Interaction between convective and elliptical instabilities in rotating fluids

湍流对流是自然界中普遍存在的流体动力学过程，发生在工业应用以及许多恒星和行星的内部。椭圆形流体流线对于称为椭圆形不稳定性的一般流体动力学不稳定性是不稳定的，椭圆形不稳定性可以驱动惯性波变得不稳定并且潜在地导致湍流。这两种不稳定性在旋转流体中的相互作用以前没有被详细研究过，但人们认为这两种不稳定性在几种应用中同时发生，包括潮汐变形行星。本项目将使用分析和数值方法研究椭圆不稳定性和对流之间的基本相互作用。特别是，两个不稳定性的非线性结果将进行数值模拟，以确定如何湍流传输和由此产生的流量，由于每个不稳定性的存在下，其他的影响。这项研究将有助于我们理解两种不同的流体动力学不稳定性和由此产生的湍流的一般相互作用，但它也有具体的应用潮汐变形行星在天体物理学。

Turbulent convection is a ubiquitous fluid dynamical process in nature, occurring in industrial applications as well as in the interiors of many stars and planets. Elliptical fluid streamlines are unstable to a generic fluid dynamical instability referred as the elliptical instability, which can drive inertial waves to become unstable and potentially lead to turbulence. The interaction of these two instabilities in rotating fluids has not been studied in detail previously, and yet both are believed to occur together in several applications, including in tidally-deformed planets. This project will study the fundamental interaction between elliptical instabilities and convection, using both analytical and numerical approaches. In particular, the nonlinear outcome of the two instabilities will be simulated numerically with the goal to determine how the turbulent transport and resulting flows due to each instability are affected by the presence of the other. This study will benefit our understand of the general interaction of two distinct fluid dynamical instabilities and the resulting turbulence, but it also has specific applications to tidally-deformed planets in astrophysics.