The Mathematical Description of Homogeneous Turbulence for Incompressible Fluids

Abstract

The present article establishes the mathematical description of turbulence for incompressible fluids as a response to an important question: “Is a complete mathematical description of turbulence possible?” in ResearchGate.net website discussion started August 26, 2018. Since inhomogeneous turbulence is too complex, this article will limit the discussion to homogeneous turbulence. This article provides the necessary propositions for a mathematical description of homogeneous turbulence for incompressible fluids which is achievable via a probabilistic formulation, deterministic chaos, and the Kolmogorov’s -5/3 law.

Erratum in “On the Holographic Principle Description for the Viscous Incompressible Fluids” and “The Mathematical Description of Homogeneous Turbulence for Incompressible Fluids

“…The author takes full responsibility for the errors made in [1] and [2], and in no way hold APAM responsible for them. The first error in [1] is a very rookie mathematical or logical error which I obviously was aware of (and everyone else also for that matter), but like when one is scaling a cliff one takes risks to fulfill the desire to reach the summit.…”

“…This will obviously impact my latest article, "The Mathematical Description of Homogeneous Turbulence for Incompressible Fluids" [2], also since it uses the Laplace equation of the Lagrangian as a reference, and all of the results of the spectrum of the pressure are therefore incorrect. Although, I still believe the three propositions of the article [2] are still correct and unaffected by the errors in [1].…”

“…Acknowledgements. The author would like to thank Professor Filippo M. Denaro and chief editor of APAM for their patience with me and effort spent in reviewing articles [1] and [2].…”