A New Conserved Energy for Incompressible Navier-Stokes Equations

TL;DR

This paper introduces a new conserved energy concept for incompressible Navier-Stokes equations, highlighting how pressure conditions can preserve total energy and prevent kinetic energy blow-up in fluid volumes.

Contribution

It proposes a novel conserved energy formulation based on pressure conditions that counteract viscous dissipation in incompressible flows.

Findings

Total energy conservation under specific pressure conditions

Prevents kinetic energy blow-up in fluid volumes

Provides a new perspective on energy dynamics in incompressible flows

Abstract

Pressure conditions in incompressible Navier-Stokes equations give rise to conservation of total energy. The energy rate getting into a volume is the same energy rate that gets out from it. Suitable choice of pressure counteracts energy disipation of viscosity term in such a way that total energy is preserved. As consequence, this prevents kinetic energy blow-up in a given volume of the fluid.