{
  "annotation_id": "31756c63-6cdc-4541-a0b1-cf8c90dc577f",
  "date_created": "2026-03-02T18:01:07.208000Z",
  "date_modified": "2026-03-02T18:01:07.208000Z",
  "file_hash": "902cbcd7c5d647e5303118d0d490cc9908d19d76f637f5da7b744f0e50e0ca17",
  "private": false,
  "record": {
    "abstract": "Upper bounds on the bulk energy dissipation rate $\\epsilon$ and enstrophy\ndissipation rate $\\chi$ are derived for the statistical steady state of body\nforced two dimensional turbulence in a periodic domain. For a broad class of\nexternally imposed body forces it is shown that $\\epsilon \\le k_{f} U^3\nRe^{-1/2}(C_1+C_2 Re^{-1})^{1/2}$ and $\\chi \\le k_{f}^{3}U^3 (C_1+C_2 Re^{-1})$\nwhere $U$ is the root-mean-square velocity, $k_f$ is a wavenumber (inverse\nlength scale) related with the forcing function, and $Re = U /\\nu k_f$. The\npositive coefficients $C_1$ and $C_2$ are uniform in the the kinematic\nviscosity $\\nu$, the amplitude of the driving force, and the system size. We\ncompare these results with previously obtained bounds for body forces involving\nonly a single length scale, or for velocity dependent a constant-energy-flux\nforces acting at finite wavenumbers. Implications of our results are discussed.",
    "arxiv_id": "physics/0605090",
    "authors": [
      "Alexandros Alexakis",
      "Charles R. Doering"
    ],
    "categories": [
      "physics.flu-dyn",
      "physics.geo-ph"
    ],
    "doi": "10.1016/j.physleta.2006.07.048",
    "title": "Energy and enstrophy dissipation in steady state 2-d turbulence",
    "url": "https://arxiv.org/abs/physics/0605090"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0181df53-ba56-4d6d-9857-b3610b4a47d7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}