Thin shell limit and the derivation of the viscosity operator on the ellipsoid

TL;DR

This paper derives four new intrinsic viscosity operators on an ellipsoid using the thin shell limit method, highlighting the dependence on averaging techniques and boundary conditions.

Contribution

It introduces novel viscosity operators on ellipsoids via asymptotic expansion and explores the influence of boundary conditions and averaging methods.

Findings

Four new viscosity operators derived for ellipsoids

Dependence of the thin shell limit on averaging method

Geometric representation of boundary conditions

Abstract

In this paper we derive four new candidates for an intrinsic viscosity operator on an ellipsoid by using the heuristic of the thin shell limit along the scaling direction of the ellipsoid. We show that the general method of the thin shell limit through the asymptotic expansion depends on the averaging method used. We consider both the homogeneous Navier and Hodge boundary conditions. We also obtain a geometric representation of these two boundary conditions.