Abstract:
This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present-day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, the damping of velocity fluctuations by the Lorentz force, and the development of anisotropies can be characterized at different scales. In this context we consider three different configurations often studied in the literature: mechanically forced turbulence, freely decaying turbulence, and turbulence in the presence of a uniform magnetic field. Each configuration is of interest for different geophysical and astrophysical applications. Local and nonlocal transfers are discussed for each case. Whereas the transfer between scales of solely kinetic or solely magnetic energy is local, transfers between kinetic and magnetic fields are observed to be local or nonlocal depending on the configuration. Scale interactions in the cascade of magnetic helicity are also reviewed. Based on the results, the validity of several usual assumptions in hydrodynamic turbulence, such as isotropy of the small scales or universality, is discussed. © 2011 by Annual Reviews. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | Scale interactions in magnetohydrodynamic turbulence |
Autor: | Mininni, P.D. |
Filiación: | Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina NCAR, Boulder, CO 80307-3000, United States
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Palabras clave: | isotropy; magnetohydrodynamics; modeling; simulation; universality; Astrophysical applications; Computing power; Decaying turbulence; Different scale; Dynamo action; Hydrodynamic turbulence; isotropy; Magnetic energies; Magnetic helicity; Magnetohydrodynamic turbulence; modeling; Nonlocal; Scale interactions; Shell-to-shell transfers; simulation; Small scale; universality; Velocity fluctuations; Electric generators; Lorentz force; Magnetic fields; Magnetohydrodynamics; Turbulence; anisotropic medium; damping; geodynamo; isotropy; kinetic energy; literature review; magnetic field; magnetohydrodynamics; turbulence |
Año: | 2011
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Volumen: | 43
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Página de inicio: | 377
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Página de fin: | 397
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DOI: |
http://dx.doi.org/10.1146/annurev-fluid-122109-160748 |
Título revista: | Annual Review of Fluid Mechanics
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Título revista abreviado: | Ann. Rev. Fluid Mech.
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ISSN: | 00664189
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CODEN: | ARVFA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00664189_v43_n_p377_Mininni |
Referencias:
- Alexakis, A., Nonlocal phenomenology for anisotropic magnetohydrodynamic turbulence (2007) Astrophys. J., 667, pp. L93-96
- Alexakis, A., Bigot, B., Politano, H., Galtier, S., Anisotropic fluxes and nonlocal interactions in magneto-hydrodynamic turbulence (2007) Phys. Rev. e, 76, p. 056313
- Alexakis, A., Mininni, P.D., Pouquet, A., Imprint of large-scale flows on turbulence (2005) Phys. Rev. Lett., 95, p. 264503
- Alexakis, A., Mininni, P.D., Pouquet, A., Shell to shell energy transfer in MHD. I. Steady state turbulence (2005) Phys. Rev. e, 72, p. 046301
- Alexakis, A., Mininni, P.D., Pouquet, A., On the inverse cascade of magnetic helicity (2006) Astrophysical Journal, 640 (I1), pp. 335-343. , DOI 10.1086/500082
- Alexakis, A., Mininni, P.D., Pouquet, A., Turbulent cascades, transfer, and scale interactions in magneto-hydrodynamics (2007) New J. Phys., 9, p. 298
- Aluie, H., Eyink, G.L., Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter (2009) Phys. Fluids, 21, p. 115108
- Aluie, H., Eyink, G.L., Scale locality of magnetohydrodynamic turbulence (2010) Phys. Rev. Lett., 104, p. 081101
