[
{
"id": "https://authors.library.caltech.edu/records/b4sjp-adb21",
"eprint_id": 52993,
"eprint_status": "archive",
"datestamp": "2023-08-20 05:43:07",
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"type": "article",
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"creators": {
"items": [
{
"id": "Buntine-J-D",
"name": {
"family": "Buntine",
"given": "J. D."
}
},
{
"id": "Saffman-P-G",
"name": {
"family": "Saffman",
"given": "P. G."
}
}
]
},
"title": "Inviscid Swirling Flows and Vortex Breakdown",
"ispublished": "pub",
"full_text_status": "restricted",
"note": "\u00a9 1995 The Royal Society.\n\nReceived 19 April 1994; accepted 19 October 1994.\n\nThis work was supported by the Department of Energy Grant No. DE-FG03-89ER25073. The\nauthors thank Professor D. I. Pullin, Dr S. J. Cowley, Professor D. W. Moore and Professor J.\nM. Lopez for constructive criticism. Dr Cowley has independently considered questions similar\nto those presently investigated.",
"abstract": "The steady axisymmetric Euler flow of an inviscid incompressible swirling fluid\nis described exactly by the Squire-Long equation. This equation is studied numerically\nfor the case of diverging flow to investigate the dependence of solutions\non upstream, or inlet, and downstream, or outlet, boundary conditions and flow\ngeometry. The work is performed with a view to understanding how the phenomenon\nof vortex breakdown occurs. It is shown that solutions fail to exist or,\nalternatively, that the axial flow ceases to be unidirectional, so that breakdown\ncan be inferred, when a parameter measuring the relative magnitude of rotation\nand axial flow (the Squire number) exceeds critical values depending upon the geometry\nand inlet profiles. A 'quasi-cylindrical' simplification of the Squire-Long\nequation is compared with the more complete Euler model and shown to be able\nto account for most of the latter's behaviour. The relationship is examined between\n'failure' of the quasi-cylindrical model and the occurrence of a 'critical'\nflow state in which disturbances can stand in the flow.",
"date": "1995-04-08",
"date_type": "published",
"publication": "Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences",
"volume": "449",
"number": "1935",
"publisher": "Royal Society",
"pagerange": "139-153",
"id_number": "CaltechAUTHORS:20141217-153936617",
"issn": "0962-8444",
"official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141217-153936617",
"rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.",
"funders": {
"items": [
{
"agency": "Department of Energy (DOE)",
"grant_number": "DE-FG03-89ER25073"
}
]
},
"resource_type": "article",
"pub_year": "1995",
"author_list": "Buntine, J. D. and Saffman, P. G."
},
{
"id": "https://authors.library.caltech.edu/records/wpg3x-9cj19",
"eprint_id": 3268,
"eprint_status": "archive",
"datestamp": "2023-08-22 10:02:16",
"lastmod": "2023-10-16 15:46:06",
"type": "article",
"metadata_visibility": "show",
"creators": {
"items": [
{
"id": "Pullin-D-I",
"name": {
"family": "Pullin",
"given": "D. I."
}
},
{
"id": "Buntine-J-D",
"name": {
"family": "Buntine",
"given": "James D."
}
},
{
"id": "Saffman-P-G",
"name": {
"family": "Saffman",
"given": "P. G."
}
}
]
},
"title": "On the spectrum of a stretched spiral vortex",
"ispublished": "pub",
"full_text_status": "public",
"keywords": "TURBULENT FLOW; VORTEX FLOW; ENERGY SPECTRA; ENERGY LOSSES; VISCOUS FLOW; SCALING LAWS; REYNOLDS NUMBER; INCOMPRESSIBLE FLOW; FINE STRUCTURE; CUT\u2013OFF",
"note": "Copyright \u00a9 1994 American Institute of Physics \n\n(Received 2 December 1993; accepted 9 May 1994) \n\nThe authors wish to thank Professor D. W. Moore and Professor A. Leonard for helpful discussions. D.I.P. was partially supported by NSF Grant No. CTS-9311811 and P.G.S. was partially supported by the Department of Energy under Grant No. DE-FG03-89ER25073. We wish to thank Dr. Maurice Meneguzzi for providing unpublished data on velocity-derivative moments.",
"abstract": "Corrections are found to the k^\u20135/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time tau1 in the time integral for the nonaxisymmetric contribution. The identity nuomega2 = 2nu[integral]_{0}^{[infinity]}k^2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k^\u20135/3-spectrum result is asymptotically valid in the inertial range provided atau1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(\u2013B1k2) and an exp(\u2013B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show \u2013log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation.",
"date": "1994-09-01",
"date_type": "published",
"publication": "Physics of Fluids",
"volume": "6",
"number": "9",
"publisher": "Physics of Fluids",
"pagerange": "3010-3027",
"id_number": "CaltechAUTHORS:PULpof94b",
"issn": "1070-6631",
"official_url": "https://resolver.caltech.edu/CaltechAUTHORS:PULpof94b",
"rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.",
"local_group": {
"items": [
{
"id": "GALCIT"
}
]
},
"doi": "10.1063/1.868127",
"primary_object": {
"basename": "PULpof94b.pdf",
"url": "https://authors.library.caltech.edu/records/wpg3x-9cj19/files/PULpof94b.pdf"
},
"resource_type": "article",
"pub_year": "1994",
"author_list": "Pullin, D. I.; Buntine, James D.; et el."
}
]