可压缩各向同性湍流统计特性的进一步研究

可压缩湍流在高超声速飞行器设计、超声速燃烧、惯性约束核聚变和超新星爆炸等工程问题和自然现象中都起到重要的作用。本项目在已有的研究基础上，进一步研究可压缩各向同性湍流在不同湍流马赫数条件下的速度谱和压力谱、动能和内能的多尺度传输、小尺度流动结构和间歇性等问题。通过亥姆霍兹分解方法，研究可压缩各向同性湍流场的剪切部分和胀压部分的多尺度统计性质。在弱可压缩的情况下，将胀压部分进一步分解为声波模态和伪声模态，并研究声波模态和伪声模态的多尺度统计性质。在强可压缩的情况下，研究微激波和大激波对可压缩各向同性湍流场的统计性质的影响。为研究复杂条件下的可压缩湍流的流动机理和发展可靠的可压缩湍流模型提供理论支持。

Compressible turbulence is of fundamental importance to a number of industrial applications and natural phenomena, including the design of hypersonic aircraft, supersonic combustion, inertial confinement fusion and supernova explosion. On the basis of previous researches, the present proposal aims to further study statistics of compressible isotropic turbulence at different turbulent Mach numbers, including spectra of velocity and pressure, multi-scale transfer of kinetic energy and internal energy, small scale structures and intermittency. Multi-scale statistics of the solenoidal and compressible components of compressible isotropic turbulence are investigated by Helmholtz decomposition method. For weakly compressible turbulence, the compressible component of turbulent flow is further decomposed into an acoustic component and a pseudo-sound component. Multi-scale statistics of the acoustic and pseudo-sound components of turbulent flow are investigated. For highly compressible turbulence, the effects of eddy shocklets and large-scale shock waves on the statistics of compressible isotropic turbulence are investigated. This proposal will provide theoretical support for study of complex compressible turbulent flows and development of reliable models of compressible turbulence.