{
  "annotation_id": "7e67d8dd-9a05-44e4-951c-2f35e36e21e0",
  "date_created": "2026-03-02T18:00:46.957000Z",
  "date_modified": "2026-03-02T18:00:46.957000Z",
  "file_hash": "5fb0469283c288605e22ef946bf73a275a998625232686d0648802b8ef13f006",
  "private": false,
  "record": {
    "abstract": "The linearized Navier-Stokes equations for a system of superposed immiscible\ncompressible ideal fluids are analyzed. The results of the analysis reconcile\nthe stabilizing and destabilizing effects of compressibility reported in the\nliterature. It is shown that the growth rate $n$ obtained for an inviscid,\ncompressible flow in an infinite domain is bounded by the growth rates obtained\nfor the corresponding incompressible flows with uniform and exponentially\nvarying density. As the equilibrium pressure at the interface $p_\\infty$\nincreases (less compressible flow), $n$ increases towards the uniform density\nresult, while as the ratio of specific heats $\\gamma$ increases (less\ncompressible fluid), $n$ decreases towards the exponentially varying density\nincompressible flow result. This remains valid in the presence of surface\ntension or for viscous fluids and the validity of the results is also discussed\nfor finite size domains. The critical wavenumber imposed by the presence of\nsurface tension is unaffected by compressibility. However, the results show\nthat the surface tension modifies the sensitivity of the growth rate to a\ndifferential change in $\\gamma$ for the lower and upper fluids. For the viscous\ncase, the linearized equations are solved numerically for different values of\n$p_\\infty$ and $\\gamma$. It is found that the largest differences compared with\nthe incompressible cases are obtained at small Atwood numbers. The most\nunstable mode for the compressible case is also bounded by the most unstable\nmodes corresponding to the two limiting incompressible cases.",
    "arxiv_id": "physics/0310072",
    "authors": [
      "Daniel Livescu"
    ],
    "categories": [
      "physics.flu-dyn"
    ],
    "doi": "10.1063/1.1630800",
    "title": "Compressibility effects on the Rayleigh-Taylor instability growth   between immiscible fluids",
    "url": "https://arxiv.org/abs/physics/0310072"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e70a9d5f-13c9-4a76-8b95-bd79a33e244d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}