Turbulence arises in fluid dynamics as a nonlinear instability solution of the Navier-Stokes equations.
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Available scientific literature notes that traditional efforts to solve turbulence directly from the Navier-Stokes equations have failed or struggle to capture turbulence fully, conflicting with the claim that turbulence arises as a straightforward solution of those equations.
Theoretical chemists have been actively engaged for some time in processes such as ozone photodissociation, overtone photodissociation in nitric acid, pernitric acid, sulphuric acid, clusters and in small organic acids. The last of these have shown very different behaviours in the gas phase, liquid phase and importantly at the air–water interface in aqueous aerosols. The founder of molecular dynamics, B J Alder, pointed out long ago that hydrodynamic behaviour emerged when the symmetry of a random, thermalised population of hard spheres—billiard balls—was broken by a flux of energetic molecules. Despite this, efforts over two centuries to solve turbulence by finding top-down solutions to the Navier–Stokes equation have failed. It is time for theoretical chemistry to try a bottom-up solution. Gibbs free energy that drives the circulation arises from the entropy difference between the incoming low-entropy beam of visible and ultraviolet photons and the outgoing higher-entropy flux of infrared photons over the whole 4π solid angle. The role of the most energetic molecules with the highest velocities will affect the rovibrational line shapes of water, carbon dioxide and ozone in the far wings, where there is the largest effect on radiative transfer and hence on calculations of atmospheric temperature. The atmospheric state is determined by the interaction of radiation, chemistry and fluid dynamics on the microscopic scale, with propagation through the mesoscale to the macroscale.
The Navier-Stokes equation has served as the foundation of fluid dynamics, yet its inability to fully capture turbulence and energy dissipation remains a fundamental challenge, particularly in astrophysical and high-energy environments. We argue that this limitation arises from an incomplete representation of the governing physical principles, necessitating a paradigm shift in our approach to fluid dynamics. In this study, we introduce a novel framework based on information fluid dynamics, incorpo- rating two fundamental parameters: Transaction Density (ρT ), representing the frequency of energy and momentum exchange, and Convergence Rate (λc), which quantifies the localization of energy dissipation. By embedding these parameters into the governing equations, we propose a reformu- lation of the Navier-Stokes equation that naturally regulates turbulence through information-based constraints. Our analysis reveals that energy dissipation follows an entropy-regulated scaling law, diverg- ing from the classical Kolmogorov -5/3 turbulence spectrum. The extended formulation successfully accounts for: • The scale-dependent dissipation of turbulence, reconciling observations from black hole accretion disks (EHT data) and solar wind turbulence (PSP data). • The role of information entropy flow (Sinfo) in governing energy cascade dynamics, establishing a fundamental link between turbulence and quantum information theory. • The emergence of energy localization effects, where increasing λ
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