## Abstract

We study Lyapunov exponents of tracers in compressible homogeneous isotropic turbulence at different turbulent Mach numbers M_{t} and Taylor-scale Reynolds numbers R e λ . We demonstrate that statistics of finite-time Lyapunov exponents have the same form as that in incompressible flow due to density-velocity coupling. The modulus of the smallest Lyapunov exponent λ_{3} provides the principal Lyapunov exponent of the time-reversed flow, which is usually wrong in a compressible flow. This exponent, along with the principal Lyapunov exponent λ_{1}, determines all the exponents due to 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 λ 1 τ η , where τ η is the Kolmogorov timescale, is a decreasing function of M_{t}. Its dependence on R e λ is weak when the driving force is solenoidal, while it is an increasing function of R e λ when the solenoidal and compressible forces are comparable.

Original language | English |
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Article number | 125114 |

Journal | Physics of Fluids |

Volume | 35 |

Issue number | 12 |

DOIs | |

State | Published - 1 Dec 2023 |

## ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes