A model of non-equilibrium turbulence with an asymmetric stress. Application to the problems of thermal convection

Berezin, Yu. A.; Trofimov, V. M.

doi:10.1007/s001610050022

Cited by 1 publication

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“…The situation becomes quite different if we consider complex fluids, e.g., liquid crystals [65], where the orientation of particles plays an important role, and therefore particle rotations cannot be ignored. One may expect that the same is true for turbulent flows of simple Newtonian fluids [66,67]. Fig.…”

Section: Arbitrary Incompressible and Compressible Flowsmentioning

confidence: 87%

A hyperbolic model for viscous Newtonian flows

Peshkov

Romenski

2014

Continuum Mech. Thermodyn.

145

221

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We discuss a pure hyperbolic alternative to the Navier-Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use of the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of material particles connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows, arbitrary incompressible and compressible flows of Newtonian fluids and demonstrate that Newton's viscous law can be obtained in the framework of the developed hyperbolic theory as a steady-state limit. A basic relation between the viscosity coefficient, PSL time, and the shear sound velocity is also obtained.

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Section: Arbitrary Incompressible and Compressible Flowsmentioning

confidence: 87%