Observer-invariant time derivatives on moving surfaces

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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Observer-invariance is a minimum requirement for defining time derivatives, and various time derivatives can be systematically derived from a spacetime setting using Ricci calculus. These derivatives are applicable for numerical computations and have been analyzed and compared for different tensor fields.