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References

Published online by Cambridge University Press:  09 February 2017

P. A. Davidson
P. A. Davidson
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University of Cambridge
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Introduction to Magnetohydrodynamics , pp. 544 - 550
Publisher: Cambridge University Press
Print publication year: 2016

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References

Primary Sources

Davidson, P.A., 1999, Magnetohydrodynamics in material processing. Annual Reviews Fluid Mech. 31, 273–300.Google Scholar
Feynman, R.P., Leighton, R.B. and Sands, M., 1964, The Feynman lectures on physics, Addison-Wesley.Google Scholar
Jackson, J.D., 1999, Classical electrodynamics, 3rd ed., Wiley.CrossRefGoogle Scholar
Lorrain, P. and Corson, D., 1970, Electromagnetic fields and waves, 2nd ed., W.H. Freeman & Co.Google Scholar
Acheson, D.J., 1990, Elementary fluid dynamics, Clarendon Press.Google Scholar
Batchelor, G.K., 1967, An introduction to fluid mechanics, Cambridge University Press.Google Scholar
Davidson, P.A., 2004, Turbulence: an introduction for scientists and engineers, Oxford University Press.Google Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.CrossRefGoogle Scholar
Davidson, P.A., Staplehurst, P.J. and Dalziel, S.B., 2006, On the evolution of eddies in a rapidly rotating system. J. Fluid Mech., 557, 135–144.Google Scholar
Feynman, R.P., Leighton, R.B. and Sands, M., 1964, The Feynman lectures on physics, Vol. II. Addison-Wesley.Google Scholar
Ranjan, A. and Davidson, P.A., 2014, Evolution of a turbulent cloud under rotation. J. Fluid Mech., 756, 488–509.Google Scholar
Tennekes, H. and Lumley, J.L., 1972, A first course in turbulence, The MIT Press.Google Scholar

Secondary Sources

Davidson, P.A., 1999, Magnetohydrodynamics in material processing. Annual Reviews Fluid Mech. 31, 273–300.Google Scholar
Feynman, R.P., Leighton, R.B. and Sands, M., 1964, The Feynman lectures on physics, Addison-Wesley.Google Scholar
Jackson, J.D., 1999, Classical electrodynamics, 3rd ed., Wiley.CrossRefGoogle Scholar
Lorrain, P. and Corson, D., 1970, Electromagnetic fields and waves, 2nd ed., W.H. Freeman & Co.Google Scholar
Acheson, D.J., 1990, Elementary fluid dynamics, Clarendon Press.Google Scholar
Batchelor, G.K., 1967, An introduction to fluid mechanics, Cambridge University Press.Google Scholar
Davidson, P.A., 2004, Turbulence: an introduction for scientists and engineers, Oxford University Press.Google Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.CrossRefGoogle Scholar
Davidson, P.A., Staplehurst, P.J. and Dalziel, S.B., 2006, On the evolution of eddies in a rapidly rotating system. J. Fluid Mech., 557, 135–144.Google Scholar
Feynman, R.P., Leighton, R.B. and Sands, M., 1964, The Feynman lectures on physics, Vol. II. Addison-Wesley.Google Scholar
Ranjan, A. and Davidson, P.A., 2014, Evolution of a turbulent cloud under rotation. J. Fluid Mech., 756, 488–509.Google Scholar
Tennekes, H. and Lumley, J.L., 1972, A first course in turbulence, The MIT Press.Google Scholar
Biskamp, D., 1993, Nonlinear magnetohydrodynamics, Cambridge University Press.CrossRefGoogle Scholar
Galloway, D.J. and Weiss, N.O., 1981, Convection and magnetic fields is stars., Astrophys. J., 243, 309–316.Google Scholar
Moffatt, H.K., 1978, Magnetic field generation in electrically conducting fluids, Cambridge University Press.Google Scholar
Priest, E., 2014, Magnetohydrodynamics of the sun, Cambridge University Press.CrossRefGoogle Scholar
Shercliff, J.A., 1965, A textbook of magnetohydrodynamics, Pergamon Press.Google Scholar
Chandrasekhar, S., 1961, Hydrodynamic stability, Dover.Google Scholar
Davidson, P.A., 1997, The role of angular momentum in the magnetic damping of turbulence, J. Fluid Mech., 336, 123–150.Google Scholar
Moreau, R., 1990, Magnetohydrodynamics, Kluwer Acad. Pub.Google Scholar
Müller, U. and Bühler, L., 2001, Magnetofluiddynamics in channels and containers, Springer.Google Scholar
Shercliff, J.A., 1965, A textbook of magnetohydrodynamics, Pergamon Press.Google Scholar
