Papers
Turbulence, minimum dissipation and maximum macroscopic momentum exchange
Abstract
The minimum dissipation requirement of the thermodynamics of irreversible processes is applied to characterize the existence of laminar and non-laminar, and the co-existence of laminar and turbulent flow zones. Local limitations of the different zones and three different forms of transition are defined. For the Couette flow a non-local “corpuscular” flow mechanism explains the logarithmic law-of-the-wall, maximum turbulent dimensions and a value χ = 0,415 for the v. Kármán constant. Limitations of the logarithmic law near the wall and in the centre of the experiment are interpreted.
Turbulence, the Millennium Stokes Problem
Abstract
The Navier-Stokes equations can be considered the most important and most fascinating equations of fluid dynamics research. Never the less, the Clay Mathematics Institute named the Navier-Stokes equations a millennium problem and the status of the problem “unsolved”. The “solution” and the focus are described by sufficient literature and an internet-lecture, it is valued a prize of 1 Mio. US $. The initiated discussion will lead to the limitations of the Navier-Stokes equations, especially concerning features of turbulence. That kind of discussion is not new. Some well-known “classical” results of v. Karmán, Prandtl, Taylor (“mixing length hypothesis”, “similarity hypothesis”) are focused at turbulence, but not based on the Navier-Stokes equations. New is Ph. Spalart’s ”“fundamental paradox” in turbulence modeling between the local character of the partial difference equations … and the nonlocal physical nature of turbulence” described in his paper “philosophies and fallacies in turbulence modeling” /21/. This paper uses the minimum dissipation requirement of the thermodynamics of irreversible processes and of an older theorem of Helmholtz and Rayleigh for that discussion, applying that to Navier-Stokes flow mechanisms and other “corpuscular” or “nonlocal” fluid flow models. The turbulent logarithmic flow profile based on the “similarity hypothesis” (v. Karmán, Prandtl, Taylor), is this time explained analytically by the minimum dissipation requirement, which is a physical thermodynamic basis and no hypothesis. The discussion is performed with the example Couette flow.
The minimum dissipation requirement of the thermodynamics of irreversible processes and the co-existence of fluid flow zones with local and non-local character (PDF version)
Abstract
The minimum dissipation requirement of the thermodynamics of irreversible processes is applied to characterize the existence of different flow zones in a flow experiment. The flow zones might be laminar, non-laminar or transition forms with local and non-local character. Local limitations of the different zones and three different forms of transition are defined with stable results. There is nothing like “hydrodynamic instability” and there are no turbulent Navier-Stokes solutions for the turbulent Couette flow zones. An application to a non-local “corpuscular” flow mechanism verifies the logarithmic law of the wall and gives an analytical value 𝜒=0,415 for the Kármán constant, indicating that turbulent dimensions assume maximum values.
Remark on the 1. Stokes’ problem (PDF version)