DOI: 10.1017/s0022112072000497. Equilibrium and relaxation in turbulent wakes

Equilibrium and relaxation in turbulent wakes

10.1017/s0022112072000497

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

In order to study the memory of the larger eddies in turbulent shear flow, experiments have been conducted on plane turbulent wakes undergoing transition from an initial (carefully prepared) equilibrium state to a different final one, as a result of a nearly impulsive pressure gradient. It is shown that under the conditions of the experiments the equations of motion possess self-preserving solutions in the sense of Townsend (1956), but the observed behaviour of the wake is appreciably different when the pressure gradient is not very small, as the flow goes through a slow relaxation process before reaching final equilibrium. Measurements of the Reynolds stresse show that the approach to a new equilibrium state is exponential, with a relaxation length of the order of 103 momentum thicknesses. It is suggested that a flow satisfying the conditions required by a self-preservation analysis will exhibit equilibrium only if the relaxation length is small compared with a characteristic streamwise length scale of the flow.

Bibliography

Narasimha, R., & Prabhu, A. (1972). Equilibrium and relaxation in turbulent wakes. Journal of Fluid Mechanics, 54(1), 1â17.

Authors 2

R. Narasimha (first)
A. Prabhu (additional)

References 20 Referenced 75

Hill, P. G. 1962 M.I.T. Gas Turbine Lab. Rep. no. 65.
Clauser, F. 1956 Adv. Appl. Mech. 4,1. (10.1016/S0065-2156(08)70370-3)
Tani, I. 1969 In:Kline et al. (1969).
Bradshaw, P. 1966 J. Fluid Mech. 25,225. (10.1017/S0022112066001204)
Batchelor, G. K. & Proudman, I. 1954 Quart. J. Mech. Appl. Math. 7,83. (10.1093/qjmam/7.1.83)
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow .Cambridge University Press.
Clauser, F. 1954 J. Aero. Sci. 21,91.
Ramjee, V. , Badri Narayanan, M. A. & Narasimha, R. 1972 Z. angew. Math. Phys. to appear.
Gartshore, I. S. 1967 J. Fluid Mech. 30,547. (10.1017/S0022112067001600)
Bradshaw, P. , Ferriss, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28,593. (10.1017/S0022112067002319)
Schlichting, H. 1955 Boundary Layer Theory. Pergamon Press.
Coles, D. 1969 In:Kline et al. (1969).
Prabhu, A. & Narasimha, R. 1972 J. Fluid Mech. 54,1. (10.1017/S0022112072000503)
Townsend, A. A. 1949 Aust. J. Sci. Res. 2,451.
Prabhu, A. 1966 A.I.A.A. J. 4,925. (10.2514/3.3570)
Uberoi, M. S. & Freymuth, P. 1969 Phys. Fluids,12,1359. (10.1063/1.1692675)
Prabhu, A. 1968 I.I.Sc. Aero Rep. AE 228 A.
Narasimha, R. & Prabhu, A. 1971 I.I.Sc. Aero Rep. 71FM3.
Kline, S. J. , Morkovin, M. V. , Sovran, G. & Cockrell, D. J. (eds)1969 Computation of Turbulent Boundary Layers. Proc. AFOSR-IFP-Stanford Conference . Thermosciences Division, Department of Mechanical Engineering, Stanford.
Coles, D. 1956 J. Fluid Mech. 1,191. (10.1017/S0022112056000135)

Dates

Type	When
Created	19 years, 4 months ago (March 29, 2006, 1:40 a.m.)
Deposited	6 years, 4 months ago (April 2, 2019, 12:36 p.m.)
Indexed	2 months ago (June 21, 2025, 4:23 a.m.)
Issued	53 years, 1 month ago (July 11, 1972)
Published	53 years, 1 month ago (July 11, 1972)
Published Online	19 years, 4 months ago (March 29, 2006)
Published Print	53 years, 1 month ago (July 11, 1972)

