Detrended fluctuation analysis of numerical density and viscous fingering patterns

¹ Laboratório Associado de Computação e Matemática Aplicada, Instituto Nacional de Pesquisas Espaciais (INPE) 12201-970, São José dos Campos-SP, Brazil
² Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université Libre de Bruxelles (ULB) CP 231, 1050 Brussels, Belgium, EU

^a reinaldo.rosa@pq.cnpq.br

Received: 9 August 2010
Accepted: 2 December 2010

Abstract

We study transversely averaged concentration profiles of fingering dynamics from numerical simulations. Such profiles are studied here for a comparative fluctuation analysis between density fingering (DF) and viscous fingering (VF) envolving in a quite similar nonlinear regime. Although many physical properties influence the fingering pattern formation in miscible displacements, there are few measurements obtained from the averaged profiles, as the mixing length, that help to characterize concentration fluctuations due to self-correlations in the interfacial structure. Besides mixing length, scaling exponents (α) from detrended fluctuation analysis (DFA) are computed here for DF and VF simulations. The scaling exponent evolution is compared between DF and VF cases providing a specific signature for each kind of process: DF with α = 1.93±0.04 and VF with α = 1.82±0.04. Our analysis, based on DFA, provides a new approach for quantifying the fingering pattern formation and, in particular, the fine fluctuations differences between viscous and density fingering in miscible fluids displacements.