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Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence by Yu, Haijun; Fouxon, Itzhak; Wang, Jianchun; Li, Xiangru; Yuan, Li; Mao, Shipeng; Mond, Michael is a scholarly article available to read on EtoBox.

What is Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence about?

We study Lyapunov exponents of tracers in compressible homogeneous isotropic turbulence at different turbulent Mach number $M_t$ and Taylor-scale Reynolds number $Re_\lambda$. We demonstrate that statistics of finite-time Lyapunov exponents have the same form as in incompressible flow due to density-velocity coupling. Modulus of the smallest Lyapunov exponent $\lambda_3$ provides the principal Lyapunov exponent of the time-reversed flow, which usually is wrong in a compressible flow. This exponent, along with the principal Lyapunov exponent $\lambda_1$, determines all the exponents due to the vanishing of the sum of all Lyapunov exponents. Numerical results by high-order schemes for solving the Navier-Stokes equations and tracking particles verify these theoretical predictions. We found that: 1) The largest normalized Lyapunov exponent $\lambda_1 \tau_\eta$, where $\tau_\eta$ is the Kolmogorov time scale, is a decreasing function of $M_t$. Its dependence on $Re_\lambda$ is weak when the driving force is solenoidal, while it is an increasing function of $Re_\lambda$ when the solenoidal and compressible forces are comparable. Similar facts hold for $|\lambda_3|$, in contrast with wel

Author

Yu, Haijun; Fouxon, Itzhak; Wang, Jianchun; Li, Xiangru; Yuan, Li; Mao, Shipeng; Mond, Michael

Published

2023

Language

EN