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Volumn 22, Issue 6, 2008, Pages 433-470

A continuum mechanical theory for turbulence: A generalized Navier-Stokes-α equation with boundary conditions

Author keywords

Hyperstress; Hyperviscosity; Second grade fluid; Turbulence

Indexed keywords

A-PLANE; CLASSICAL PROBLEMS; CLASSICAL SCALING; DYNAMICAL THEORIES; EQUATION BASED; FILTERED VELOCITIES; FIXED SURFACES; FLOW EQUATIONS; HYPERSTRESS; HYPERVISCOSITY; INTEGRAL LENGTH SCALES; ISOTHERMAL SYSTEMS; KOLMOGOROV; LAGRANGIAN; LENGTH SCALES; MECHANICAL FORMULATIONS; MECHANICAL THEORIES; RECTANGULAR CHANNELS; SECOND-GRADE FLUID; SLIP CONDITIONS; TURBULENT KINETIC ENERGIES; VISCOUS TERMS;

EID: 54949118689     PISSN: 09354964     EISSN: 14322250     Source Type: Journal    
DOI: 10.1007/s00162-008-0083-4     Document Type: Article
Times cited : (33)

References (33)
  • 1
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • D.D. Holm J.E. Marsden T. Ratiu 1998 The Euler-Poincaré equations and semidirect products with applications to continuum theories Adv. Math. 137 1 81
    • (1998) Adv. Math. , vol.137 , pp. 1-81
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.3
  • 2
    • 11744318899 scopus 로고    scopus 로고
    • Euler-Poincaré models of ideal fluids with nonlinear dispersian
    • D.D. Holm J.E. Marsden T. Ratiu 1998 Euler-Poincaré models of ideal fluids with nonlinear dispersian Phys. Rev. Lett. 80 4273 4277
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 4273-4277
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.3
  • 3
    • 0001262719 scopus 로고    scopus 로고
    • The Camassa-Holm equations as a closure model for turbulent channel and pipe flow
    • S. Chen C. Foias D.D. Holm E. Olson E.S. Titi S. Wynne 1998 The Camassa-Holm equations as a closure model for turbulent channel and pipe flow Phys. Rev. Lett. 81 5338 5341
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 5338-5341
    • Chen, S.1    Foias, C.2    Holm, D.D.3    Olson, E.4    Titi, E.S.5    Wynne, S.6
  • 5
    • 0032614269 scopus 로고    scopus 로고
    • A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
    • S. Chen C. Foias D.D. Holm E. Olson E.S. Titi S. Wynne 1999 A connection between the Camassa-Holm equations and turbulent flows in channels and pipes Phys. Fluids 11 2343 2353
    • (1999) Phys. Fluids , vol.11 , pp. 2343-2353
    • Chen, S.1    Foias, C.2    Holm, D.D.3    Olson, E.4    Titi, E.S.5    Wynne, S.6
  • 7
    • 0036131798 scopus 로고    scopus 로고
    • A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations
    • M.E. Gurtin 2002 A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations J. Mech. Phys. Solids 50 809 819
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 809-819
    • Gurtin, M.E.1
  • 8
    • 33947115698 scopus 로고    scopus 로고
    • Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small length scales
    • E. Fried M.E. Gurtin 2006 Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small length scales Arch. Ration. Mech. Anal. 182 513 554
    • (2006) Arch. Ration. Mech. Anal. , vol.182 , pp. 513-554
    • Fried, E.1    Gurtin, M.E.2
  • 11
    • 33947180779 scopus 로고
    • Elastic materials with couple stresses
    • R.A. Toupin 1962 Elastic materials with couple stresses Arch. Ration. Mech. Anal. 11 385 414
    • (1962) Arch. Ration. Mech. Anal. , vol.11 , pp. 385-414
    • Toupin, R.A.1
  • 12
    • 34250940617 scopus 로고
    • Theory of elasticity with couple stresses
    • R.A. Toupin 1964 Theory of elasticity with couple stresses Arch. Ration. Mech. Anal. 17 85 112
    • (1964) Arch. Ration. Mech. Anal. , vol.17 , pp. 85-112
    • Toupin, R.A.1
  • 13
    • 0035873331 scopus 로고    scopus 로고
    • The Navier-Stokes-alpha model offluid turbulence
    • Foias, C., Holm, D.D., Titi, E.S.: The Navier-Stokes-alpha model offluid turbulence. Phys. D 152-153, 505-519 (2001)
    • (2001) Phys. D , vol.152-153 , pp. 505-519
    • Foias, C.1    Holm, D.D.2    Titi, E.S.3
  • 14
    • 0001526376 scopus 로고
    • Stress-deformation relations for isotropic materials
    • R.S. Rivlin J.L. Ericksen 1955 Stress-deformation relations for isotropic materials J. Ration. Mech. Anal. 4 323 425
    • (1955) J. Ration. Mech. Anal. , vol.4 , pp. 323-425
    • Rivlin, R.S.1    Ericksen, J.L.2
  • 15
    • 0002565890 scopus 로고
    • The non-linear field theories ofmechanics
    • Flügge, S. (ed.). Springer, Berlin
    • Truesdell, C.A., Noll, W.: The non-linear field theories ofmechanics. In: Flügge, S. (ed.) Handbuch der Physik III/3. Springer, Berlin (1965)
    • (1965) Handbuch der Physik , vol.3 , Issue.3
    • Truesdell, C.A.1    Noll, W.2
  • 16
    • 0001008393 scopus 로고
    • The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids
    • R.S. Rivlin 1957 The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids Q. Appl. Math. 15 212 215
    • (1957) Q. Appl. Math. , vol.15 , pp. 212-215
    • Rivlin, R.S.1
  • 17
    • 34347245852 scopus 로고
