Mathematical Sciences: Nonlinear Wave Phenomena in Hydrodynamics

这项研究工作涉及当前应用数学中的几个感兴趣的主题，特别是与连续介质力学中的非线性现象相关的那些主题。重点介绍了用于描述水动力学中的非线性波浪和稳定性特性的物理现象和数学理论。具体地说，将对一种新的非线性稳定性理论方法进行系统的研究。这一发展强调了平均流动/一次谐波相互作用的重要性，而不是更常见的涉及高次谐波产生的相互作用，作为剪切流中三维扰动演变的驱动机制。已经审议了一些特殊情况，人们认为，这种做法可能会对广泛的不稳定问题产生重要后果。私隐专员公署打算考虑若干进一步的申请，以便全面评估其适用范围。

This research effort is concerned with several topics of current interest in applied mathematics, especially those associated with nonlinear phenomena in continuum mechanics. Emphasis is placed on both the physical phenomena and the mathematical theories used to describe nonlinear wave and stability characteristics in hydrodynamics. Specifically, a systematic study will be made of a new theoretical approach to nonlinear stability. This development emphasizes the importance of mean flow/first harmonic interactions, rather than the more usual ones that involve the generation of higher harmonics, as the driving mechanism underlying the evolution of 3-D disturbances in shear flows. Some special cases have already been considered and it is believed that this approach could have important consequences to a broad range of instability problems. The PI intends to consider a number of further applications so that the range of its applicability can be fully assessed.