Observer-invariant time derivatives on moving surfaces

TL;DR

This paper develops observer-invariant time derivatives for tangential tensor fields on moving surfaces, ensuring covariance and providing computationally applicable formulations for different tensor types.

Contribution

It systematically derives observer-invariant derivatives on moving surfaces using Ricci-calculus, covering various tensor fields and comparing different derivatives to reveal underlying physics.

Findings

Derived formulations for observer-invariant derivatives

Compared material and convected derivatives for specific tensor fields

Demonstrated physical differences in derivative types

Abstract

Observer-invariance is regarded as a minimum requirement for an appropriate definition and derived systematically from a spacetime setting, where observer-invariance is a special case of a covariance principle and covered by Ricci-calculus. The analysis is considered for tangential n-tensor fields on moving surfaces and provides formulations which are applicable for computations. For various special cases, e.g., vector fields (n = 1) and symmetric and trace-less tensor fields (n = 2) we compare material and convected derivatives and demonstrate the different underlying physics.