- Batchelor, G.K., On the spontaneous magnetic field in a conducting liquid in turbulent motion (1950) Proc. R. Soc. Lond. Ser.A, 201, pp. 405-16
- Beresnyak, A., Lazarian, A., Comparison of spectral slopes of magnetohydrodynamic and hydrodynamic turbulence and measurements of alignment effects (2009) Astrophys. J., 702, pp. 1190-98
- Boldyrev, S., Spectrum of magnetohydrodynamic turbulence (2006) Phys. Rev. e, 96, p. 115002
- Brandenburg, A., The inverse cascade and nonlinear α-effect in simulations of isotropic helical hydro-magnetic turbulence (2001) Astrophys. J., 550, pp. 824-40
- Brandenburg, A., Subramanian, K., Astrophysical magnetic fields and nonlinear dynamo theory (2005) Physics Reports, 417 (1-4), pp. 1-209. , DOI 10.1016/j.physrep.2005.06.005, PII S037015730500267X
- Bruno, R., Carbone, V., The solar wind as a turbulence laboratory (2005) Living Rev. Solar Phys., 2, p. 4
- Carati, D., Debliquy, O., Knaepen, B., Teaca, B., Verma, M., Energy transfers in forced MHD turbulence (2006) J. Turbul., 7, p. 51
- Carlier, J., Laval, J.-P., Stanislas, M., Some experimental support at a high Reynolds number to a new hypothesis for turbulence modeling (2001) Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, 329 (1), pp. 35-40. , DOI 10.1016/S1620-7742(00)01281-2
- Chandrasekhar, S., The invariant theory of isotropic turbulence in magnetohydrodynamics (1951) Proc. R. Soc. Lond. Ser. A, 204, pp. 435-49
- Childress, S., Gilbert, A.D., (1995) Stretch, Twist, Fold: The Fast Dynamo, , Berlin: Springer- Verlag
- Dar, G., Verma, M.K., Eswaran, V., Energy transfer in two-dimensional magnetohydrodynamic turbulence: Formalism and numerical results (2001) Physica D: Nonlinear Phenomena, 157 (3), pp. 207-225. , DOI 10.1016/S0167-2789(01)00307-4, PII S0167278901003074
- Debliquy, O., Verma, M.K., Carati, D., Energy fluxes and shell-to-shell transfers in three-dimensional decaying magnetohydrodynamic turbulence (2005) Phys. Plasmas, 12, p. 042309
- Dmitruk, P., Gómez, D.O., Matthaeus, W.H., Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics (2003) Phys. Plasmas, 10, pp. 3584-91
- Domaradzki, J.A., Analysis of energy transfer in direct numerical simulations of isotropic turbulence (1988) Phys. Fluids, 31, pp. 2747-49
- Domaradzki, J.A., Carati, D., An analysis of the energy transfer and the locality of nonlinear interactions in turbulence (2007) Phys. Fluids, 19, p. 085112
- Domaradzki, J.A., Carati, D., A comparison of spectral sharp and smooth filters in the analysis of nonlinear interactions and energy transfer in turbulence (2007) Phys. Fluids, 19, p. 085111
- Domaradzki, J.A., Rogallo, R.S., Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence (1990) Phys. Fluids, 2, pp. 413-26
- Eyink, G.L., Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer (1994) Physica D, 78, pp. 222-40
- Eyink, G.L., Locality of turbulent cascades (2005) Physica D: Nonlinear Phenomena, 207 (1-2), pp. 91-116. , DOI 10.1016/j.physd.2005.05.018, PII S0167278905002253
- Eyink, G.L., Aluie, H., Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining (2009) Phys. Fluids, 21, p. 115107
- Galtier, S., Nazarenko, S.V., Newell, A.C., Pouquet, A., A weak turbulence theory for incompressible mag-netohydrodynamics (2000) J. Plasma Phys., 63, pp. 447-88
- Galtier, S., Pouquet, A., Mangeney, A., On spectral scaling laws for incompressible anisotropic magneto-hydrodynamic turbulence (2005) Phys. Plasmas, 12, p. 092310
- Ghosh, S., Matthaeus, W.H., Montgomery, D.C., The evolution of cross helicity in driven/dissipative two-dimensional magnetohydrodynamics (1988) Phys. Fluids, 31, pp. 2171-84
- Goldreich, P., Sridhar, P., Toward a theory of interstellar turbulence. 2. Strong Alfvenic turbulence (1995) Astrophys. J., 438, pp. 763-75
- Gomez, D.O., Mininni, P.D., Direct numerical simulations of helical dynamo action: MHD and beyond (2004) Nonlinear Processes in Geophysics, 11 (5-6), pp. 619-629
