{
  "annotation_id": "800b943a-8024-4f44-b91c-52a48dda4b9a",
  "date_created": "2026-03-02T18:01:25.422000Z",
  "date_modified": "2026-03-02T18:01:25.422000Z",
  "file_hash": "4d67b308f3497b6d0b02376dbb44b9f06bc09cffe01a4bcdb7825117fdce7198",
  "private": false,
  "record": {
    "abstract": "We study the long-time, large scale transport in a three-parameter family of\nisotropic, incompressible velocity fields with power-law spectra. Scaling law\nfor transport is characterized by the scaling exponent $q$ and the Hurst\nexponent $H$, as functions of the parameters. The parameter space is divided\ninto regimes of scaling laws of different {\\em functional forms} of the scaling\nexponent and the Hurst exponent. We present the full three-dimensional phase\ndiagram.\n  The limiting process is one of three kinds: Brownian motion ($H=1/2$),\npersistent fractional Brownian motions ($1/2\u003cH\u003c1$) and regular (or smooth)\nmotion (H=1).\n  We discover that a critical wave number divides the infrared cutoffs into\nthree categories, critical, subcritical and supercritical; they give rise to\ndifferent scaling laws and phase diagrams. We introduce the notions of sampling\ndrift and eddy diffusivity, and formulate variational principles to estimate\nthe eddy diffusivity. We show that fractional Brownian motions result from a\ndominant sampling drift.",
    "arxiv_id": "physics/9906018",
    "authors": [
      "Albert C. Fannjiang"
    ],
    "categories": [
      "physics.flu-dyn",
      "math-ph",
      "math.MP",
      "physics.data-an"
    ],
    "doi": "10.1016/S0167-2789(99)00150-5",
    "title": "Phase Diagram for Turbulent Transport: Sampling Drift, Eddy Diffusivity   and Variational Principles",
    "url": "https://arxiv.org/abs/physics/9906018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6b737d0b-bb30-4d3e-abcf-d515b738112b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}