Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence

不可压缩流体中turbulence的临界理论

Critical theory of turbulence in incompressible fluids

纳维-斯托克斯方程描述了不可压缩流体的确定性演化。研究了随机初始条件对该方程解的影响。它表明，有一个红外稳定的固定点内的粘度膨胀，约$d_c=4,$与特定的选择。通常粘性流体的行为作为关于该固定点的相关扰动而获得，通常粘度用作$T-T_c.$

Dual Scale Invariance Spontaneous Symmetry Breaking and Turbulence

We discuss spontaneous symmetry breaking of dual (space and time) scale invariance in the context of turbulence.

New equation for lagrangian incompressible fluid flows applied to turbulence

Theoretical developments in the field of Lagrangian turbulence are made difficult by the fact that equations governing the evolution of lagrangian flows are implicit contrary to eulerian flows. In this article, an {\it exact} explicit equation for incompressible lagrangian fluid flows at high-Reynolds number is constructed. The method to arrive at the equation of motion and the proof that it describes the motion of an incompressible fluid are provided. A truncated version of this new equation is used to show how the lagrangian turbulent spectrum ($E_\mathrm{lag}(ω)$) could be inferred. This ex…

On Scale Versus Conformal Symmetry in Turbulence

We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally covariant, with the only possible exception being the direct enstrophy cascade in two space dimensions. We argue that the same conclusions hold for compressible non-relativistic turbulence as well as for relativistic turbulence. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operators. We consid…

相对论流体力学Turbulence中的精确标度关系

Exact Scaling Relations In Relativistic Hydrodynamic Turbulence

我们考虑一般类耗散流体动力学方程中湍流的稳态统计，其中波动由集中在大尺度上的随机源维持。众所周知，在某些特殊情况下，如非相对论不可压湍流，一个关联函数的Kolmogorov型精确标度关系成立。我们表明，所有这样的标度关系遵循从电流密度关联函数的一般关系。推导过程不需要能量级联图，并表明对不可压缩湍流的Kolmogorov关系的传统解释可能会产生误导。利用这一点，我们推导出精确的缩放结果可压缩湍流在相对论流体力学，这减少了在慢运动限制的Kolmogorov关系。我们讨论了实验结果的影响。

Turbulence and Random Geometry

We outline our proposal for a field theory description of steady state incompressible fluid turbulence at the inertial range of scales in a general number of space dimensions. The theory consists of a Kolmogorov linear scaling mean field theory dressed by a Nambu-Goldstone dilaton mode that induces a random measure on the inertial range. We derive a KPZ-type formula for the anomalous scalings of the velocity structure functions, the velocity gradients and the local energy dissipation, and relate the dimensionless intermittency parameter to the boundary conformal anomaly.