Fluctuations of Lyapunov Exponents in homogeneous and isotropic turbulence

Abstract

In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite time Lyapunov exponent (FTLE) and its relation to Reynolds number, lattice size and the choice of the steptime used to compute the Lyapunov exponents. The results show that using the FTLE method produces Lyapunov exponents that are remarkably stable under the variation of the steptime and lattice size. Furthermore, it reaches such stability faster than other characteristic quantities such as energy and dissipation rate. These results remain even if the steptime is made arbitrarily small. A discrepancy is also resolved between previous measurements of the dependence on the Reynolds number of the Lyapunov exponent. The signal produced by different variables in the steady state is analyzed and the self decorrelation time is used to determine the run time needed in the simulations to obtain proper statistics for each variable. Finally, a brief analysis on MHD flows is also presented, which shows that the Lyapunov exponent is still a robust measure in the simulations, although the Lyapunov exponent scaling with Reynolds number is significantly different from that of magnetically neutral hydrodynamic fluids.

arXiv comment22 pages, 22 figures

References in corpus (19)

• Predictability: a way to characterize Complexity
• Predictability in the large: an extension of the concept of Lyapunov exponent
• Mixing structures in the Mediterranean Sea from Finite-Size Lyapunov Exponents
• Lagrangian statistics of particle pairs in homogeneous isotropic turbulence
• Chaotic stirring by a mesoscale surface-ocean flow
• Predictability of large-scale atmospheric motions: Lyapunov exponents and error dynamics
• Multi-particle dispersion in fully developed turbulence
• Chaos and predictability of homogeneous-isotropic turbulence
• Chaotic properties of a turbulent isotropic fluid
• Energy transfer and dissipation in forced isotropic turbulence
• Scaling of Lyapunov Exponents in Homogeneous Isotropic Turbulence
• Detection of coherent structures in photospheric turbulent flows
• Predictability of the energy cascade in 2D turbulence
• Lagrangian coherent structures and plasma transport processes
• Supergranular turbulence in a quiet Sun: Lagrangian coherent structures
• Sudden relaminarisation and lifetimes in forced isotropic turbulence
• Stochastically perturbed bred vectors in multi-scale systems
• Chaotic behavior of Eulerian MHD turbulence
• Statistics of finite scale local Lyapunov exponents in fully developed homogeneous isotropic turbulence

Cited by in corpus (5)

• The production of uncertainty in three-dimensional Navier-Stokes turbulence
• Chaotic measure of the transition between two and three dimensional turbulence
• Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles
• Eulerian-Lagrangian scaling of the Lyapunov exponent in homogeneous turbulence
• Critical transition to a non-chaotic regime in isotropic turbulence