Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces

TL;DR

This paper introduces an orthogonal coordinate system based on the signed-distance function for boundary layers around evolving surfaces and curves, along with vector calculus identities to facilitate geometric analysis in physical systems.

Contribution

It provides a new, elementary derivation of orthogonal coordinates and collates useful vector calculus identities, extending previous work on signed-distance functions.

Findings

Derived an orthogonal coordinate system for evolving surfaces and curves.

Compiled useful vector calculus identities for these coordinates.

Enabled consistent geometric analysis in boundary layer asymptotics.

Abstract

We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results and provided code enable consistent accounting of geometric effects in the derivation of boundary layer asymptotics for a wide range of physical systems.