Article history: Available online 30 October 2010

We consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. Various notions of weak solution are considered and compared. We establish existence and regularity results. In particular we study the boundedness of weak solutions. We also establish an existence result for a classical solution.

Related Articles Effect of secondary convective cells on turbulence intensity profiles, flow generation, and transport Phys. Plasmas 19, 112506 (2012) Asymmetric chiral alignment in magnetized plasma turbulence Phys. Plasmas 19, 112301 (2012) Three-dimensional modeling of beam emission spectroscopy measurements in fusion plasmas Rev. Sci. Instrum. 83, 113501 (2012) An electromagnetic theory of ...

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in st...

1 Goal In this Lecture, we shall present the main ideas behind the simulation of fluid turbulence. We firts discuss the case of the direct numerical simulation, in which all scales of motion within the grid resolution are simulated and then move on to turbulence modeling, where the effect of unresolved scales on the resolved ones is taken into account by various forms of modeling, 1

Abstract Turbulence is a prevalent phenomenon in the interstellar medium, and particular, environment at centers of galaxies. For example, detailed observations Milky Way’s Central Molecular Zone (CMZ) revealed that it has complex turbulent structure. on galactic scales often modeled using star formation feedback. However, these effects do not appear to be sufficient for explaining high-velocit...

Accurate prediction for a self-propelled ship is a challenging task for CFD computation. While turbulence modeling is a crucial issue, more physical modeling is involved in a propeller simulation: transition, cavitation, turbulence, ventilation, etc. More advanced numerical technique is also required to capture very small scale flow motion such as tip vortex. The ISIS-CFD RANSE code has been fu...

Several questions that are relevant to turbulence modeling are addressed on the basis of recently obtained direct numerical simulation results of turbulent supersonic channel flow. In particular, this concerns the turbulence frequency production mechanism, wall damping effects on turbulence model parameters, and the relevance of compressibility effects. Limited support is found for usually appl...

The numerical analysis of the mechanisms governing the flow in the porous region is of a priority interest for modeling porous media flows. The present study is a prerequisite for elaborating the efficient turbulence modeling techniques in porous media flows. The main objective of present study is to provide a detailed pore scale description of fluid flow and to analyze the formation of the coh...