Observer-invariant time derivatives on moving surfaces

Abstract

Observer-invariance is regarded as a minimum requirement for an appropriate definition of time derivatives. We derive various time derivatives 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 numerical 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.