- Gomez, T., Politano, H., Pouquet, A., On the validity of a nonlocal approach for MHD turbulence (1999) Physics of Fluids, 11 (8), pp. 2298-2306
- Graham, J.P., Cameron, R., Schuessler, M., Turbulent small-scale dynamo action insolar surface simulations (2010) Astrophys. J., 714, pp. 1606-16
- Graham, J.P., Mininni, P.D., Pouquet, A., Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks (2009) Phys. Rev. e, 80, p. 016313
- Grappin, R., Pouquet, A., Léorat, J., Dependence on correlation of MHD turbulence spectra (1983) Astron. Astrophys., 126, pp. 51-56
- Haugen, N.E.L., Brandenburg, A., Dobler, W., Is nonhelical hydromagnetic turbulence peaked at small scales? (2003) Astrophysical Journal, 597 (II2), pp. L141-L144. , DOI 10.1086/380189
- Haugen, N.E.L., Brandenburg, A., Dobler, W., Simulations of nonhelical hydromagnetic turbulence (2004) Phys. Rev. e, 70, p. 016308
- Iroshnikov, P.S., Turbulence of a conducting fluid in a strong magnetic field (1963) Sov. Astron., 7, pp. 566-71
- Kazanstev, A.P., Enhancement of a magnetic field by a conducting fluid (1968) Sov. Phys. JETP, 26, pp. 1031-34
- Kinney, R., McWilliams, J.C., Tajima, T., Coherent structures and turbulent cascades in two-dimensional incompressible magnetohydrodynamic turbulence (1995) Phys. Plasmas, 2, pp. 3623-39
- Knaepen, B., Moreau, R.J., Magnetohydrodynamic turbulence at low magnetic Reynolds number (2008) Annual Review of Fluid Mechanics, 40, pp. 25-45. , DOI 10.1146/annurev.fluid.39.050905.110231
- Kraichnan, R.H., The structure of isotropic turbulence at very high Reynolds numbers (1959) J. Fluid Mech., 5, pp. 497-543
- Kraichnan, R.H., Inertial-range spectrum of hydromagnetic turbulence (1965) Phys. Fluids, 8, pp. 1385-87
- Krause, F., Raedler, K.H., (1980) Mean-Field Magnetohydrodynamics and Dynamo Theory, , New York: Pergamon
- Lee, E., Brachet, M.E., Pouquet, A., Mininni, P.D., Lack of universality in decaying magnetohydrodynamic turbulence (2009) Phys. Rev. e, 81, p. 016318
- Lessinnes, T., Carati, D., Verma, M.K., Energy transfers in shell models for magnetohydrodynamic turbulence (2009) Phys. Rev. e, 79, p. 066307
- Mason, J., Cattaneo, F., Boldyrev, S., Dynamic alignment in driven magnetohydrodynamic turbulence (2006) Phys. Rev. Lett., 97, p. 255002
- Mason, J., Cattaneo, F., Boldyrev, S., Numerical measurements of the spectrum in magnetohydrodynamic turbulence (2008) Phys. Rev. e, 77, p. 036403
- Matthaeus, W.H., Montgomery, D., Selective decay hypothesis at high mechanical and magnetic Reynolds numbers (1980) Ann. N. Y. Acad. Sci., 357, pp. 203-22
- Matthaeus, W.H., Pouquet, A., Mininni, P.D., Dmitruk, P., Breech, B., Rapid alignment of velocity and magnetic field in magnetohydrodynamic turbulence (2008) Phys. Rev. Lett., 100, p. 085003
- Matthaeus, W.H., Zhou, Y., Extended inertial range phenomenology of magnetohydrodynamic turbulence (1989) Phys. Fluids B, 1, pp. 1929-31
- Meneguzzi, M., Frisch, U., Pouquet, A., Helical and nonhelical turbulent dynamos (1981) Phys. Rev. Lett., 47, pp. 1060-64
- Milano, L.J., Matthaeus, W.H., Dmitruk, P., Montgomery, D.C., Local anisotropy in incompressible magnetohydrodynamic turbulence (2001) Physics of Plasmas, 8 (6), pp. 2673-2681. , DOI 10.1063/1.1369658
- Mininni, P.D., Alexakis, A., Pouquet, A., Shell to shell energy transfer in MHD. II. Kinematic dynamo (2005) Phys. Rev. e, 72, p. 046302
- Mininni, P.D., Alexakis, A., Pouquet, A., Large-scale flow effects, energy transfer, and self-similarity on turbulence (2006) Phys. Rev. e, 74, p. 016303
- Mininni, P.D., Alexakis, A., Pouquet, A., Energy transfer in Hall-MHD turbulence: Cascades, backscatter, and dynamo action (2007) Journal of Plasma Physics, 73 (3), pp. 377-401. , DOI 10.1017/S0022377806004624, PII S0022377806004624
- Mininni, P.D., Alexakisa Pouquet, A., Nonlocal interactions inhydrodynamic turbulence at high Reynolds numbers: The slow emergence of scaling laws (2008) Phys. Rev. e, 77, p. 036306
