-
2
-
-
34250488505
-
Bounds on the transport of mass and momentum by turbulent flow
-
Busse, F. H. 1969a Bounds on the transport of mass and momentum by turbulent flow. Z. Angew. Math. Phys. 20, 1-14.
-
(1969)
Z. Angew. Math. Phys.
, vol.20
, pp. 1-14
-
-
Busse, F.H.1
-
3
-
-
0014543531
-
On Howard's upper bound for heat transport by turbulent convection
-
Busse, F. H. 1969b On Howard's upper bound for heat transport by turbulent convection. J. Fluid Mech. 37, 457-477.
-
(1969)
J. Fluid Mech.
, vol.37
, pp. 457-477
-
-
Busse, F.H.1
-
4
-
-
0014748934
-
Bounds for turbulent shear flow
-
Busse, F. H. 1970 Bounds for turbulent shear flow. J. Fluid Mech. 41, 219-240.
-
(1970)
J. Fluid Mech.
, vol.41
, pp. 219-240
-
-
Busse, F.H.1
-
5
-
-
33748254405
-
Upper bound on turbulent heat convection for infinite Prandtl number
-
PhD thesis, Massachusetts Institute of Technology
-
Chan, S. K. 1970 Upper bound on turbulent heat convection for infinite Prandtl number. PhD thesis, Massachusetts Institute of Technology.
-
(1970)
-
-
Chan, S.K.1
-
6
-
-
0015037568
-
Infinite Prandtl number turbulent convection
-
Chan, S. K. 1971 Infinite Prandtl number turbulent convection. Stud. Appl. Maths 50, 13-49.
-
(1971)
Stud. Appl. Maths
, vol.50
, pp. 13-49
-
-
Chan, S.K.1
-
7
-
-
26744476261
-
Variational bounds on energy-dissipation in incompressible flows: II. Channel flow
-
Constantin, P. & Doering, C. R. 1995 Variational bounds on energy-dissipation in incompressible flows: II. Channel flow. Phys. Rev. E 51, 3192-3198.
-
(1995)
Phys. Rev. E
, vol.51
, pp. 3192-3198
-
-
Constantin, P.1
Doering, C.R.2
-
10
-
-
0000916434
-
Energy dissipation in shear driven turbulence
-
Doering, C. R. & Constantin, P. 1992 Energy dissipation in shear driven turbulence. Phys. Rev. Lett. 69, 1648-1651.
-
(1992)
Phys. Rev. Lett.
, vol.69
, pp. 1648-1651
-
-
Doering, C.R.1
Constantin, P.2
-
11
-
-
29444448503
-
Variational bounds on energy dissipation in incompressible flows: Shear flow
-
Doering, C. R. & Constantin, P. 1994 Variational bounds on energy dissipation in incompressible flows: Shear flow. Phys. Rev. E 49, 4087-4099.
-
(1994)
Phys. Rev. E
, vol.49
, pp. 4087-4099
-
-
Doering, C.R.1
Constantin, P.2
-
12
-
-
0001088644
-
Variational bounds on energy dissipation in incompressible flows: III. Convection
-
Doering, C. R. & Constantin, P. 1996 Variational bounds on energy dissipation in incompressible flows: III. Convection. Phys. Rev. E 53, 5957-5981.
-
(1996)
Phys. Rev. E
, vol.53
, pp. 5957-5981
-
-
Doering, C.R.1
Constantin, P.2
-
13
-
-
33748268887
-
Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh-Bénard convection
-
Doering, C. R., Otto, F. & Reznikoff, M. G. 2005 Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh-Bénard convection. J. Fluid Mech. 560, 229-241.
-
(2005)
J. Fluid Mech.
, vol.560
, pp. 229-241
-
-
Doering, C.R.1
Otto, F.2
Reznikoff, M.G.3
-
14
-
-
0000273884
-
Computing Fourier transforms and convolutions on the 2-sphere
-
Driscoll, J. R. & Healy, D. M. 1994 Computing Fourier transforms and convolutions on the 2-sphere. Adv. Appl. Maths 15, 202-250.
-
(1994)
Adv. Appl. Maths
, vol.15
, pp. 202-250
-
-
Driscoll, J.R.1
Healy, D.M.2
-
15
-
-
0011402423
-
Ein allgemeiner endlichkeitssatz der hydrodynamik
-
Hopf, E. 1941 Ein allgemeiner endlichkeitssatz der hydrodynamik. Mathematische Annalen 117, 764-775.
