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Multifractal structure of chaotically advected chemical fields
Neufeld1, Lopez, Hernandez-Garcia
1Instituto Mediterraneo de Estudios Avanzados, (IMEDEA), CSIC-Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambri.
Summary
Investigating chemical fields in fluid dynamics reveals nonuniformities in the Holder exponent, especially in open flows where intermittency is restricted to fractal manifolds. This study links scaling exponents to Lyapunov exponents in advection dynamics.
Area of Science:
- Fluid Dynamics
- Chemical Physics
- Nonlinear Dynamics
Background:
- Investigating the concentration field of decaying substances in fluid flow.
- Focusing on nonuniformities of the Holder exponent in filamental chemical fields.
- Examining spatial intermittency in open flows and its restriction to fractal manifolds.
Purpose of the Study:
- To analyze the nonuniformities of the Holder exponent in chemical fields.
- To understand the impact of nonuniform stretching on chemical field irregularities in closed flows.
- To relate scaling exponents of structure functions to local Lyapunov exponents.
Main Methods:
- Analysis of the Holder exponent in two-dimensional incompressible flow.
- Theoretical investigation of scaling exponents and anomalous scaling.
- Comparison of theoretical predictions with numerical experiments.
Main Results:
- Nonuniformities of the Holder exponent are evident in open flows, restricted to fractal manifolds.
- In closed flows, nonuniformities arise from nonuniform stretching of fluid elements.
- Anomalous scaling is observed in structure functions, linked to local Lyapunov exponents.
Conclusions:
- The study elucidates the complex structure of chemical fields in fluid dynamics.
- It highlights the role of fractal geometry and Lyapunov exponents in determining field properties.
- Findings provide a theoretical framework validated by numerical simulations.
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