The averaged Lagrangian method

On Incompressible Averaged Lagrangian Hydrodynamics

Variational principles for Lagrangian-averaged fluid dynamics

Abstract The Lagrangian average (LA) of the ideal fluid equations preserves their fundamental transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its potential vorticity convection and helicity conservation. We show that Lagrangian averaging also preserves the Euler–Poincaré variational framework that implies the exact i...

The Anisotropic Lagrangian Averaged Euler and Navier-Stokes Equations

The purpose of this paper is twofold. First, we give a derivation of the Lagrangian averaged Euler (LAE-α) and Navier-Stokes (LANS-α) equations. This theory involves a spatial scale α and the equations are designed to accurately capture the dynamics of the Euler and Navier-Stokes equations at length scales larger than α, while averaging the motion at scales smaller than α. The derivation involv...

On Global Well-Posedness of the Lagrangian Averaged Euler Equations

We study the global well-posedness of the Lagrangian averaged Euler equations in three dimensions. We show that a necessary and sufficient condition for the global existence is that the BMO norm of the stream function is integrable in time. We also derive a sufficient condition in terms of the total variation of certain level set functions, which guarantees the global existence. Furthermore, we...

Explicit wave-averaged primitive equations using a Generalized Lagrangian Mean

The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvat...