Abstract
The stability of incompressible turbulent fluids with respect to weak mean flow perturbations is discussed. It is shown that for a statistically homogeneous, isotropic, and stationary model such perturbations will decay. This is in marked contrast to the compressible case.
Similar content being viewed by others
References
G. K. Batchelor,The Theory of Homogeneous Turbulence (Cambridge University Press, 1953).
H. Fiedler (ed.),Structure and Mechanisms of Turbulence II (Springer-Verlag, Berlin).
L. Shtilman and G. Sivashinsky,J. Phys. (Paris) 34:1137 (1986).
A. Libin, G. Sivashinsky, and E. Levich,Phys. Fluids 30:2984 (1987).
D. Galloway and U. Frisch,J. Fluid Mech. 180:557 (1987).
B. J. Bayly,Phys. Rev. Lett. 57:2160 (1986).
G. Sivashinsky and V. Yakhot,Phys. Fluids 28:1040 (1985).
B. J. Bayly and V. Yakhot,Phys. Rev. A 34:381 (1986).
A. Pouquet, J.-D. Fournier, and P.-L. Sulem,J. Phys. Lett. (Paris) 39:L199 (1978).
R. H. Kraichnan,J. Fluid Mech. 59:745 (1973).
V. Yakhot and R. Pelz,Phys. Fluids 30:1272 (1987).
H. K. Moffatt,J. Fluid Mech. 166:359 (1986).
S. S. Moiseev, R. Z. Sagdeev, A. V. Tur, G. A. Khomenko, and V. V. Yanovskii,Sov. Phys. JETP 58:1149 (1983).
S. Goldstein (ed.),Modern Developments in Fluid Dynamics, Vol. 1 (Dover, New York, 1965).
A. S. Monin and A. G. Yaglom,Statistical Fluid Mechanics (MIT Press, Cambridge, Massachusetts, 1965).
E. A. Novikov,Sov. Phys. JETP 20:1290 (1965).
K. J. Furutsu,J. Opt. Soc. Am. 62:240 (1972).
J. Mathews and R. L. Walker,Mathematical Methods of Physics (Benjamin, Menlo Park, California, 1964).
H. K. Moffatt,Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, 1978).
I. S. Gradshteyn and I. M. Ryzhik,Tables of Integrals, Series, and Products (Academic Press, 1980).
G. K. Batchelor,An Introduction to Fluid Dynamics (Cambridge University Press, 1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lipscombe, T., Frenkel, A.L. & ter Haar, D. Stability of isotropic incompressible turbulence against weak mean flow perturbations. J Stat Phys 53, 95–108 (1988). https://doi.org/10.1007/BF01011547
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011547