    • Correction to my paper: The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids
    • R.S. Rivlin 1960 Correction to my paper: the relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids Q. Appl. Math. 17 447
    • (1960) Q. Appl. Math. , vol.17 , pp. 447
    • Rivlin, R.S.1
  • 18
    • 0016013907 scopus 로고
    • Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade
    • J.E. Dunn R.L. Fosdick 1974 Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade Arch. Ration. Mech. Anal. 56 191 252
    • (1974) Arch. Ration. Mech. Anal. , vol.56 , pp. 191-252
    • Dunn, J.E.1    Fosdick, R.L.2
  • 19
    • 0003987999 scopus 로고    scopus 로고
    • Cambridge University Press Cambridge
    • Pope S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)
    • (2000) Turbulent Flows
    • Pope, S.B.1
  • 20
    • 0023155294 scopus 로고
    • Turbulence statistics in fully developed channel flow at low Reynolds number
    • J. Kim P. Moin R.D. Moser 1987 Turbulence statistics in fully developed channel flow at low Reynolds number J. Fluid Mech. 177 133 166
    • (1987) J. Fluid Mech. , vol.177 , pp. 133-166
    • Kim, J.1    Moin, P.2    Moser, R.D.3
  • 22
    • 0003220540 scopus 로고
    • Das Ähnlichkeitsgesetz bei ReibungsvorgÄngen in Flüssigkeiten
    • P.R.H. Blasius 1913 Das Ähnlichkeitsgesetz bei ReibungsvorgÄ ngen in Flüssigkeiten Forschg. Arb. Ing.-Wes. 131 1 39
    • (1913) Forschg. Arb. Ing.-Wes. , vol.131 , pp. 1-39
    • Blasius, P.R.H.1
  • 23
    • 0001277608 scopus 로고
    • The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers
    • A.N. Kolmogorov 1941 The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers Dokl. Akad. Nauk S.S.S.R. 30 301 305
    • (1941) Dokl. Akad. Nauk S.S.S.R. , vol.30 , pp. 301-305
    • Kolmogorov, A.N.1
  • 24
    • 0002385458 scopus 로고
    • On degeneration of isotropic turbulence in an incompressible viscous fluid
    • A.N. Kolmogorov 1941 On degeneration of isotropic turbulence in an incompressible viscous fluid Dokl. Akad. Nauk SSSR 31 538 540
    • (1941) Dokl. Akad. Nauk SSSR , vol.31 , pp. 538-540
    • Kolmogorov, A.N.1
  • 25
    • 0002385458 scopus 로고
    • Dissipation of energy in locally isotropic turbulence
    • A.N. Kolmogorov 1941 Dissipation of energy in locally isotropic turbulence Dokl. Akad. Nauk SSSR 32 16 18
    • (1941) Dokl. Akad. Nauk SSSR , vol.32 , pp. 16-18
    • Kolmogorov, A.N.1
  • 26
    • 33645506839 scopus 로고    scopus 로고
    • Statistical properties of coherent fine eddies in wall-bounded turbulent flows by direct numerical simulation
    • S.K. Das M. Tanahashi K. Shoji T. Miyauchi 2006 Statistical properties of coherent fine eddies in wall-bounded turbulent flows by direct numerical simulation Theor. Comput. Fluid Dyn. 20 55 71
    • (2006) Theor. Comput. Fluid Dyn. , vol.20 , pp. 55-71
    • Das, S.K.1    Tanahashi, M.2    Shoji, K.3    Miyauchi, T.4
  • 27
    • 28644444970 scopus 로고    scopus 로고
    • Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces
    • P. Cermelli E. Fried M.E. Gurtin 2005 Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces J. Fluid Mech. 544 339 351
    • (2005) J. Fluid Mech. , vol.544 , pp. 339-351
    • Cermelli, P.1    Fried, E.2    Gurtin, M.E.3
  • 28
    • 0038345303 scopus 로고    scopus 로고
    • Objectivity in classical continuum physics: Arationale for discarding the 'principle of invariance undersuperposed rigid body motions' in favour of purely objectiveconsiderations.
    • A.I. Murdoch 2003 Objectivity in classical continuum physics: arationale for discarding the 'principle of invariance undersuperposed rigid body motions' in favour of purely objectiveconsiderations. Continuum Mech. Thermodyn. 15 309 320
    • (2003) Continuum Mech. Thermodyn. , vol.15 , pp. 309-320
    • Murdoch, A.I.1
  • 30
    • 34548190303 scopus 로고    scopus 로고
    • General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids
    • D.M. Anderson P. Cermelli E. Fried M.E. Gurtin G.B. McFadden 2007 General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids J. Fluid Mech. 581 323 370
    • (2007) J. Fluid Mech. , vol.581 , pp. 323-370
    • Anderson, D.M.1    Cermelli, P.2    Fried, E.3    Gurtin, M.E.4
  • 31
    • 34648825963 scopus 로고    scopus 로고
    • Thermomechanics of the interface between a body and its environment
    • E. Fried M.E. Gurtin 2007 Thermomechanics of the interface between a body and its environment Continuum Mech. Thermodyn. 19 253 271
    • (2007) Continuum Mech. Thermodyn. , vol.19 , pp. 253-271
    • Fried, E.1    Gurtin, M.E.2
  • 33
    • 0035400701 scopus 로고    scopus 로고
    • On the characterization of geometrically necessary dislocations in finite plasticity
    • P. Cermelli M.E. Gurtin 2001 On the characterization of geometrically necessary dislocations in finite plasticity J. Mech. Phys. Solids 49 1539 1568
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 1539-1568
    • Cermelli, P.1    Gurtin, M.E.2


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