NEW FORMULATION FOR CHAOTIC INTERMITTENCY WITH NOISE

ELASKAR, SERGIO; DEL RIO, EZEQUIEL; KRAUSE, GUSTAVO

Bariloche

Congreso; ENIEF 2014; 2014

Asociación Argentina de Mecánica Computacional e Inst. Balseiro

The proper description of turbulent flows presents difficulty for researchers in fluid mechan-ics. One feature of some of these flows is intermittency. The intermittency phenomenon in ChaoticDynamics theory is understood as a specific route to the deterministic chaos when spontaneous transi-tions between laminar and chaotic dynamics occur. A correct characterization of the intermittency isvery important, principally, to study those problems having partially unknown governing equations orthere are experimental or numerical data series. In this paper a new methodology to investigate systemsshowing chaotic intermittency phenomenon with noise is presented. The methodology used for systemwithout noise is extended to evaluate the noisy reinjection probability density (NRPD), the noisy proba-bility of the laminar length and the noisy characteristic relation. The approach also provides informationto accurately describe the noiseless system. It also was found that, for type-II and type-III intermitten-cies, for large values of the instability parameter the characteristic relations approach the associated onesto the noiseless intermittency. However, for low values of the instability parameter, the characteristicrelations reach a saturation level that depends on the NRPD. Also, this new methodology does not needto satisfy noise strength lower that the control parameter, it allows to analyze the noise effect on theintermittency statistical properties for large noise strengths. However, in few cases for type-I intermit-tency, the description of the noiseless system using the noisy data can be inaccurate. In addition, it isshown that occasionally the presence of noise could be not detected due to the results behave as theywould be corresponding to a noiseless system. This aspect may have important consequences especiallywhen working with experimental data.To validate the new theoretical formulation, the analytical resultsare tested by several numerical computations, showing an excellent agreement between the analyticalmodels and the numerical results