Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence

Yu，Haijun1,2; Fouxon，Itzhak3,4; Wang，Jianchun5; Li，Xiangru1,2; Yuan，Li1,2; Mao，Shipeng1,2; Mond，Michael3

2023-12-01

10.1063/5.0175016

Physics of Fluids   影响因子和分区

1070-6631

1089-7666

We study Lyapunov exponents of tracers in compressible homogeneous isotropic turbulence at different turbulent Mach numbers M 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 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, 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. 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. Similar facts hold for | λ 3 | , in contrast to well-studied short-correlated model; (2) the ratio of the first two Lyapunov exponents λ 1 / λ 2 decreases with R e λ and is virtually independent of M for M t ≤ 1 in the case of solenoidal force but decreases as M increases when solenoidal and compressible forces are comparable; (3) for purely solenoidal force, λ 1 : λ 2 : λ 3 ≈ 4 : 1 : − 5 for R e λ > 80 , which is consistent with incompressible turbulence studies; and (4) the ratio of dilation-to-vorticity is a more suitable parameter to characterize Lyapunov exponents than M

EI

英语

其他

20235115232888

Computational complexity ; Incompressible flow ; Lyapunov functions ; Lyapunov methods ; Reynolds number ; Solenoids ; Turbulence

Fluid Flow, General:631.1 ; Electric Components:704.1 ; Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Mathematics:921 ; Calculus:921.2 ; Systems Science:961

PHYSICS

2-s2.0-85179623905

Scopus

1.NCMIS & LSEC,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Beijing,100190,China
2.School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,China
3.Department of Mechanical Engineering,Ben-Gurion University of the Negev,Beer-Sheva,84105,Israel
4.Department of Computational Science and Engineering,Yonsei University,Seoul,03722,South Korea
5.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Yu，Haijun,Fouxon，Itzhak,Wang，Jianchun,et al. Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence[J]. Physics of Fluids,2023,35(12).

Yu，Haijun.,Fouxon，Itzhak.,Wang，Jianchun.,Li，Xiangru.,Yuan，Li.,...&Mond，Michael.(2023).Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence.Physics of Fluids,35(12).

Yu，Haijun,et al."Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence".Physics of Fluids 35.12(2023).