- Mininni, P.D., Montgomery, D.C., Pouquet, A., Numerical solutions of the three-dimensional magneto-hydrodynamic α model (2005) Phys. Rev. e, 71, p. 046304
- Mininni, P.D., Montgomery, D.C., Pouquet, A., A numerical study of the α model for two-dimensional magnetohydrodynamic turbulent flows (2005) Phys. Fluids, 17, p. 035112
- Mininni, P.D., Pouquet, A., Energy spectra stemming from interactions of Alfven waves and turbulent eddies (2007) Phys. Rev. Lett., 99, p. 254502
- Mininni, P.D., Pouquet, A., Finite dissipation and intermittency in magnetohydrodynamics (2009) Phys. Rev. e, 80, p. 025401
- Moffatt, H.K., (1978) Magnetic Field Generation in Electrically Conducting Fluids, , Cambridge, UK: Cambridge Univ. Press
- Moffatt, H.K., Saffman, P.G., Comment on "growth of a weak magnetic field in a turbulent conducting fluid with large magnetic Prandtl number." (1964) Phys. Fluids, 7, p. 155
- Monchaux, R., Berhanu, M., Bourgoin, M., Moulin, M., Odier, P., Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium (2007) Phys. Rev. Lett., 98, p. 044502
- Müller, W.C., Biskamp, D., Grappin, R., Statistical anisotropy of magnetohydrodynamic turbulence (2003) Phys. Rev. e, 67, p. 066302
- Müller, W.C., Grappin, R., Spectral energy dynamics in magnetohydrodynamic turbulence (2005) Phys. Rev. Lett., 95, p. 114502
- Nazarenko, S.V., Newell, A.C., Galtier, S., Non-local MHD turbulence (2001) Physica D: Nonlinear Phenomena, 152-153, pp. 646-652. , DOI 10.1016/S0167-2789(01)00197-X, PII S016727890100197X
- Ohkitani, K., Kida, S., Triad interactions in a forced turbulence (1992) Phys. Fluids A, 4, pp. 794-802
- Perez, J.C., Boldyrev, S., Role of cross-helicity in magnetohydrodynamic turbulence (2009) Phys. Rev. Lett., 102, p. 025003
- Plunianf Stepanov, R., A non-local shell model of hydrodynamic and magnetohydrodinamic turbulence (2007) New J. Phys., 9, p. 294
- Podesta, J.J., Roberts, D.A., Goldstein, M.L., Spectral exponents of kinetic and magnetic energy spectra in solar wind turbulence (2007) Astrophys. J., 664, pp. 543-48
- Politano, H., Pouquet, A., Dynamical length scales for turbulent magnetized flows (1998) Geophysical Research Letters, 25 (3), pp. 273-276
- Politano, H., Pouquet, A., Von Kármán-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions (1998) Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 57 (1), pp. R21-R24
- Poulain, C., Mazellier, N., Chevillard, L., Gagne, Y., Baudet, C., Dynamics of spatial Fourier modes in turbulence : Sweeping effect, long-time correlations and temporal intermittency (2006) European Physical Journal B, 53 (2), pp. 219-224. , DOI 10.1140/epjb/e2006-00354-y
- Pouquet, A., Frisch, U., Léorat, J., Strong MHD helical turbulence and the nonlinear dynamo effect (1976) J. Fluid Mech., 77, pp. 321-54
- Pouquet, A., Meneguzzi, M., Frisch, U., The growth of correlations in MHD turbulence (1986) Phys. Rev.A, 33, pp. 4266-76
- Schekochihin, A., Cowley, S.C., Yousef, T.A., MHD turbulence: Nonlocal, anisotropic, nonuniversalIn IUTAM Symp (2008) Comput. Phys. New Perspect. Turbul., pp. 347-54. , ed. Y Kaneda Dordrecht, The Neth.: Springer
- Schekochihin, A.A., Cowley, S.C., Hammett, G.W., Maron, J.L., McWilliams, J.C., A model of nonlinear evolution and saturation of the turbulent MHD dynamo (2002) New J. Phys., 4, pp. 1-22
- Schekochihin, A.A., Cowley, S.C., Taylor, S.F., Maron, J.L., McWilliams, J.C., Simulations of the small-scale turbulent dynamo (2004) Astrophysical Journal, 612 (I1), pp. 276-307. , DOI 10.1086/422547
- Schekochihin, A.A., Maron, J.L., Cowley, S.C., McWilliams, J.C., The small-scale structure of magnetohydrodynamic turbulence with large magnetic Prandtl numbers (2002) Astrophysical Journal, 576 (I2), pp. 806-813. , DOI 10.1086/341814
- Servidio, S., Matthaeus, W.H., Dmitruk, P., Depression of nonlinearity in decaying isotropic MHD turbulence (2008) Phys. Rev. Lett., 100, p. 095005
- Shebalin John, V., Matthaeus William, H., Montgomery David, ANISOTROPY IN MHD TURBULENCE DUE TO A MEAN MAGNETIC FIELD (1983) Journal of Plasma Physics, 29 (PART 3), pp. 525-547
