Energy dissipation in a shear layer with suction
dc.contributor.author | Doering, Charles R. | en_US |
dc.contributor.author | Spiegel, Edward A. | en_US |
dc.contributor.author | Worthing, Rodney A. | en_US |
dc.date.accessioned | 2010-05-06T21:01:27Z | |
dc.date.available | 2010-05-06T21:01:27Z | |
dc.date.issued | 2000-08 | en_US |
dc.identifier.citation | Doering, Charles R.; Spiegel, Edward A.; Worthing, Rodney A. (2000). "Energy dissipation in a shear layer with suction." Physics of Fluids 12(8): 1955-1968. <http://hdl.handle.net/2027.42/69712> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/69712 | |
dc.description.abstract | The rate of viscous energy dissipation in a shear layer of incompressible Newtonian fluid with injection and suction is studied by means of exact solutions, nonlinear and linearized stability theory, and rigorous upper bounds. The injection and suction rates are maintained constant and equal and this leads to solutions with constant throughput. For strong enough suction, expressed in terms of the entry angle between the injection velocity and the boundaries, a steady laminar flow is nonlinearly stable for all Reynolds numbers. For a narrow range of small but nonzero angles, the laminar flow is linearly unstable at high Reynolds numbers. The upper bound on the energy dissipation rate—valid even for turbulent solutions of the Navier–Stokes equations—scales with viscosity in the same way as the laminar dissipation in the vanishing viscosity limit. For both the laminar and turbulent flows, the energy dissipation rate becomes independent of the viscosity for high Reynolds numbers. Hence the laminar energy dissipation rate and the largest possible turbulent energy dissipation rate for flows in this geometry differ by only a prefactor that depends only on the angle of entry. © 2000 American Institute of Physics. | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 179096 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Energy dissipation in a shear layer with suction | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109 | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109 | en_US |
dc.contributor.affiliationother | Department of Astronomy, Columbia University, New York, New York 10027 | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/69712/2/PHFLE6-12-8-1955-1.pdf | |
dc.identifier.doi | 10.1063/1.870443 | en_US |
dc.identifier.source | Physics of Fluids | en_US |
dc.identifier.citedreference | G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1969). | en_US |
dc.identifier.citedreference | J. Frank, A. King, and D. Raine, Accretion Power in Astrophysics, Cambridge Astrophysics Series, Vol. 21 (Cambridge University Press, Cambridge, 1992). | en_US |
dc.identifier.citedreference | L. Prandtl, “Ueber die ausgebildete Turbulenz,” Proc. 2nd Intern, Cong. Appl. Mech. Zurich (1926), p. 62. | en_US |
dc.identifier.citedreference | H. Tenekes and J. Lumley, A First Course in Turbulence (MIT, Cambridge, MA, 1972). | en_US |
dc.identifier.citedreference | J. Nikuradse, “Strömungsgesetze in rauhen Rohren,” VDI-Forschungsheft 361 (1933). | en_US |
dc.identifier.citedreference | D. Lathrop, J. Feinberg, and H. Swinney, “Transition to shear-driven turbulence in Couette-Taylor flow,” Phys. Rev. A PLRAAN46, 6390 (1992). | en_US |
dc.identifier.citedreference | O. Cadot, Y. Couder, A. Daerr, S. Douady, and A. Tsinober, “Energy injection in closed turbulent flows: Stirring through boundary layers versus inertial stirring,” Phys. Rev. E PLEEE856, 427 (1997). | en_US |
dc.identifier.citedreference | D. D. Joseph, “Stability of fluid motions,” Springer Tracts in Natural Philosophy (Springer-Verlag, Berlin, 1976). | en_US |
