{
  "annotation_id": "664c3704-4f81-4668-a224-452da0879158",
  "date_created": "2026-03-02T18:01:24.170000Z",
  "date_modified": "2026-03-02T18:01:24.170000Z",
  "file_hash": "5b9183297865e5382780f2d445996f887bb1ca65a0e8bbaa32a125f24db6fbe5",
  "private": false,
  "record": {
    "abstract": "In previous work Majda and McLaughlin computed explicit expressions for the\n$2N$th moments of a passive scalar advected by a linear shear flow in the form\nof an integral over ${\\bf R}^N$. In this paper we first compute the asymptotics\nof these moments for large moment number. We are able to use this information\nabout the large N behavior of the moments, along with some basic facts about\nentire functions of finite order, to compute the asymptotics of the tails of\nthe probability distribution function. We find that the probability\ndistribution has Gaussian tails when the energy is concentrated in the largest\nscales. As the initial energy is moved to smaller and smaller scales we find\nthat the tails of the distribution grow longer, and the distribution moves\nsmoothly from Gaussian through exponential and ``stretched exponential\u0027\u0027. We\nalso show that the derivatives of the scalar are increasingly intermittent, in\nagreement with experimental observations, and relate the exponents of the\nscalar derivative to the exponents of the scalar.",
    "arxiv_id": "physics/9909013",
    "authors": [
      "J. C. Bronski",
      "R. M. McLaughlin"
    ],
    "categories": [
      "physics.flu-dyn",
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "title": "Rigorous estimates of the tails of the probability distribution function   for the random linear shear model",
    "url": "https://arxiv.org/abs/physics/9909013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a6fbe1e0-c19a-4b12-ab74-c08efca6ccb2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}