Discover the GLM and pseudo-Lagrangian equations of fluid dynamics on four pages

TL;DR

This paper elucidates the derivation principles of the General Lagrangian Mean (GLM) and pseudo-Lagrangian equations in fluid dynamics, focusing on an inviscid, incompressible fluid to aid learners in understanding these averaged flow equations.

Contribution

It provides a clear, methodical derivation of GLM and pseudo-Lagrangian equations, differing from previous approaches and aimed at educational clarity.

Findings

Derived pseudo-Lagrangian equations for inviscid, incompressible fluids

Clarified principles behind GLM theory and its formulations

Enhanced understanding of mean flow and wave interactions

Abstract

The General Lagrangian Mean (GLM) theory uses a set of averaged equations of fluid dynamics to describe interactions between mean flows and waves. These equations are formulated in coordinates that follow the fluid's average velocity and are often referred to as `pseudo-Lagrangian' or `semi-Lagrangian'. This paper focuses on the principles for deriving the pseudo-Lagrangian and GLM equations, using an inviscid, incompressible, homogeneous fluid as a demonstration case. Our exposition differs methodically from that of others and is aimed at the learners of the subject. Keywords: fluid flows, pseudo-Lagrangian description, GLM theory, inviscid incompressible fluid, Lagrangian displacements, mean flows, waves, averaged equations.