scholarly journals Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents

2017 ◽  
Vol 27 (6) ◽  
pp. 063103 ◽  
Author(s):  
Hessam Babaee ◽  
Mohamad Farazmand ◽  
George Haller ◽  
Themistoklis P. Sapsis
Keyword(s):  
Lyapunov Exponents ◽  
Finite Time ◽  
Reduced Order ◽  
Finite Time Lyapunov Exponents

scholarly journals Surface Ocean Mixing Inferred from Different Multisatellite Altimetry Measurements

2010 ◽  
Vol 40 (11) ◽  
pp. 2466-2480 ◽  
Author(s):  
Francisco J. Beron-Vera ◽  
María J. Olascoaga ◽  
Gustavo J. Goni
Keyword(s):  
Lyapunov Exponents ◽  
Coherent Structures ◽  
Diagnostic Tool ◽  
Turbulent Mixing ◽  
Finite Time ◽  
The Other ◽  
Sea Surface ◽  
Anomaly Field ◽  
Finite Time Lyapunov Exponents ◽  
Surface Ocean

Abstract Two sea surface height (SSH) anomaly fields distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) Altimetry are evaluated in terms of the effects that they produce on mixing. One SSH anomaly field, tagged REF, is constructed using measurements made by two satellite altimeters; the other SSH anomaly field, tagged UPD, is constructed using measurements made by up to four satellite altimeters. Advection is supplied by surface geostrophic currents derived from the total SSH fields resulting from the addition of these SSH anomaly fields to a mean SSH field. Emphasis is placed on the extraction from the currents of Lagrangian coherent structures (LCSs), which, acting as skeletons for patterns formed by passively advected tracers, entirely control mixing. The diagnostic tool employed to detect LCSs is provided by the computation of finite-time Lyapunov exponents. It is found that currents inferred using UPD SSH anomalies support mixing with characteristics similar to those of mixing produced by currents inferred using REF SSH anomalies. This result mainly follows from the fact that, being more easily characterized as chaotic than turbulent, mixing as sustained by currents derived using UPD SSH anomalies is quite insensitive to spatiotemporal truncations of the advection field.

On the Scaling Function of Lyapunov Exponents for Intermittent Maps

1993 ◽  
Vol 48 (5-6) ◽  
pp. 641-642
Author(s):  
R. Stoop ◽  
J. Parisi
Keyword(s):  
Random Walk ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Scaling Function ◽  
External Parameter ◽  
Scaling Properties ◽  
Finite Time Lyapunov Exponents ◽  
Gaussian Fluctuations ◽  
Non Gaussian ◽  
The Scaling Function

Abstract The scaling function of Lyapunov exponents for intermittent systems is full of particularities if compared with hyperbolic cases or the usual, nonhyperbolic, parabola. One particularity arises when this function is calculated from finite-time Lyapunov exponents: Different scaling properties with respect to the length of the finite-time chains emerge. As expected from random walk models, the scaling of an ensemble with non-Gaussian fluctuations evolves for certain values of the external parameter.

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