2013/01/07 by J. Vass, Vass, József
Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #37A30 (Secondary) #76F20 (Primary) 76F25 #Advanced Thermodynamics and Statistical Mechanics #Atmospheric and Oceanic Physics (physics.ao-ph) #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.1301.1380
openalex publication_date 2013/01/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Fully Developed Turbulence (FDT) is a theoretical asymptotic phenomenon which\ncan only be approximated experimentally or computationally, so its defining\ncharacteristics are hypothetical. It is considered to be a chaotic stationary\nflow field, with self-similar fractalline features. A number of approximate\nmodels exist, often exploiting this self-similarity. The idealized mathematical\nmodel of Fractal Potential Flows is hereby presented, and linked\nphilosophically to the phenomenon of FDT on a free surface, based on its\nexperimental characteristics. The model hinges on the recursive iteration of a\nfluid dynamical transfer operator. The existence of its unique attractor -\ncalled the invariant flow - is shown in an appropriate function space, which\nwill serve as our suggested model for the FDT flow field. Its sink\nsingularities are shown to form an IFS fractal, explicitly resolving\nMandelbrot's Conjecture. Meanwhile an isometric isomorphism is defined between\nflows and probability measures, hinting at a wealth of future research. The\ninverse problem of representing turbulent flow fields with this model is\ndiscussed in closing, along with explicit practical considerations for\nexperimental verification and visualization.\n