Geometric Lagrangian averaged Euler–Boussinesq and primitive equations

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...

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...

On Incompressible Averaged Lagrangian Hydrodynamics

On the Lagrangian Averaged Euler Equations: Local Well-posedness and Blow-up Criterion

In this article we study local and global well-posedness of the Lagrangian Averaged Euler equations. We show local well-posedness in TriebelLizorkin spaces and further prove a Beale-Kato-Majda type necessary and sufficient condition for global existence involving the stream function. We also establish new sufficient conditions for global existence in terms of mixed Lebesgue norms of the general...