Recasting Navier-Stokes Equations

TL;DR

This paper introduces a new class of continuum flow models called re-casted Navier-Stokes equations, which address limitations of classical equations by incorporating mass diffusion and thermo-mechanical consistency, and are validated through stability analysis and experimental data.

Contribution

It proposes a novel transformation-based methodology to derive more complete and stable continuum models that better explain experimental phenomena where classical Navier-Stokes equations fail.

Findings

Re-casted Navier-Stokes models are linearly stable under small perturbations.

These models better fit Rayleigh-Brillouin scattering experimental data.

They naturally incorporate mass diffusion and thermo-mechanical consistency.

Abstract

Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes fail.