- Shen, X., Warhaft, Z., The anisotropy of the small-scale structure in high Reynolds number (ra; ∼ 1000) turbulent shear flow (2000) Phys. Fluids, 12, pp. 2976-89
- Steenbeck, M., Krause, F., Rädler, K.H., Berechnung der mittleren Lorentz-Feldstaerke v × b fuer ein elektrisch leitendendes Medium in turbulenter, durch Coriolis-Kraefte beeinflußter Bewegung (1966) Z. Naturforsch., 21 A, pp. 369-76
- Stepanov, R., Plunian, F., Phenomenology of turbulent dynamo growth and saturation (2008) Astrophys. J., 680, pp. 809-15
- Stribling, T., Matthaeus, W.H., Relaxation processes in a low-order three-dimensional magnetohydrody-namics model (1991) Phys. Fluids B, 3, pp. 1848-64
- Strumik, M., MacEk, W.M., Statistical analysisoftransfer offluctuationsinsolar wind turbulence.Nonlinear Process (2008) Geophys., 15, pp. 607-13
- Strumik, M., MacEk, W.M., Testing for Markovian character and modeling of intermittency in solar wind turbulence (2008) Phys. Rev. e, 78, p. 026414
- Teaca, B., Verma, M.K., Knaepen, B., Carati, D., Energy transfer in anisotropic magnetohydrodynamic turbulence (2009) Phys. Rev. e, 79, p. 046312
- Ting, A.C., Matthaeus, W.H., Montgomery, D., Turbulent relaxation processes in magnetohydrodynamics (1986) Phys. Fluids, 29, pp. 3261-74
- Vainshtein, S.I., Zeldovich, Y.B., Origin of magnetic fields in astrophysics (1972) Sov. Phys. Usp., 15, pp. 159-72
- Verma, M.K., Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence (2003) Pramana, 61, pp. 577-94
- Verma, M.K., Statistical theory of magnetohydrodynamic turbulence: Recent results (2004) Physics Reports, 401 (5-6), pp. 229-380. , DOI 10.1016/j.physrep.2004.07.007, PII S0370157304003163
- Verma, M.K., Ayyer, A., Chandra, A.V., Energy transfers and locality in magnetohydrodynamic turbulence (2005) Phys. Plasmas, 12, p. 082307
- Wiltse, J.M., Glezer, A., Manipulation of free shear flows using piezoelectric actuators (1993) J. Fluid Mech., 249, pp. 261-85
- Wiltse, J.M., Glezer, A., Direct excitation of small-scale motions in free shear flows (1998) Physics of Fluids, 10 (8), pp. 2026-2036
- Yeung, P.K., Brasseur, J.G., Qunzhen Wang, Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views (1995) Journal of Fluid Mechanics, 283, pp. 43-95
- Yousef, T.A., Rincon, F., Schekochihin, A.A., Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence (2007) Journal of Fluid Mechanics, 575, pp. 111-120. , DOI 10.1017/S0022112006004186, PII S0022112006004186
- Zel'dovich, Ya.B., Ruzmaikin, A.A., Molchanov, S.A., Sokoloff, D.D., KINEMATIC DYNAMO PROBLEM IN A LINEAR VELOCITY FIELD (1984) Journal of Fluid Mechanics, 144, pp. 1-11
- Zhou, Y., Interacting scales and energy transfer in isotropic turbulence (1993) Phys. Fluids A, 5, pp. 2511-24
- Zhou, Y., Matthaeus, W.H., Dmitruk, P., Colloquium: Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas (2004) Reviews of Modern Physics, 76 (4), pp. 1015-1035. , http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype= pdf&id=RMPHAT000076000004001015000001&idtype=cvips, DOI 10.1103/RevModPhys.76.1015
Citas:
---------- APA ----------
(2011)
. Scale interactions in magnetohydrodynamic turbulence. Annual Review of Fluid Mechanics, 43, 377-397.
http://dx.doi.org/10.1146/annurev-fluid-122109-160748---------- CHICAGO ----------
Mininni, P.D.
"Scale interactions in magnetohydrodynamic turbulence"
. Annual Review of Fluid Mechanics 43
(2011) : 377-397.
http://dx.doi.org/10.1146/annurev-fluid-122109-160748---------- MLA ----------
Mininni, P.D.
"Scale interactions in magnetohydrodynamic turbulence"
. Annual Review of Fluid Mechanics, vol. 43, 2011, pp. 377-397.
http://dx.doi.org/10.1146/annurev-fluid-122109-160748---------- VANCOUVER ----------
Mininni, P.D. Scale interactions in magnetohydrodynamic turbulence. Ann. Rev. Fluid Mech. 2011;43:377-397.
http://dx.doi.org/10.1146/annurev-fluid-122109-160748