-
(1941)
Mathematische Annalen
, vol.117
, pp. 764-775
-
-
Hopf, E.1
-
16
-
-
5344252236
-
Heat transport by turbulent convection
-
Howard, L. N. 1963 Heat transport by turbulent convection. J. Fluid Mech. 17, 405-432.
-
(1963)
J. Fluid Mech.
, vol.17
, pp. 405-432
-
-
Howard, L.N.1
-
17
-
-
0001607262
-
Bounds on flow quantities
-
Howard, L. N. 1972 Bounds on flow quantities. Annu. Rev. Fluid Mech. 4, 473-494.
-
(1972)
Annu. Rev. Fluid Mech.
, vol.4
, pp. 473-494
-
-
Howard, L.N.1
-
18
-
-
1942507764
-
The Borel sum of a divergent Barnes hypergeometric series and its application to a partial differential equation
-
Ichinobe, K. 2001 The Borel sum of a divergent Barnes hypergeometric series and its application to a partial differential equation. Publ. Res. Inst. Math. Sci. 37 (1), 91-117.
-
(2001)
Publ. Res. Inst. Math. Sci.
, vol.37
, Issue.1
, pp. 91-117
-
-
Ichinobe, K.1
-
19
-
-
0031084479
-
A class of sparse spectral operators for inversion of powers of the Laplacian in N dimensions
-
Ierley, G. R. 1997 A class of sparse spectral operators for inversion of powers of the Laplacian in N dimensions. J. Sci. Comput. 12 (1), 57-63.
-
(1997)
J. Sci. Comput.
, vol.12
, Issue.1
, pp. 57-63
-
-
Ierley, G.R.1
-
20
-
-
0022768047
-
Analytical and numerical solutions of a nonlinear boundary layer problem
-
Ierley, G. R. & Ruehr, O. G. 1986 Analytical and numerical solutions of a nonlinear boundary layer problem. Stud. Appl. Maths 75, 1-36.
-
(1986)
Stud. Appl. Maths
, vol.75
, pp. 1-36
-
-
Ierley, G.R.1
Ruehr, O.G.2
-
21
-
-
0035949175
-
Bound to improve: A variational approach to convective heat transport
-
Ierley, G. R. & Worthing, R. A. 2001 Bound to improve: A variational approach to convective heat transport. J. Fluid Mech. 441, 223-253.
-
(2001)
J. Fluid Mech.
, vol.441
, pp. 223-253
-
-
Ierley, G.R.1
Worthing, R.A.2
-
22
-
-
0023348198
-
A boundary-layer analysis of Rayleigh-Bénard convection at large Rayleigh number
-
Jimenez, J. & Zufiria, J. A. 1987 A boundary-layer analysis of Rayleigh-Bénard convection at large Rayleigh number. J. Fluid Mech. 178, 53-71.
-
(1987)
J. Fluid Mech.
, vol.178
, pp. 53-71
-
-
Jimenez, J.1
Zufiria, J.A.2
-
23
-
-
0030208654
-
Upper bounds on the energy dissipation in turbulent precession
-
Kerswell, R. R. 1996 Upper bounds on the energy dissipation in turbulent precession. J. Fluid Mech. 321, 335-370.
-
(1996)
J. Fluid Mech.
, vol.321
, pp. 335-370
-
-
Kerswell, R.R.1
-
24
-
-
22244454149
-
Variational bounds on shear-driven turbulence and turbulent Boussinesq convection
-
Kerswell, R. R. 1997 Variational bounds on shear-driven turbulence and turbulent Boussinesq convection. Physica D 100, 355-376.
-
(1997)
Physica D
, vol.100
, pp. 355-376
-
-
Kerswell, R.R.1
-
25
-
-
0034746270
-
New results in the variational approach to turbulent Boussinesq convection
-
Kerswell, R. R. 2001 New results in the variational approach to turbulent Boussinesq convection. Phys. Fluids 13, 192-209.
-
(2001)
Phys. Fluids
, vol.13
, pp. 192-209
-
-
Kerswell, R.R.1
-
26
-
-
0037173227
-
Upper bounds on general dissipation functionals in turbulent shear flows: Revisiting the 'Efficiency' functional
-
Kerswell, R. R. 2002 Upper bounds on general dissipation functionals in turbulent shear flows: Revisiting the 'Efficiency' functional. J. Fluid Mech. 461, 239-275.
