Fractal-induced flow dynamics: Viscous flow around Mandelbrot and Julia sets
Document Type
Article
Source of Publication
Chaos Solitons and Fractals
Publication Date
10-1-2025
Abstract
This study explores viscous flow dynamics around fractal geometries, specifically the Mandelbrot and Julia sets, using finite element simulations. We analyze the impact of fractal roughness on flow characteristics across different Reynolds numbers Re0. At low Reynolds numbers, the influence of fractal roughness is minimal. However, as the Reynolds number increases, Kármán vortex shedding emerges, exhibiting distinct fractal-dependent patterns at specific thresholds (Re0=342.87 for the Mandelbrot set, Re0=289.553 for the San Marco fractal, and Re0=178.25,356.5,891.248 for the Siegel disk fractal). At sufficiently high Reynolds numbers, chaotic flow structures detach from the fractal boundary, destabilizing the boundary layer. To better capture the transition from laminar to turbulent regimes, we propose an alternative modeling approach using fractional derivatives in time. These findings provide new insights into flow behavior over complex geometries, with implications for turbulence modeling and engineering applications.
DOI Link
ISSN
Publisher
Elsevier BV
Volume
199
Disciplines
Mathematics
Keywords
Finite element method, Fractal geometries, Fractional derivatives, Julia set, Kármán vortex shedding, Mandelbrot set, Turbulence modeling, Viscous flow
Scopus ID
Recommended Citation
Mohammad, Mutaz and Trounev, Alexander, "Fractal-induced flow dynamics: Viscous flow around Mandelbrot and Julia sets" (2025). All Works. 7392.
https://zuscholars.zu.ac.ae/works/7392
Indexed in Scopus
yes
Open Access
no