{
  "id": "2009.10770",
  "version": "v1",
  "published": "2020-09-22T19:17:45.000Z",
  "updated": "2020-09-22T19:17:45.000Z",
  "title": "Speed-direction description of turbulent flows",
  "authors": [
    "Maxim A. Olshanskii"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "In this note we introduce speed and direction variables to describe the motion of incompressible viscous flows. Fluid velocity ${\\bf u}$ is decomposed into ${\\bf u}=u{\\bf r}$, with $u=|{\\bf u}|$ and ${\\bf r}={\\bf u}/|{\\bf u}|$. We consider a directional split of the Navier-Stokes equations into a coupled system of equations for $u$ and for ${\\bf r}$. Equation for $u$ is particularly simple but solely maintains the energy balance of the system. Under the assumption of a weak correlation between fluctuations in speed and direction in a developed turbulent flow, we further illustrate the application of $u$-${\\bf r}$ variables to describe mean statistics of a shear turbulence. The standard (full) Reynolds stress tensor does not appear in a resulting equation for the mean flow profile.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-22T19:17:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "speed-direction description",
      "reynolds stress tensor",
      "direction variables",
      "fluid velocity",
      "energy balance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}