-
(2002)
J. Fluid Mech.
, vol.461
, pp. 239-275
-
-
Kerswell, R.R.1
-
27
-
-
0030425727
-
Upper bounds for turbulent Couette flow incorporating the poloidal power constraint
-
Kerswell, R. R. & Soward, A. M. 1996 Upper bounds for turbulent Couette flow incorporating the poloidal power constraint. J. Fluid Mech. 328, 161-176.
-
(1996)
J. Fluid Mech.
, vol.328
, pp. 161-176
-
-
Kerswell, R.R.1
Soward, A.M.2
-
29
-
-
0000109675
-
Discrete transitions in turbulent convection
-
Malkus, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. R. Soc. Lond. A 225, 185-195.
-
(1954)
Proc. R. Soc. Lond. A
, vol.225
, pp. 185-195
-
-
Malkus, W.V.R.1
-
30
-
-
0000109675
-
The heat transport and spectrum of thermal turbulence
-
Malkus, W. V. R. 1954b The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225, 196-212.
-
(1954)
Proc. R. Soc. Lond. A
, vol.225
, pp. 196-212
-
-
Malkus, W.V.R.1
-
31
-
-
84974055065
-
Outline of a theory for turbulent shear flow
-
Malkus, W. V. R. 1956 Outline of a theory for turbulent shear flow. J. Fluid Mech. 1, 521-539.
-
(1956)
J. Fluid Mech.
, vol.1
, pp. 521-539
-
-
Malkus, W.V.R.1
-
32
-
-
0031078492
-
Improved variational principle for bounds on energy dissipation in turbulent shear flow
-
Nicodemus, R., Grossmann, S. & Holthaus, M. 1997a Improved variational principle for bounds on energy dissipation in turbulent shear flow. Physica D 101, 178-190.
-
(1997)
Physica D
, vol.101
, pp. 178-190
-
-
Nicodemus, R.1
Grossmann, S.2
Holthaus, M.3
-
33
-
-
0001268673
-
Variational bound on energy dissipation in plane Couette flow
-
Nicodemus, R., Grossmann, S. & Holthaus, M. 1997b Variational bound on energy dissipation in plane Couette flow. Phys. Rev. E 56, 6774-6786.
-
(1997)
Phys. Rev. E
, vol.56
, pp. 6774-6786
-
-
Nicodemus, R.1
Grossmann, S.2
Holthaus, M.3
-
34
-
-
1542307219
-
Bounds for the heat transport in turbulent convection
-
PhD thesis, University of Michigan
-
Otero, J. 2002 Bounds for the heat transport in turbulent convection. PhD thesis, University of Michigan.
-
(2002)
-
-
Otero, J.1
-
35
-
-
3543086818
-
Turbulence has its limits: A priori estimates of transport properties in turbulent fluid flows
-
PhD thesis, University of Bristol
-
Plasting, S. C. 2004 Turbulence has its limits: A priori estimates of transport properties in turbulent fluid flows. PhD thesis, University of Bristol.
-
(2004)
-
-
Plasting, S.C.1
-
36
-
-
27844564860
-
Estimates of heat transport in infinite Prandtl number convection. Part 1. Conservative bounds
-
Plasting, S. C. & Ierley, G. R. 2005 Estimates of heat transport in infinite Prandtl number convection. Part 1. Conservative bounds. J. Fluid Mech. 542, 343-363.
-
(2005)
J. Fluid Mech.
, vol.542
, pp. 343-363
-
-
Plasting, S.C.1
Ierley, G.R.2
-
37
-
-
0037465214
-
Improved upper bound on the energy dissipation rate in plane couette flow: The full solutions to Busse's problem and the Constantin-Doering-Hopf problem with one-dimensional background field
-
Plasting, S. C. & Kerswell, R. R. 2003 Improved upper bound on the energy dissipation rate in plane couette flow: The full solutions to Busse's problem and the Constantin-Doering-Hopf problem with one-dimensional background field. J. Fluid Mech. 477, 363-379.
-
(2003)
J. Fluid Mech.
, vol.477
, pp. 363-379
-
-
Plasting, S.C.1
Kerswell, R.R.2
-
38
-
-
8144220661
-
Bounds on horizontal convection
-
Siggers, J. H., Kerswell, R. R. & Balmforth, N. J. 2004 Bounds on horizontal convection. J. Fluid Mech. 517, 55-70.