Arnold, V.I., 1966, Sur un principe variationnel pour les écoulements stationaires des liquides parfaits et ses applications aux problèmes de stabilité non-linéaires. J. Méc., 5, 9–15.Google Scholar
Balbus, S.A. and Hawley, J. F., 1998, Instability, turbulence and enhanced transport in accretion disks. Rev. Modern Phys., 70 (1), 1–53.CrossRefGoogle Scholar
Bernstein, I.B., et al., 1958, An energy principle for hydromagnetic stability problems. Proc. Roy. Soc. Lond. A., 244.Google Scholar
Biskamp, D., 1993, Non-linear magnetohydrodynamics, Cambridge University Press.Google Scholar
Chandrasekhar, S., 1960, The stability of non-dissipative Couette flow in hydromagnetics. Proc. Nat. Acad. Sci., 46, 253–257.Google Scholar
Chandrasekhar, S., 1961, Hydrodynamic and hydromagnetic stability, Oxford University Press.Google Scholar
Davidson, P.A., 2000, An energy criterion for the linear stability of conservative flows. J. Fluid Mech., 402, 329–348.CrossRefGoogle Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.Google Scholar
Frieman, E. and Rotenberg, M., 1960, On hydromagnetic stability of stationary equilibria. Rev. Mod. Phys., 32(4), 898–939.Google Scholar
Kelvin, Lord, 1887, On the stability of steady and of periodic fluid motion. – Maximum and minimum energy in vortex motion. Phil. Mag., 23, 529.Google Scholar
Moffatt, H.K., 1978, Magnetic field generation in electrically conducting fluids, Cambridge University Press.Google Scholar
Moffatt, H.K., 1986, Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations. J. Fluid Mech., 166, 359–378.Google Scholar
Velikhov, E.P., 1959, Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Soviet Physics JETP, 36, 1398–1404.Google Scholar
Batchelor, G.K., 1953, The theory of homogeneous turbulence, Cambridge University Press.Google Scholar
Batchelor, G.K. and Proudman, I., 1956, The large-scale structure of homogeneous turbulence. Phil. Trans. R. Soc. Lond. A 248, 369–405.Google Scholar
Biskamp, D., 2003, Magnetohydrodynamic turbulence, Cambridge University Press.Google Scholar
Davidson, P.A., 2009, The role of angular momentum conservation in homogeneous turbulence. J. Fluid Mech., 632, 329–358.Google Scholar
Davidson, P.A., 2010, On the decay of saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech., 663, 268–292.Google Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.CrossRefGoogle Scholar
Davidson, P.A., 2015, Turbulence: an introduction for scientists and engineers, 2nd ed., Oxford University Press.CrossRefGoogle Scholar
Davidson, P.A., Okamoto, N. and Kaneda, Y., 2012, On freely decaying, anisotropic, axisymmetric, Saffman turbulence. J. Fluid Mech., 706, 150–172.CrossRefGoogle Scholar
Gödecke, K., 1935, Messungen der atmospharischen Turbulenz in Bodennähe mit einer Hitzdrahtmethode. Ann. Hydrogr., 10, 400–410.Google Scholar
Ishida, T., Davidson, P.A. and Kaneda, Y., 2006, On the decay of isotropic turbulence. J. Fluid Mech., 564, 455–475.Google Scholar
Kolmogorov, A.N., 1941a, Local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30(4), 299–303.Google Scholar
Kolmogorov, A.N., 1941b, Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR, 32(1), 19–21.Google Scholar
Kolmogorov, A.N., 1941c, On the degeneration of isotropic turbulence in an incompressible viscous fluid. Dokl. Akad. Nauk. SSSR, 31(6), 538–541.Google Scholar
Kolmogorov, A.N., 1962, A refinement of the concept of the local structure of turbulence in an incompressible viscous fluid at large Reynolds number. J. Fluid Mech., 13 (1), 82.Google Scholar
Krogstad, P.-A. and Davidson, P.A., 2010, Is grid turbulence Saffman turbulence? J. Fluid Mech. 642, 373–394.Google Scholar
Landau, L.D. and Lifshitz, E.M., 1959, Fluid mechanics, 1st ed., Pergamon.Google Scholar
Proudman, I. and Reid, W.H., 1954, On the decay of a normally distributed and homogeneous turbulent velocity field. Phil. Trans. R. Soc. Lond. A, 247, 163–189.Google Scholar
Saffman, P.G., 1967, The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27(3), 581–593.Google Scholar
