可压缩槽道湍流的多模态分解和多尺度分析

可压缩湍流在超声速航空飞行器设计、受控热核反应、超新星爆炸等各类工程问题和自然现象中起到关键的作用。与不可压缩湍流相比，可压缩湍流具有更加丰富的流动结构，包括旋涡、声波、激波、膨胀波。本项目主要通过直接数值模拟研究可压缩槽道湍流在不同马赫数和不同雷诺数情况下的流动机理。研究内容包括：速度、密度、温度和压力等重要物理量的谱和小尺度结构，以及动能和热力学量的多尺度传输。采用亥姆霍兹分解，重点研究速度场的胀压部分的谱和小尺度结构，以及动能的胀压部分的多尺度传输。然后通过对速度场的胀压部分做进一步分解，研究速度场的声波模态和伪声模态的空间结构和统计特性。通过本项目的实施，系统地了解可压缩槽道湍流的多模态结构和多尺度行为，为研究复杂条件下的可压缩湍流的流动机理提供参考依据。

Compressible turbulence plays an important role in many industrial problems and natural phenomena, including the development of supersonic aircraft, controlled thermonuclear reaction, explosion of supernova. As compared to the situation of incompressible turbulence, there are more types of flow structures in compressible turbulence, including vortex, acoustic waves, shock waves, expansion waves. In this proposal, we perform direct numerical simulations to study the properties of compressible turbulent channel flow at different Mach numbers and different Reynolds numbers. The contents of this proposal include: spectra and small-scale structures of velocity, density, temperature and pressure, and multi-scale transfer of kinetic energy and thermodynamic variables. By Helmholtz decomposition, our study is focused on the spectrum and small-scale structures of compressible component of the velocity, and the multi-scale transfer of compressible component of kinetic energy. By further performing decomposition on the compressible component of the velocity, we investigate the spatial structures and statistical properties of the acoustic mode and the pseudo-sound mode of the velocity. Through the implementation of this project, we seek to systematically understand the multi-mode structures and multi-scale behaviors of compressible turbulent channel flow, and provide the basis for the further study of the properties of complex compressible turbulence.