Molecular dissipation in the nonlinear eddy viscosity in the Navier-Stokes equations: modelling of accretion discs

TL;DR

This paper introduces a new formulation for the kinematic viscosity coefficient in the Navier-Stokes equations that incorporates molecular parameters, enhancing the physical accuracy of turbulence and accretion disc models.

Contribution

A novel formulation of the kinematic viscosity coefficient that includes molecular parameters, improving the physical realism of turbulent dissipation modeling.

Findings

2D flow structure comparisons show differences in shockless viscous transport.

Damping of chaotic turbulence is affected by the new viscosity formulation.

Application to accretion disc modeling demonstrates practical relevance.

Abstract

Physical damping, regarding the nonlinear Navier-Stokes viscous flow dynamics, refers to a tensorial turbulent dissipation term, attributed to adjacent moving macroscopic flow components. Mutual dissipation among these parts of fluid is described by a braking term in the momentum equation together with a heating term in the energy equation, both responsible of the damping of the momentum variation and of the viscous conversion of mechanical energy into heat. A macroscopic mixing scale length is currently the only characteristic length needed in the nonlinear modelling of viscous fluid dynamics describing the nonlinear eddy viscosity through the kinematic viscosity coefficient in the viscous stress tensor, without any reference to the chemical composition and to the atomic dimensions. Therefore, in this paper, we write a new formulation for the kinematic viscosity coefficient to the turbulent viscous physical dissipation in the Navier-Stokes equations, where molecular parameters are also included. Results of 2D tests are shown, where comparisons among flow structures are made on 2D shockless radial viscous transport and on 2D damping of collisional chaotic turbulence. An application to the 3D accretion disc modelling in low mass cataclysmic variables is also discussed. Consequences of the kinematic viscosity coefficient reformulation in a more strictly physical terms on the thermal conductivity coefficient for dilute gases are also discussed. The physical nature of the discussion here reported excludes any dependence by the pure mathematical aspect of the numerical modelling.