Statistical Law and Energy Transfer Mechanism in Turbulence

1.结果表明，在均匀各向同性湍流中，通过试相互作用的能量传递在惯性范围内是局部的，而在耗散范围内是非局部的。前者与Kolmogorov理论相一致，而后者可能对湍流模拟提供有益的建议。从涡量矢量动力学的角度分析了均匀剪切湍流中各种涡结构的产生、发展和破裂。阐明了平均流、平流、非线性自相互作用和粘性项在能量传递过程中的相对重要性.求解了两旋转球间边缘对流状态下的局域结构。随着Reyleigh数的增加，出现了一个新的分支分支.通过直接数值模拟，实现了一组具有强螺旋度的泰勒柱.通过对涡量场和密度场的分析，探讨了受迫可压缩湍流中能量传递的机理。利用Helmholtz分解将动能分解为可压缩部分和转动部分。定量评价了平流项、斜压项和粘性项在这些分量与内能之间能量交换中的相对重要性.利用弱非线性理论阐明了Rayleigh-Benard对流斑图形成的机制.用基本解之间的相互作用解释了复杂Ginzburg-Landau湍流中的统计规律。

1. It was found in the homogeneous isotropic turbulence that the energy transfer through the trial interaction is local in the inertial range but it is nonlocal in the dissipation range. The former agrees with the Kolmogorov theory while the latter may give a useful suggestion to turbulence modelling. The generation, development and breakdown of various vortical structures in a uniformly sheared turbulence were analyzed in terms of the dynamics of the vorticity vector. The relative importance of the mean flow, advection, nonlinear selfinteraction and viscous terms in the energy transfer process was clarified.2. The localized structure in the marginal convection state between two rotating spheres was solved. A new bifurcation branch was found as the Reyleigh number is increased. A bunch of Taylor columns with strong helicity were realized by the direct numerical simulation.3. The mechanism of the energy transfer in a forced compressible turbulence was investigated by analysing the vorticity and density fields. The kinetic energy was divided into the compressible and rotational parts by employing the Helmholtz decomposition. The relative importance of the advection, the baroclinic and the viscous terms in the energy exchange between these components and internal energy was evaluated quantitatively.4. The mechanism of pattern formation in a Rayleigh-Benard convection was clarified by the weakly nonlinear theory.5. The statistical law in the complex Ginzburg-Landau turbulence was explained by the interaction between the fundamental solutions.