Tennekes, H. and Lumley, J.L., 1972, A first course in turbulence, MIT Press.CrossRefGoogle Scholar
Batchelor, G.K., 1950, On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. Roy. Soc. London, A201, 405–416.Google Scholar
Batchelor, G.K., 1953. The theory of homogeneous turbulence, Cambridge University Press.Google Scholar
Davidson, P.A., 1997, The role of angular momentum in the magnetic damping of turbulence. J. Fluid Mech., 336, 123–150.Google Scholar
Davidson, P.A., 2009, The role of angular momentum conservation in homogeneous turbulence. J. Fluid Mech., 632, 329–358.Google Scholar
Davidson, P.A., 2010, On the decay of Saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech., 663, 268–292.Google Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.CrossRefGoogle Scholar
Davidson, P.A., 2015, Turbulence: an introduction for scientists and engineers, 2nd ed., Oxford University Press.Google Scholar
Federrath, C., Schober, J., Bovino, S. and Schleicher, D.R.G., 2014, The turbulent dynamo in highly compressible supersonic plasmas. Astro. Phys. Lett., 797, L19.Google Scholar
Ishida, T., Davidson, P.A. and Kaneda, Y., 2006, On the decay of isotropic turbulence. J. Fluid Mech., 564, 455–475.CrossRefGoogle Scholar
Ohkitani, K., 2002, Numerical study of comparison of vorticity and passive vectors in turbulence and inviscid flows. Phys. Rev. E., 65, 046304.Google Scholar
Okamoto, N., Davidson, P.A. and Kaneda, Y., 2010, On the decay of low magnetic Reynolds number turbulence in an imposed magnetic field. J. Fluid Mech., 651, 295–318.Google Scholar
Saffman, P.G., 1967, The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27(3),581–593.Google Scholar
Schekochihin, A.A., Iskakov, A.B., Cowley, S.C., McWilliams, J.C., Proctor, M.R.E. and Yousef, T.A., 2007, Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers. New J. Phys., 9, 300.CrossRefGoogle Scholar
Stribling, T. and Matthaeus, W.H., 1991, Relaxation processes in a low-order three-dimensional magnetohydrodynamic model. Phys. Fluids B 3, 1848–1864.Google Scholar
Taylor, J.B., 1974, Relaxation of toroidal plasma and generation of reversed magnetic fields. Phys. Rev. Lett., 33, 1139–1141.Google Scholar
Tobias, S.M., Cattaneo, F. and Boldyrev, S., 2013, MHD turbulence: Field guided, dynamo driven and magneto-rotational. In Ten chapters in turbulence, Davidson, P.A., Kaneda, Y. and Sreenivasan, K.R., eds, Cambridge University Press.Google Scholar
Zhdankin, V., Boldyrev, S., Perez, J. C. and Tobias, S.M., 2014, Energy dissipation in MHD turbulence: Coherent structures or nanoflares? Astrophys. J., 795, 127–135.CrossRefGoogle Scholar
Biskamp, D., 1993, Nonlinear magnetohydrodynamics, Cambridge University Press.CrossRefGoogle Scholar
Galloway, D.J. and Weiss, N.O., 1981, Convection and magnetic fields is stars., Astrophys. J., 243, 309–316.Google Scholar
Moffatt, H.K., 1978, Magnetic field generation in electrically conducting fluids, Cambridge University Press.Google Scholar
Priest, E., 2014, Magnetohydrodynamics of the sun, Cambridge University Press.CrossRefGoogle Scholar
Shercliff, J.A., 1965, A textbook of magnetohydrodynamics, Pergamon Press.Google Scholar
Chandrasekhar, S., 1961, Hydrodynamic stability, Dover.Google Scholar
Davidson, P.A., 1997, The role of angular momentum in the magnetic damping of turbulence, J. Fluid Mech., 336, 123–150.Google Scholar
Moreau, R., 1990, Magnetohydrodynamics, Kluwer Acad. Pub.Google Scholar
Müller, U. and Bühler, L., 2001, Magnetofluiddynamics in channels and containers, Springer.Google Scholar
Shercliff, J.A., 1965, A textbook of magnetohydrodynamics, Pergamon Press.Google Scholar
Arnold, V.I., 1966, Sur un principe variationnel pour les écoulements stationaires des liquides parfaits et ses applications aux problèmes de stabilité non-linéaires. J. Méc., 5, 9–15.Google Scholar
Balbus, S.A. and Hawley, J. F., 1998, Instability, turbulence and enhanced transport in accretion disks. Rev. Modern Phys., 70 (1), 1–53.CrossRefGoogle Scholar
Bernstein, I.B., et al., 1958, An energy principle for hydromagnetic stability problems. Proc. Roy. Soc. Lond. A., 244.Google Scholar