-
(2004)
J. Fluid Mech.
, vol.517
, pp. 55-70
-
-
Siggers, J.H.1
Kerswell, R.R.2
Balmforth, N.J.3
-
39
-
-
2242430190
-
Appendix: Asymptotic Theory in the Limit R → ∞
-
(ed. R. J. Donnelly, R. Herman & I. Prigogine) University of Chicago Press
-
Stewartson, K. 1966 Appendix: Asymptotic Theory in the Limit R → ∞ In Non-Equilibrium Thermodynamics Variational Techniques and Stability (ed. R. J. Donnelly, R. Herman & I. Prigogine), pp. 158-162. University of Chicago Press.
-
(1966)
Non-Equilibrium Thermodynamics Variational Techniques and Stability
, pp. 158-162
-
-
Stewartson, K.1
-
40
-
-
0004272984
-
A note on the multi-α solutions of the upper bounding problem for thermal convection
-
Straus, J. M. 1976a A note on the multi-α solutions of the upper bounding problem for thermal convection. Dyn. Atmos. Oceans 1, 71-76.
-
(1976)
Dyn. Atmos. Oceans
, vol.1
, pp. 71-76
-
-
Straus, J.M.1
-
41
-
-
0004341267
-
On the upper bounding approach to thermal convection at moderate Rayleigh numbers, II. Rigid boundaries
-
Straus, J. M. 1976b On the upper bounding approach to thermal convection at moderate Rayleigh numbers, II. Rigid boundaries. Dyn. Atmos. Oceans 1, 77-90.
-
(1976)
Dyn. Atmos. Oceans
, vol.1
, pp. 77-90
-
-
Straus, J.M.1
-
42
-
-
0041577305
-
Upper bound on the heat transport in a horizontal fluid layer of infinite Prandtl number
-
Vitanov, N. K. 1998 Upper bound on the heat transport in a horizontal fluid layer of infinite Prandtl number. Phys. Lett. A 248, 338-346.
-
(1998)
Phys. Lett. A
, vol.248
, pp. 338-346
-
-
Vitanov, N.K.1
-
43
-
-
0010468551
-
Convective heat transport in a fluid layer of infinite Prandtl number: Upper bounds for the case of rigid lower boundary and stress-free upper boundary
-
Vitanov, N. K. 2000a Convective heat transport in a fluid layer of infinite Prandtl number: Upper bounds for the case of rigid lower boundary and stress-free upper boundary. Eur. Phys. J. B 15, 349-355.
-
(2000)
Eur. Phys. J. B
, vol.15
, pp. 349-355
-
-
Vitanov, N.K.1
-
44
-
-
0010429064
-
Upper bounds on the heat transport in a fluid layer of infinite Prandtl number, rigid lower boundary and stress-free upper boundary
-
Vitanov, N. K. 2000b Upper bounds on the heat transport in a fluid layer of infinite Prandtl number, rigid lower boundary and stress-free upper boundary. Phys. Rev. E 61, 956-959.
-
(2000)
Phys. Rev. E
, vol.61
, pp. 956-959
-
-
Vitanov, N.K.1
-
45
-
-
0031522539
-
Bounds on the heat transport in a horizontal fluid layer with stress-free boundaries
-
Vitanov, N. K. & Busse, F. H. 1997 Bounds on the heat transport in a horizontal fluid layer with stress-free boundaries. Z. Angew. Math. Phys. 48, 310-324.
-
(1997)
Z. Angew. Math. Phys.
, vol.48
, pp. 310-324
-
-
Vitanov, N.K.1
Busse, F.H.2
-
46
-
-
4544241853
-
Infinite Prandtl number limit of Rayleigh-Bénard convection
-
Wang, X. M. 2004 Infinite Prandtl number limit of Rayleigh-Bénard convection. Commun. Pure Appl. Maths 57, 1265-1282.
-
(2004)
Commun. Pure Appl. Maths
, vol.57
, pp. 1265-1282
-
-
Wang, X.M.1
-
47
-
-
3543063042
-
On limits to convective heat transport at infinite Prandtl number with or without rotation
-
Yan, X. D. 2004 On limits to convective heat transport at infinite Prandtl number with or without rotation. J. Math. Phys. 45, 2718-2743.
-
(2004)
J. Math. Phys.
, vol.45
, pp. 2718-2743
-
-
Yan, X.D.1
|