Funders 0

None

BibTeX

@article{Narasimha_1972, title={Equilibrium and relaxation in turbulent wakes}, volume={54}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112072000497}, DOI={10.1017/s0022112072000497}, number={1}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Narasimha, R. and Prabhu, A.}, year={1972}, month=jul, pages={1–17} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        6,
        21
      ]
    ],
    "date-time": "2025-06-21T08:23:43Z",
    "timestamp": 1750494223585
  },
  "reference-count": 20,
  "publisher": "Cambridge University Press (CUP)",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2006,
            3,
            29
          ]
        ],
        "date-time": "2006-03-29T00:00:00Z",
        "timestamp": 1143590400000
      },
      "content-version": "unspecified",
      "delay-in-days": 12314,
      "URL": "https://www.cambridge.org/core/terms"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1972,
        7,
        11
      ]
    ]
  },
  "abstract": "<jats:p>In order to study the memory of the larger eddies in turbulent shear flow, experiments have been conducted on plane turbulent wakes undergoing transition from an initial (carefully prepared) equilibrium state to a different final one, as a result of a nearly impulsive pressure gradient. It is shown that under the conditions of the experiments the equations of motion possess self-preserving solutions in the sense of Townsend (1956), but the observed behaviour of the wake is appreciably different when the pressure gradient is not very small, as the flow goes through a slow relaxation process before reaching final equilibrium. Measurements of the Reynolds stresse show that the approach to a new equilibrium state is exponential, with a relaxation length of the order of 10<jats:sup>3</jats:sup> momentum thicknesses. It is suggested that a flow satisfying the conditions required by a self-preservation analysis will exhibit equilibrium only if the relaxation length is small compared with a characteristic streamwise length scale of the flow.</jats:p>",
  "DOI": "10.1017/s0022112072000497",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        3,
        29
      ]
    ],
    "date-time": "2006-03-29T06:40:27Z",
    "timestamp": 1143614427000
  },
  "page": "1-17",
  "source": "Crossref",
  "is-referenced-by-count": 75,
  "title": "Equilibrium and relaxation in turbulent wakes",
  "prefix": "10.1017",
  "volume": "54",
  "author": [
    {
      "given": "R.",
      "family": "Narasimha",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "A.",
      "family": "Prabhu",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "56",
  "published-online": {
    "date-parts": [
      [
        2006,
        3,
        29
      ]
    ]
  },
  "reference": [
    {
      "key": "S0022112072000497_ref009",
      "unstructured": "Hill, P. G. 1962 M.I.T. Gas Turbine Lab. Rep. no. 65."
    },
    {
      "key": "S0022112072000497_ref005",
      "doi-asserted-by": "crossref",
      "unstructured": "Clauser, F. 1956 Adv. Appl. Mech. 4,1.",
      "DOI": "10.1016/S0065-2156(08)70370-3"
    },
    {
      "key": "S0022112072000497_ref017",
      "unstructured": "Tani, I. 1969 In:Kline et al. (1969)."
    },
    {
      "key": "S0022112072000497_ref002",
      "doi-asserted-by": "crossref",
      "unstructured": "Bradshaw, P. 1966 J. Fluid Mech. 25,225.",
      "DOI": "10.1017/S0022112066001204"
    },
    {
      "key": "S0022112072000497_ref001",
      "doi-asserted-by": "crossref",
      "unstructured": "Batchelor, G. K. & Proudman, I. 1954 Quart. J. Mech. Appl. Math. 7,83.",
      "DOI": "10.1093/qjmam/7.1.83"
    },
    {
      "key": "S0022112072000497_ref019",
      "unstructured": "Townsend, A. A. 1956 The Structure of Turbulent Shear Flow .Cambridge University Press."
    },
    {
      "key": "S0022112072000497_ref004",
      "unstructured": "Clauser, F. 1954 J. Aero. Sci. 21,91."
    },
    {
      "key": "S0022112072000497_ref015",
      "unstructured": "Ramjee, V. , Badri Narayanan, M. A. & Narasimha, R. 1972 Z. angew. Math. Phys. to appear."
    },
    {
      "key": "S0022112072000497_ref008",
      "doi-asserted-by": "crossref",
      "unstructured": "Gartshore, I. S. 1967 J. Fluid Mech. 30,547.",
      "DOI": "10.1017/S0022112067001600"
    },
    {
      "key": "S0022112072000497_ref003",
      "doi-asserted-by": "crossref",
      "unstructured": "Bradshaw, P. , Ferriss, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28,593.",
      "DOI": "10.1017/S0022112067002319"
    },
    {
      "key": "S0022112072000497_ref016",
      "unstructured": "Schlichting, H. 1955 Boundary Layer Theory. Pergamon Press."
    },
    {
      "key": "S0022112072000497_ref007",
      "unstructured": "Coles, D. 1969 In:Kline et al. (1969)."
    },
    {
      "key": "S0022112072000497_ref014",
      "doi-asserted-by": "crossref",
      "unstructured": "Prabhu, A. & Narasimha, R. 1972 J. Fluid Mech. 54,1.",
      "DOI": "10.1017/S0022112072000503"
    },
    {
      "key": "S0022112072000497_ref018",
      "unstructured": "Townsend, A. A. 1949 Aust. J. Sci. Res. 2,451."
    },
    {
      "key": "S0022112072000497_ref012",
      "doi-asserted-by": "crossref",
      "unstructured": "Prabhu, A. 1966 A.I.A.A. J. 4,925.",
      "DOI": "10.2514/3.3570"
    },
    {
      "key": "S0022112072000497_ref020",
      "doi-asserted-by": "crossref",
      "unstructured": "Uberoi, M. S. & Freymuth, P. 1969 Phys. Fluids,12,1359.",
      "DOI": "10.1063/1.1692675"
    },
    {
      "key": "S0022112072000497_ref013",
      "unstructured": "Prabhu, A. 1968 I.I.Sc. Aero Rep. AE 228 A."
    },
    {
      "key": "S0022112072000497_ref011",
      "unstructured": "Narasimha, R. & Prabhu, A. 1971 I.I.Sc. Aero Rep. 71FM3."
    },
    {
      "key": "S0022112072000497_ref010",
      "unstructured": "Kline, S. J. , Morkovin, M. V. , Sovran, G. & Cockrell, D. J. (eds)1969 Computation of Turbulent Boundary Layers. Proc. AFOSR-IFP-Stanford Conference . Thermosciences Division, Department of Mechanical Engineering, Stanford."
    },
    {
      "key": "S0022112072000497_ref006",
      "doi-asserted-by": "crossref",
      "unstructured": "Coles, D. 1956 J. Fluid Mech. 1,191.",
      "DOI": "10.1017/S0022112056000135"
    }
  ],
  "container-title": "Journal of Fluid Mechanics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112072000497",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        4,
        2
      ]
    ],
    "date-time": "2019-04-02T16:36:29Z",
    "timestamp": 1554222989000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.cambridge.org/core/product/identifier/S0022112072000497/type/journal_article"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1972,
        7,
        11
      ]
    ]
  },
  "references-count": 20,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          1972,
          7,
          11
        ]
      ]
    }
  },
  "alternative-id": [
    "S0022112072000497"
  ],
  "URL": "http://dx.doi.org/10.1017/S0022112072000497",
  "relation": {},
  "ISSN": [
    "0022-1120",
    "1469-7645"
  ],
  "subject": [],
  "container-title-short": "J. Fluid Mech.",
  "published": {
    "date-parts": [
      [
        1972,
        7,
        11
      ]
    ]
  }
}