Lagrangian Transport Through Surfaces in Compressible Flows

Noisy Lagrangian Tracers for Filtering Random Rotating Compressible Flows

The recovery of a random turbulent velocity field using Lagrangian tracers that move with the fluid flow is a practically important problem. This paper studies the filtering skill of L noisy Lagrangian tracers in recovering random rotating compressible flows that are a linear combination of random incompressible geostrophically balanced (GB) flow and random rotating compressible gravity waves. ...

Lagrangian Averaging, Nonlinear Waves, and Shock Regularization

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in the material frame. The particle relabeling symme...

Lagrangian Finite Element Analysis of Newtonian Fluid Flows

A fully Lagrangian nite element method for the analysis of Newtonian ows is developed. The approach furnishes, in e ect, a Lagrangian implementation of the compressible Navier–Stokes equations. As the ow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass. The principal advantage of the present approach lies in the treatment of boundary conditi...

Sticky Particle Dynamics with Interactions

We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a differential inclusion on the space of transport maps, in particular when a sticky particle dynamics is assumed. We study a discrete particle approximation a...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows