Hydrodynamic Fluctuations in Laminar Fluid Flow. I. Fluctuating Orr-Sommerfeld Equation

Journal of Statistical Physics

Volumn 144, Issue 4, 2011, Pages 774-792

  de Ortiz Zarate J M ^a   Sengers, J V ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b University of Maryland   (United States)

Author keywords

Hydrodynamic fluctuations; Laminar fluid flow; Orr Sommerfeld equation; Plane Couette flow

Indexed keywords

EID: 80052034050     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-011-0256-1     Document Type: Article

References (32)

1. Landau, L. D., Lifshitz, E. M.: Fluid Mechanics, 2nd edn. Pergamon, Oxford (1987).
2. Fox, R. F., Uhlenbeck, G. E.: Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations. Phys. Fluids 13, 1893-1902 (1970).
3. Ortiz de Zárate, J. M., Sengers, J. V.: Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier, Amsterdam (2006).
4. Farrell, B. F., Ioannou, P. J.: Stochastic forcing of the linearized Navier-Stokes equations. Phys. Fluids A, Fluid Dyn. 5, 2600-2609 (1993).
5. Farrell, B. F., Ioannou, P. J.: Variance maintained by stochastic forcing of non-normal dynamical systems associated with linearly stable shear flows. Phys. Rev. Lett. 72, 1188-1191 (1994).
6. Bamieh, B., Dahleh, M.: Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13, 3258-3269 (2001).
7. Jovanovic, M. R., Bamieh, B.: Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145-183 (2005).
8. Eckhardt, B., Pandit, R.: Noise correlations in shear flows. Eur. Phys. J. B 33, 373-378 (2003).
9. Tremblay, A.-M. S., Arai, M., Siggia, E. D.: Fluctuations about simple nonequilibrium states. Phys. Rev. A 23, 1451-1480 (1981).
10. Dufty, J. W., Lutsko, J.: Structure and stability of hydrodynamic models for shear flow. KINAM 6, 169-181 (1984).
11. Lutsko, J. F., Dufty, J. W.: Hydrodynamic fluctuations at large shear rate. Phys. Rev. A 32, 3040-3054 (1985).
12. Lutsko, J. F., Dufty, J. W.: Long-ranged correlations in sheared fluids. Phys. Rev. E 66, 041206 (2002).
13. Wada, H., Sasa, S.-I.: Anomalous pressure in fluctuating shear flow. Phys. Rev. E 67, 065302R (2003).
14. Ortiz de Zárate, J. M., Sengers, J. V.: Transverse-velocity fluctuations in a liquid under steady shear. Phys. Rev. E 77, 026306 (2008).
15. Ortiz de Zárate, J. M., Sengers, J. V.: Nonequilibrium velocity fluctuations and energy amplification in planar Couette flow. Phys. Rev. E 79, 046308 (2009).
16. Sengers, J. V., Ortiz de Zárate, J. M.: Velocity fluctuations in laminar fluid flow. J. Non-Newton. Fluid Mech. 165, 925-931 (2010).
17. Schmid, P. J., Henningson, D. S.: Stability and Transition in Shear Flows. Springer, Berlin (2001).
18. Drazin, P. G., Reid, W. H.: Hydrodynamic Stability, 2nd edn. Cambridge University Press, Cambridge (2004).
19. Grossmann, S.: The onset of shear flow turbulence. Rev. Mod. Phys. 72, 603-618 (2000).
20. Sagués, F., Sancho, J. M., García-Ojalvo, J.: Spatiotemporal order out of noise. Rev. Mod. Phys. 79, 829-882 (2007).
21. Mannevile, P.: Instabilities, Chaos, and Turbulence, 2nd edn. World Scientific, Singapore (2010).
22. Schmitz, R., Cohen, E. G. D.: Fluctuations in a fluid under a stationary heat flux. I. General theory. J. Stat. Phys. 39, 285-316 (1985).
23. Schmitz, R., Cohen, E. G. D.: Fluctuations in a fluid under a stationary heat flux. II. Slow part of the correlation matrix. J. Stat. Phys. 40, 431-316 (1985).
24. Zubarev, D. N., Morozov, V. G.: Statistical mechanics of nonlinear hydrodynamic fluctuations. Physica A 120, 411-467 (1983).
25. Romanov, V. A.: Stability of the plane Couette flow. Dokl. Akad. Nauk SSSR 196, 1049-1051 (1971).
26. Dyachenko, A. V., Shkalikov, A. A.: On a model problem for the Orr-Sommerfeld equation with linear profile. Funct. Anal. Appl. 36, 228-232 (2002).
27. Boon, J. P., Yip, S.: Molecular Hydrodynamics. McGraw-Hill, New York (1980), Dover edition (1991).
28. Hansen, J. P., McDonald, I. R.: Theory of Simple Liquids, 2nd edn. Academic Press, London (1986).
29. Kirkpatrick, T. R., Belitz, D., Sengers, J. V.: Long-time tails, weak localization, and classical and quantum critical behavior. J. Stat. Phys. 109, 373-405 (2002).
30. Skorokhodov, S. L.: Numerical analysis of the spectrum of the Orr-Sommerfeld problem. Comput. Math. Math. Phys. 47, 1603-1621 (2007).
31. Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions. Dover, New York (1964).
32. Dolph, C. L., Lewis, D. C.: On the application of infinite systems of ordinary differential equations to perturbations of plane Poiseuille flow. Q. Appl. Math. 16, 97-110 (1958).