1)波束对短尺度亚谐扰动的不稳定性，这是最近的实验和数值研究表明的一个重要的击穿和湍流产生机制；(2)非线性光束从倾斜边界的三维反射，包括当入射到水平方向的角度与边界斜率几乎匹配时发生的近临界反射的情况；(3)非线性光束的三维碰撞和相关的能量散射。这些物理现象是通过建立数学模型来解决的，这些数学模型用渐近和数值方法进行分析。将理论预测与相关的实验室实验和现场观测结果进行了比较。内波束在海洋、湖泊和大气等天然流体中发挥着重要作用，这些流体的密度分层主要是由温度变化引起的；由于雷暴，以及由于潮流与大陆架和海底地形的相互作用，在大气中以及在海洋中都观察到了内波束。该项目的动机是需要了解负责将能量从潮汐产生的内波束转移到深海混合的机制并对其进行量化建模，这反过来又会影响海洋环流、气候变化、污染物扩散和营养循环。此外，该研究结果在地球物理流体动力学和应用数学中具有基础价值。

AkylasDMS-1107335 A theoretical investigation is made of the propagation and interactions of nonlinear internal wave beams in density-stratified fluids. These are fundamental time-harmonic disturbances that derive from the non-isotropic nature of internal gravity-wave motion. Attention is focused on the following specific problems: (i) the instability of wave beams to short-scale subharmonic disturbances, a prominent mechanism of breakdown and turbulence generation according to recent experimental and numerical studies; (ii) three-dimensional reflections of nonlinear beams from a sloping boundary, including the case of near-critical reflection, that occurs when the angle of incidence to the horizontal nearly matches the boundary slope; (iii) three-dimensional collisions of nonlinear beams and the associated scattering of energy. These physical phenomena are tackled by formulating mathematical models that are analyzed by asymptotic and numerical methods. The theoretical predictions are compared against related laboratory experiments and field observations. Internal wave beams play an important part in natural fluid bodies, like the oceans, lakes, and the atmosphere, where density stratification is mainly caused by temperature variations; there are numerous observations of internal wave beams in the atmosphere due to thunderstorms, as well as in oceans due to the interaction of tidal currents with the continental shelf and sea-floor topography. This project is motivated by the need to understand and model quantitatively the mechanisms responsible for the transfer of energy from tide-generated internal wave beams to deep-ocean mixing, which in turn affects ocean circulation, climate change, pollutant dispersal, and nutrient cycles. Moreover, the results of this study would be of basic value in geophysical fluid dynamics and applied mathematics.