TY - JOUR

T1 - Lyapunov Exponents of Two Stochastic Lorenz 63 Systems

AU - Geurts, Bernard J.

AU - Holm, Darryl D.

AU - Luesink, Erwin

N1 - Springer deal

PY - 2020/6/1

Y1 - 2020/6/1

N2 - Two different types of perturbations of the Lorenz 63 dynamical system for Rayleigh–Bénard convection by multiplicative noise—called stochastic advection by Lie transport (SALT) noise and fluctuation–dissipation (FD) noise—are found to produce qualitatively different effects, possibly because the total phase-space volume contraction rates are different. In the process of making this comparison between effects of SALT and FD noise on the Lorenz 63 system, a stochastic version of a robust deterministic numerical algorithm for obtaining the individual numerical Lyapunov exponents was developed. With this stochastic version of the algorithm, the value of the sum of the Lyapunov exponents for the FD noise was found to differ significantly from the value of the deterministic Lorenz 63 system, whereas the SALT noise preserves the Lorenz 63 value with high accuracy. The Lagrangian averaged version of the SALT equations (LA SALT) is found to yield a closed deterministic subsystem for the expected solutions which is isomorphic to the original Lorenz 63 dynamical system. The solutions of the closed chaotic subsystem, in turn, drive a linear stochastic system for the fluctuations of the LA SALT solutions around their expected values.

AB - Two different types of perturbations of the Lorenz 63 dynamical system for Rayleigh–Bénard convection by multiplicative noise—called stochastic advection by Lie transport (SALT) noise and fluctuation–dissipation (FD) noise—are found to produce qualitatively different effects, possibly because the total phase-space volume contraction rates are different. In the process of making this comparison between effects of SALT and FD noise on the Lorenz 63 system, a stochastic version of a robust deterministic numerical algorithm for obtaining the individual numerical Lyapunov exponents was developed. With this stochastic version of the algorithm, the value of the sum of the Lyapunov exponents for the FD noise was found to differ significantly from the value of the deterministic Lorenz 63 system, whereas the SALT noise preserves the Lorenz 63 value with high accuracy. The Lagrangian averaged version of the SALT equations (LA SALT) is found to yield a closed deterministic subsystem for the expected solutions which is isomorphic to the original Lorenz 63 dynamical system. The solutions of the closed chaotic subsystem, in turn, drive a linear stochastic system for the fluctuations of the LA SALT solutions around their expected values.

KW - UT-Hybrid-D

UR - http://www.scopus.com/inward/record.url?scp=85077067435&partnerID=8YFLogxK

U2 - 10.1007/s10955-019-02457-3

DO - 10.1007/s10955-019-02457-3

M3 - Article

AN - SCOPUS:85077067435

VL - 179

SP - 1343

EP - 1365

JO - Journal of statistical physics

JF - Journal of statistical physics

SN - 0022-4715

IS - 5-6

ER -