Biskamp, D., 1993, Non-linear magnetohydrodynamics, Cambridge University Press.Google Scholar
Chandrasekhar, S., 1960, The stability of non-dissipative Couette flow in hydromagnetics. Proc. Nat. Acad. Sci., 46, 253–257.Google Scholar
Chandrasekhar, S., 1961, Hydrodynamic and hydromagnetic stability, Oxford University Press.Google Scholar
Davidson, P.A., 2000, An energy criterion for the linear stability of conservative flows. J. Fluid Mech., 402, 329–348.CrossRefGoogle Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.Google Scholar
Frieman, E. and Rotenberg, M., 1960, On hydromagnetic stability of stationary equilibria. Rev. Mod. Phys., 32(4), 898–939.Google Scholar
Kelvin, Lord, 1887, On the stability of steady and of periodic fluid motion. – Maximum and minimum energy in vortex motion. Phil. Mag., 23, 529.Google Scholar
Moffatt, H.K., 1978, Magnetic field generation in electrically conducting fluids, Cambridge University Press.Google Scholar
Moffatt, H.K., 1986, Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations. J. Fluid Mech., 166, 359–378.Google Scholar
Velikhov, E.P., 1959, Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Soviet Physics JETP, 36, 1398–1404.Google Scholar
Batchelor, G.K., 1953, The theory of homogeneous turbulence, Cambridge University Press.Google Scholar
Batchelor, G.K. and Proudman, I., 1956, The large-scale structure of homogeneous turbulence. Phil. Trans. R. Soc. Lond. A 248, 369–405.Google Scholar
Biskamp, D., 2003, Magnetohydrodynamic turbulence, Cambridge University Press.Google Scholar
Davidson, P.A., 2009, The role of angular momentum conservation in homogeneous turbulence. J. Fluid Mech., 632, 329–358.Google Scholar
Davidson, P.A., 2010, On the decay of saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech., 663, 268–292.Google Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.CrossRefGoogle Scholar
Davidson, P.A., 2015, Turbulence: an introduction for scientists and engineers, 2nd ed., Oxford University Press.CrossRefGoogle Scholar
Davidson, P.A., Okamoto, N. and Kaneda, Y., 2012, On freely decaying, anisotropic, axisymmetric, Saffman turbulence. J. Fluid Mech., 706, 150–172.CrossRefGoogle Scholar
Gödecke, K., 1935, Messungen der atmospharischen Turbulenz in Bodennähe mit einer Hitzdrahtmethode. Ann. Hydrogr., 10, 400–410.Google Scholar
Ishida, T., Davidson, P.A. and Kaneda, Y., 2006, On the decay of isotropic turbulence. J. Fluid Mech., 564, 455–475.Google Scholar
Kolmogorov, A.N., 1941a, Local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30(4), 299–303.Google Scholar
Kolmogorov, A.N., 1941b, Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR, 32(1), 19–21.Google Scholar
Kolmogorov, A.N., 1941c, On the degeneration of isotropic turbulence in an incompressible viscous fluid. Dokl. Akad. Nauk. SSSR, 31(6), 538–541.Google Scholar
Kolmogorov, A.N., 1962, A refinement of the concept of the local structure of turbulence in an incompressible viscous fluid at large Reynolds number. J. Fluid Mech., 13 (1), 82.Google Scholar
Krogstad, P.-A. and Davidson, P.A., 2010, Is grid turbulence Saffman turbulence? J. Fluid Mech. 642, 373–394.Google Scholar
Landau, L.D. and Lifshitz, E.M., 1959, Fluid mechanics, 1st ed., Pergamon.Google Scholar
Proudman, I. and Reid, W.H., 1954, On the decay of a normally distributed and homogeneous turbulent velocity field. Phil. Trans. R. Soc. Lond. A, 247, 163–189.Google Scholar
Saffman, P.G., 1967, The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27(3), 581–593.Google Scholar
Tennekes, H. and Lumley, J.L., 1972, A first course in turbulence, MIT Press.CrossRefGoogle Scholar
Batchelor, G.K., 1950, On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. Roy. Soc. London, A201, 405–416.Google Scholar
Batchelor, G.K., 1953. The theory of homogeneous turbulence, Cambridge University Press.Google Scholar
Davidson, P.A., 1997, The role of angular momentum in the magnetic damping of turbulence. J. Fluid Mech., 336, 123–150.Google Scholar
Davidson, P.A., 2009, The role of angular momentum conservation in homogeneous turbulence. J. Fluid Mech., 632, 329–358.Google Scholar
