Fluid dynamics described from new dynamic hypothesis

TL;DR

This paper introduces a new dynamic hypothesis for fluid flow, deriving fundamental equations like Navier-Stokes without Stokes hypothesis, and clarifies the relationship between momentum and energy conservation in fluid dynamics.

Contribution

It proposes a novel dynamic hypothesis that redefines stress tensor symmetry and derives fluid equations, including Navier-Stokes, without relying on classical assumptions.

Findings

Reveals momentum and energy conservation are the same concept.

Derives Navier-Stokes equations from new dynamic hypothesis.

Shows vorticity reflects shear flow distribution.

Abstract

In order to address the difficulties of classical fluid kinematics in describing vorticity and the paradox of linear correlation between viscous force and vorticity in the Navier-Stokes equations, the study examines the inherent relationship between momentum conservation and energy conservation and rederives the fundamental equations of fluid flow from new dynamic hypothesis. The study reveals that momentum conservation and mechanical energy conservation are the same concept termed in different descriptions. The material derivative of velocity is to depict the acceleration of fluid particles in Eulerian perspective. In the study, it is assumed that fluids only obey the theorem of momentum, which describes the translational motion of fluids. The centroid of fluid elements can undergo translational motion under a curl force field. In the hypothesis, the symmetry of stress tensor is determined by the properties of stress field rather than the conservation of moment of momentum for fluid elements. The stress tensor is symmetric when stress field is a curl free field, and the stress tensor is asymmetric when stress field is a curl field. New dynamic equilibrium equations for fluids and the constitutive relationship for Newtonian fluid are proposed under the hypothesis. The Navier-Stokes equations are obtained. The new model of fluid dynamics does not require Stokes hypothesis. It is obtained that vorticity reflects the magnitude distribution of shear flow in flow field.