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

摘要

We propose a unified approach to the formal long-wave reduction of severalfluid models for thin-layer incompressible homogeneous flows driven by aconstant external force like gravity. The procedure is based on a mathematicalcoherence property that univoquely defines one reduced model given one rheologyand one thin-layer regime. For the first time, as far as we know, various knownreduced 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 systematicprocedure also produces new reduced models for viscoelastic non-Newtonianfluids and improves on our previous work [Bouchut & Boyaval, M3AS (23) 8,2013].