论文标题
剪切流量线性化的两相流体界面问题的不稳定性和光谱
Instability and spectrum of the linearized two-phase fluids interface problem at shear flows
论文作者
论文摘要
本文与在两个流体中的一对单调剪切流处线性性线性的2-DIM两相界面欧拉方程有关。我们扩展了霍华德的半圆定理，并研究线性化欧拉系统的特征值分布。在某些条件下，在整个复杂平面中，每个固定波数$ k \ in \ mathbb {r} $恰好有两个特征值。我们为剪切流速的某些边界值引起的光谱不稳定提供了足够的条件。典型的模式是洋气系统，其中流体的密度比足够小。我们为海洋空系统中特定类别的剪切流提供了特征值分布的完整图片。
This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard's Semicircle Theorem and study the eigenvalue distribution of the linearized Euler system. Under certain conditions, there are exactly two eigenvalues for each fixed wave number $k\in \mathbb{R}$ in the whole complex plane. We provide sufficient conditions for spectral instability arising from some boundary values of the shear flow velocity. A typical mode is the ocean-air system in which the density ratio of the fluids is sufficiently small. We give a complete picture of eigenvalue distribution for a certain class of shear flows in the ocean-air system.
