On derivations of evolving surface Navier-Stokes equations

TL;DR

This paper compares five different derivations of surface Navier-Stokes equations, showing that while they differ in modeling principles, they agree on the tangential component of the equations, providing a unified framework.

Contribution

It unifies and systematically compares five derivations of surface Navier-Stokes equations, clarifying their differences and similarities within a common framework.

Findings

All five derivations yield the same tangential surface Navier-Stokes equations.

Some derivations produce different models, highlighting the importance of modeling choices.

The framework facilitates systematic comparison of evolving surface fluid dynamics equations.

Abstract

In recent literature several derivations of incompressible Navier-Stokes type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling approach and in the coordinate systems in which the resulting equations are represented. This paper has overview character in the sense that we put five different derivations of surface Navier-Stokes equations into one framework. This then allows a systematic comparison of the resulting surface Navier-Stokes equations and shows that some, but not all, of the resulting models are the same. Furthermore, based on a natural splitting approach in tangential and normal components of the velocity we show that all five derivations that we consider yield the same tangential surface Navier-Stokes equations.