Davidson, P.A., 2010, On the decay of Saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech., 663, 268–292.Google Scholar
Davidson, P.A., 2013, Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press.CrossRefGoogle Scholar
Davidson, P.A., 2015, Turbulence: an introduction for scientists and engineers, 2nd ed., Oxford University Press.Google Scholar
Federrath, C., Schober, J., Bovino, S. and Schleicher, D.R.G., 2014, The turbulent dynamo in highly compressible supersonic plasmas. Astro. Phys. Lett., 797, L19.Google Scholar
Ishida, T., Davidson, P.A. and Kaneda, Y., 2006, On the decay of isotropic turbulence. J. Fluid Mech., 564, 455–475.CrossRefGoogle Scholar
Ohkitani, K., 2002, Numerical study of comparison of vorticity and passive vectors in turbulence and inviscid flows. Phys. Rev. E., 65, 046304.Google Scholar
Okamoto, N., Davidson, P.A. and Kaneda, Y., 2010, On the decay of low magnetic Reynolds number turbulence in an imposed magnetic field. J. Fluid Mech., 651, 295–318.Google Scholar
Saffman, P.G., 1967, The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27(3),581–593.Google Scholar
Schekochihin, A.A., Iskakov, A.B., Cowley, S.C., McWilliams, J.C., Proctor, M.R.E. and Yousef, T.A., 2007, Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers. New J. Phys., 9, 300.CrossRefGoogle Scholar
Stribling, T. and Matthaeus, W.H., 1991, Relaxation processes in a low-order three-dimensional magnetohydrodynamic model. Phys. Fluids B 3, 1848–1864.Google Scholar
Taylor, J.B., 1974, Relaxation of toroidal plasma and generation of reversed magnetic fields. Phys. Rev. Lett., 33, 1139–1141.Google Scholar
Tobias, S.M., Cattaneo, F. and Boldyrev, S., 2013, MHD turbulence: Field guided, dynamo driven and magneto-rotational. In Ten chapters in turbulence, Davidson, P.A., Kaneda, Y. and Sreenivasan, K.R., eds, Cambridge University Press.Google Scholar
Zhdankin, V., Boldyrev, S., Perez, J. C. and Tobias, S.M., 2014, Energy dissipation in MHD turbulence: Coherent structures or nanoflares? Astrophys. J., 795, 127–135.CrossRefGoogle Scholar
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Davidson, P.A., 1992, Swirling flow in an axisymmetric cavity or arbitrary profile driven by a rotating magnetic field. J. Fluid Mech. 245: 660–99.Google Scholar
Davidson, P.A.,1995, Magnetic damping of jets and vortices. J. Fluid Mech., 299: 153.Google Scholar
Davidson, P.A., 1997, The role of angular momentum in MHD turbulence. J. Fluid Mech., 336: 123–50.Google Scholar
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Davidson, P.A., Kinnear, D., Lingwood, R.J., Short, D.J. and He, X., 1999, The role of Ekman pumping and the dominance of swirl in confined flows driven by Lorentz forces. European J. Mech. B, 18, 693–711.Google Scholar
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Davidson, P.A., 1994, Global stability of two-dimensional and axisymmetric Euler flows. J. Fluid Mech., 276, 273–305.Google Scholar
Freidberg, J.P., 2014, Ideal MHD, Cambridge University Press.Google Scholar
Khan, R., Mizuguchi, N., Nakajima, N., Hayashi, T., 2007, Dynamics of the ballooning mode and the relationship to edge-localised modes in a spherical tokamak. Phys. Plasmas, 14, 062302.Google Scholar
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  • References
  • P. A. Davidson, University of Cambridge
  • Book: Introduction to Magnetohydrodynamics
  • Online publication: 09 February 2017
  • Chapter DOI: https://doi.org/10.1017/9781316672853.025
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  • References
  • P. A. Davidson, University of Cambridge
  • Book: Introduction to Magnetohydrodynamics
  • Online publication: 09 February 2017
  • Chapter DOI: https://doi.org/10.1017/9781316672853.025
Available formats
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  • References
  • P. A. Davidson, University of Cambridge
  • Book: Introduction to Magnetohydrodynamics
  • Online publication: 09 February 2017
  • Chapter DOI: https://doi.org/10.1017/9781316672853.025
Available formats
×