{
  "id": "2311.13560",
  "version": "v1",
  "published": "2023-11-22T18:10:55.000Z",
  "updated": "2023-11-22T18:10:55.000Z",
  "title": "Inverse energy cascade in ocean macroscopic turbulence: Kolmogorov self-similarity in surface drifter observations and Richardson-Obhukov constant",
  "authors": [
    "J. Dräger-Dietel",
    "A. Griesel"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "We combine two point velocity and position data from surface drifter observations in the Benguela upwelling region off the coast of Namibia. The compensated third order longitudinal velocity structure function $\\left\\langle{\\Delta u_{\\ell}^{\\rm 3}}\\right\\rangle/s$ shows a positive plateau for inertial separations $s$ roughly between $9~\\rm{km}$ and $120~\\rm{km}$ revealing an inverse energy cascade with energy transfer rate $\\varepsilon\\simeq 1.2 \\pm 0.1 \\cdot 10^{-7} m^3/s^2$. Deviations from Gaussianity of the corresponding probability distribution $P(\\Delta u_{\\ell} |s)$ of two-point velocity increments $\\Delta u_{\\ell}$ for given pair separation $s$ show up in the n$^{th}$ antisymetric structure functions $S_{-}^{(n)}(r)=\\int u^n(P(u)-P(-u)d u$, which scale in agreement with Kolmogorov's prediction, $S_{-}^{(n)}(r)\\sim r^{(n/3)}$, for $n=2,4,6$. The combination of $\\varepsilon$ with Richardson dispersion $\\left\\langle s^2(t)\\right\\rangle=g\\varepsilon t^3$, where $\\left\\langle s^2(t)\\right\\rangle$ is mean squared pair separation at time $ t$, reveals a Richardson-Obhukov constant of $g\\simeq 0.11\\pm 0.03$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T18:10:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse energy cascade",
      "surface drifter observations",
      "ocean macroscopic turbulence",
      "richardson-obhukov constant",
      "third order longitudinal velocity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}