Subtleties of Turbulence and Chaos and Mathematical and Physical Interpretation

Subtleties of Turbulence and Chaos and Mathematical and Physical Interpretation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Subtleties of Turbulence and Chaos and Mathematical and Physical Interpretation B.T. Su, F.B. Huang, X.Y. Liu, Wei Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7964323/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study elucidates the preliminary mathematical interpretation and differences between turbulence and chaos, proposing a novel mathematical framework to elaborate turbulence and local resonance. Traditionally, Rayleigh principle has been employed to explain physical resonance, positing that system integrity is compromised when forcing frequency equals the system’s natural frequency. However, with the accumulation of experimental data and advancement in observational techniques, a more profound un- derstanding of turbulence’s intrinsic nature has become increasingly imper- ative. Initially, the physical phenomena of turbulence and chaos have been considered the same or overlapping. Gradually, it becomes clear that the corresponding method to describe them differs, which leads to the different scientific technologies and engineering applications. Building upon this foundation, we propose a new conceptual framework for turbulence based on non-dissipative motion theory, which reveals that under specific conditions, local entropy may approach zero or exist in a non-dissipative state. Under these conditions, energy transfer within the system exhibits lossless characteristics, adhering to the physical laws of non-dissipative dynamics. Through the introduction of Hausdorff space concepts, we successfully elu- cidate the essential differences between turbulence and chaos mathemati- cally, proving that despite both exhibiting complexity, fundamental differ- ences exist in their topological structures and transport mechanisms. This research not only enriches non-equilibrium thermodynamics theory but also provides new perspectives for understanding the connection between local non-dissipative states and global dynamical systems, bearing significant im- plications for academic research, engineering applications, and technological development. Applied Mathematics Turbulence chaos dynamical systems local resonance nondissipative Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7964323","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":535965522,"identity":"638a7455-99f4-4d9c-a289-66d96eed5b44","order_by":0,"name":"B.T. 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