dc.identifier.citedreference | W. V. R. Malkus, “Lectures on Turbulence,” in Notes on the 1960 Summer Study Program in Geophysical Fluid Dynamics, edited by E. A. Spiegel (Woods Hole Oceanographic Inst., 1960), Vol. II, pp. 1–68. | en_US |
dc.identifier.citedreference | L. N. Howard, “Heat transport by turbulent convection,” J. Fluid Mech. JFLSA717, 405 (1963). | en_US |
dc.identifier.citedreference | L. N. Howard, “Bounds on flow quantities,” Annu. Rev. Fluid Mech. ARVFA34, 473 (1972). | en_US |
dc.identifier.citedreference | F. H. Busse, “The optimum theory of turbulence,” Adv. Appl. Mech. AAMCAY18, 77 (1978). | en_US |
dc.identifier.citedreference | E. Hopf, “Ein allgemeiner endlichkeitssatz der hydrodynamik,” Math. Ann. MAANA3117, 764 (1941). | en_US |
dc.identifier.citedreference | C. R. Doering and P. Constantin, “Energy dissipation in shear driven turbulence,” Phys. Rev. Lett. PRLTAO69, 1648 (1992). | en_US |
dc.identifier.citedreference | C. R. Doering and P. Constantin, “Variational bounds on energy dissipation in incompressible flows: Shear flow,” Phys. Rev. E PLEEE849, 4087 (1994). | en_US |
dc.identifier.citedreference | C. Marchioro, “Remark on the energy dissipation in shear driven turbulence,” Physica D PDNPDT74, 395 (1994). | en_US |
dc.identifier.citedreference | P. Constantin and C. Doering, “Variational bounds on energy dissipation in incompressible flows: II. Channel flow,” Physica D PDNPDT82, 221 (1995). | en_US |
dc.identifier.citedreference | T. Gebhardt, S. Grossmann, M. Holthaus, and M. Löhden, “Rigorous bound on the plane-shear-flow dissipation rate,” Phys. Rev. E PLEEE851, 360 (1995). | en_US |
dc.identifier.citedreference | R. Nicodemus, S. Grossmann, and M. Holthaus, “Improved variational principle for bounds on energy dissipation in turbulent shear flow,” Physica D PDNPDT101, 178 (1997). | en_US |
dc.identifier.citedreference | C. Doering and P. Constantin, “Variational bounds on energy dissipation in incompressible flows: III. Convection,” Phys. Rev. E PLEEE853, 5957 (1996). | en_US |
dc.identifier.citedreference | R. R. Kerswell, “Unification of variational principles for turbulent shear flows: the background method of Doering–Constantin and the mean-fluctuation method of Howard–Busse,” Physica D PDNPDT121, 175 (1998). | en_US |
dc.identifier.citedreference | A. Cherhabili and U. Ehrenstein, “Finite-amplitude equilibrium states in plane Couette flow,” J. Fluid Mech. JFLSA7342, 159 (1997). | en_US |
dc.identifier.citedreference | P. Drazin and W. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981). | en_US |
dc.identifier.citedreference | L. M. Hocking, “Non-linear instability of the asymptotic suction velocity profile,” Q. J. Mech. Appl. Math. QJMMAV28, 341 (1974). | en_US |
dc.identifier.citedreference | W. V. R. Malkus, “The heat transport and spectrum of thermal turbulence,” Proc. R. Soc. London, Ser. A PRLAAZ225, 196 (1954). | en_US |
dc.identifier.citedreference | R. Nicodemus, S. Grossmann, and M. Holthaus, “The background flow method. Part 1. Constructive approach to bounds on energy dissipation,” J. Fluid Mech. JFLSA7363, 281 (1998). | en_US |
dc.identifier.citedreference | X. Wang, “Time averaged energy dissipation rate for shear driven flows,” Physica D PDNPDT99, 555 (1997). | en_US |
dc.identifier.citedreference | K. Min and R. Leptow, “Circular Couette flow with pressure-driven axial flow and a porous inner cylinder,” Exp. Fluids EXFLDU17, 190 (1994). | en_US |
dc.identifier.citedreference | Y. Sumitani and N. Kasagi, “Direct numerical simulation of turbulent transport with uniform wall injection and suction,” AIAA J. AIAJAH33, 1220 (1995). | en_US |
dc.identifier.citedreference | R. Temam and X. Wang, “Boundary layers associated with incompressible Navier–Stokes equations: The noncharacteristic boundary case” (in press). | en_US |
dc.owningcollname | Physics, Department of |
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