{
  "id": "1911.06613",
  "version": "v1",
  "published": "2019-11-15T13:27:47.000Z",
  "updated": "2019-11-15T13:27:47.000Z",
  "title": "A geometric look at momentum flux and stress in fluid mechanics",
  "authors": [
    "Andrew D. Gilbert",
    "Jacques Vanneste"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review the necessary tools of differential geometry and obtain the corresponding coordinate-free form of the equations of motion for a variety of inviscid fluid models -- compressible and incompressible Euler equations, Lagrangian-averaged Euler-$\\alpha$ equations, magnetohydrodynamics and shallow-water models -- using a variational derivation which automatically yields a symmetric momentum flux. We also consider dissipative effects and discuss the geometric form of the Navier--Stokes equations for viscous fluids and of the Oldroyd-B model for visco-elastic fluids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-15T13:27:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fluid mechanics",
      "geometric look",
      "arbitrary riemannian manifolds",
      "symmetric momentum flux",
      "inviscid fluid models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}