Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence

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 λ₃ 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 λ₁, 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.