Unified formal reduction for fluid models of free-surface shallow gravity-flows

TL;DR

This paper introduces a unified mathematical framework for deriving simplified models of thin-layer free-surface fluid flows, accommodating various rheologies and flow regimes, and producing new models for viscoelastic non-Newtonian fluids.

Contribution

It provides the first unified approach to systematically derive and analyze reduced fluid models across different rheologies and flow regimes within a single framework.

Findings

Unified framework for various fluid models

Derivation of new viscoelastic non-Newtonian models

Enhanced understanding of flow regime limits

Abstract

We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence property that univoquely defines one reduced model given one rheology and one thin-layer regime. For the first time, as far as we know, various known reduced models can thus be investigated within a single mathematical framework, for various rheologies (viscous and viscoelastic) and various limit regimes (fast inertial flows and slow viscous flows). Furthermore, our systematic procedure also produces new reduced models for viscoelastic non-Newtonian fluids and improves on our previous work [Bouchut & Boyaval, M3AS (23) 8, 2013].