Abstract.
A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental data in a von Karman device filled with water. It is shown to allow for a parameter-free prediction of the PDF of power fluctuations in the case where the forcing is made at constant torque. A physical interpretation of our model is finally given, using a quasi-linear model of turbulence.
Similar content being viewed by others
References
M. Lesieur, La Turbulence (Presses universitaires de Grenoble, 1994)
E. Hopf, J. Rat. Mech. Anal. 1, 87 (1952)
A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics (MIT press, Cambridge, 1977)
R. Friedrich, J. Peinke, Phys. Rev. Lett. 78, 863 (1997)
R. Friedrich, J. Peinke, Physica D 102, 147 (1997)
A. Naert, B. Castaing, B. Chabaud, B. Hebral, J. Peinke, Physica D 113, 73 (1998)
P. Marcq, A. Naert, Phys. Fluids 13, 2590 (2001)
A. M. Obukhov, Adv. Geophys. 6, 113 (1959)
B. Castaing, Y. Gagne, E.J. Hopfinger, Physica D 46, 177 (1990)
J. Delour, J.-F. Muzy, A. Arneodo, Eur. Phys. J. B 23, 243 (2001)
R. Friedrich, Phys. Rev. Lett. 90, 084501 (2003)
C. Beck, Europhys. Lett. 64, 151 (2002)
J.-P. Laval, B. Dubrulle, S. Nazarenko, Phys. Rev. Lett. 83, 4061 (1999)
J. Carlier, J.-P. Laval, J.M. Foucaut, M. Stanislas, C.R. Acad. Sci. Ser. B 329, 1 (2001)
J.-P. Laval, B. Dubrulle, S. Nazarenko, Phys. Fluids 13, 1995 (2001)
B. Dubrulle, S. Nazarenko, Physica D 110, 123 (1997)
S. Nazarenko, N.K.-R. Kevlahan, B. Dubrulle, J. Fluid Mech. 390, 325 (1999)
J.-P. Laval, B. Dubrulle, S.V. Nazarenko, Physica D 142, 231 (2000)
B. Dubrulle, J.-P. Laval, S. Nazarenko, N.K.-R. Kevlahan, Phys. Fluids 13, 2045 (2001)
A.A. Townsend, The structure of turbulent shear flows (CUP, 1976)
J.F. Keffer, J.G. Kawall, J.C.R. Hunt, M.R. Maxey, J. Fluid Mech. 86, 465 (1978)
M.R. Maxey, J. Fluid Mech. 124, 261 (1981)
N.K.-R. Kevlahan, Appl. Sci. Res. 51, 411 (1993)
N.K.-R. Kevlahan, J.C.R. Hunt, J. Fluid Mech. 337, 333 (1997)
J.-P. Laval, B. Dubrulle, J.C. Mc Williams, Phys. Fluids 15, 1327 (2003)
R. Labbé, J.-F. Pinton, S. Fauve, J. Phys. II France 6, 1099 (1996)
O. Cadot, Y. Couder, A. Daerr, S. Douady, A. Tsinober, Phys. Rev. E 56, 427 (1997)
S. Aumaitre, S. Fauve, J.-F. Pinton, Eur. Phys. J. B 16, 563 (2000)
J.-H.C. Titon, O. Cadot, Phys. Fluids 15, 625 (2003)
S. Aumaitre, S. Fauve, S. McNamara, P. Poggi, Eur. Phys. J. B 19, 449 (2001)
R.S. Ellis, Entropy, Large deviations and statistical mechanics (Springer Verlag, New York, 1985)
Y. Oono, Progr. Theor. Phys. Suppl. 99, 165 (1989)
L. Marié, F. Daviaud, Phys. Fluids 16, 457 (2004)
P.E. Kloeden, E. Platen, Numerical solution of stochastic differential equations (Springer-Verlag, 1992)
P. Jung, P. Hänggi, Phys. Rev. A 35, 4464 (1987)
S.Z. Ke, D.J. Wu, L. Cao, Eur. Phys. J. B 12, 119 (1999)
J.-F. Pinton, P.C. Holdsworth, R. Labbé, Phys. Rev. E 60, R2452 (1999)
C.M. Bender, S.A. Orszag, Advanced mathematical methods for scientists and engineers (Mc Graw Hill, 1975)
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 29 January 2004, Published online: 18 June 2004
PACS:
47.27.-i Turbulent flows, convection, and heat transfer - 47.27.Eq Turbulence simulation and modeling
Rights and permissions
About this article
Cite this article
Leprovost, N., Marié, L. & Dubrulle, B. A stochastic model of torques in von Karman swirling flow. Eur. Phys. J. B 39, 121–129 (2004). https://doi.org/10.1140/epjb/e2004-00177-x
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2004-00177-x