Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T17:44:24.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulation of compressible homogeneous flows in the turbulent regime

Published online by Cambridge University Press:  21 April 2006

T. Passot  and
A. Pouquet
T. Passot
Affiliation:
Observatoire de Nice, B.P. 139, Nice CEDEX 06003, France
A. Pouquet
Affiliation:
Observatoire de Nice, B.P. 139, Nice CEDEX 06003, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Compressible flows with r.m.s. velocities of the order of the speed of sound are studied with direct numerical simulations using a pseudospectral method. We concentrate on turbulent homogeneous flows in the two-dimensional case. The fluid obeys the Navier-Stokes equations for a perfect gas, and viscous terms are included explicitly. No modelling of small scales is used. We show that the behaviour of the flow differs sharply at low compared with high r.m.s. Mach number Ma, with a transition at Ma = 0.3. In the large scales, temporal exchanges between longitudinal and solenoidal modes of energy retain an acoustical character; they lead to a slowing down of the decrease of the Mach number with time, which occurs with interspersed plateaux corresponding to quiescent periods. When the flow is initially supersonic, the small scales are dominated by shocks behind which vortices form. This vortex production is particularly prominent when two strong shocks collide, with the onset of shear turbulence in the region downstream of the collision. However, at the resolutions reached by our code on a 256 × 256 uniform grid, this mechanism proves insufficient to bring vortices into equipartition with shocks in the small-scale tail of the energy spectrum.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 441 - 466
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abarbanel, S., Gottlieb, D. & Tadmor, E. 1985 Spectral methods for discontinuous problems. ICASE Rep. 85–38.
Brachet, M. E., Meneguzzi, M. & Sulem, P.-L. 1985 In Macroscopic Modelling of Turbulent Flows (ed. U. Frisch, J. B. Keller, G. C. Papanicolaou & O. Pironneau). Lecture Notes in Physics, vol. 230, p. 347. Springer.
Brachet, M. E. & Sulem, P.-L. 1985 Prog. Astronaut. Aero. 100, 100.
Chacon, T. & Pironneau, O. 1986 DRET-ONERA Colloquium, Poitiers, Ecole Nationale Supérieure de Mécanique et Aérotechnique, pp. 27–38.
Chollet, J. P. & Lesieur, M. 1981 J. Atmos. Sci. 38, 2747.
Crighton, D. G. 1975 Prog. Aerospace Sci. 16, 31.
ElsÄsser, K. & Schamel, H. 1976 Z. Phys. B23, 89.
Farge, M. & Sadourny, R. 1987 Inertia-gravity wave effects on a decaying two-dimensional turbulence in rotation. J. Fluid Mech. (submitted).Google Scholar
Feiereisen, W. J., Reynolds, W. C. & Ferziger, J. H. 1981 Numerical simulation of a compressible, homogeneous turbulent shear flow. Rep. TF-13, Thesis, Stanford University.
Forster, D., Nelson, D. R. & Stephen, M. J. 1977 Phys. Rev. A 16, 732.
Frisch, U., Pouquet, A., Sulem, P. L. & Meneguzzi, M. 1983 J. Méc. Théor. Appl., numéro spécial, p. 191.
Gaffet, B. 1985 On generalized vorticity-conservation laws. J. Fluid Mech. 156, 141.Google Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods. Philadelphia: SIAM.
Ha Minh, H. & Vandromme, D. D. 1986 DRET-ONERA Colloquium, Poitiers, Ecole Nationale Supérieure de Mécanique et Aérotechnique.
Kadomtsev, B. B. & Petviashvili, V. I. 1973 Sov. Phys. Dokl. 18, 115.
Kraichnan, R. H. 1953 J. Acoust. Soc. Am. 25, 1096.
Kraichnan, R. H. 1965 Phys. Fluids 8, 1385.
Kraichnan, R. H. 1967 Phys. Fluids 10, 1417.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Larson, R. B. 1981 Mon. Not. R. Astron. Soc. 194, 809.
LÉorat, J. & Pouquet, A. 1986 DRET-ONERA, Colloquium, Poitiers Ecole Nationale Supérieure de Mécanique et Aérotechnique, pp. 101–110.
LÉorat, J., Pouquet, A. & Poyet, J.-P. 1984 Numerical simulations of supersonic turbulent flows. Meeting on supernovae—O.P.M.T., Toulouse (ed. J.-P. Zahn). Reidel.
Lesieur, M. 1984 In Combustion and Nonlinear phenomena (ed. P. Clavin, B. Larrouturou & P. Pelce). Les Houches, Les éditions de Physique.
Lighthill, M. J. 1952 Proc. R. Soc. Lond. A211, 564.
Lighthill, M. J. 1954 Proc. R. Soc. Lond. A222, 1.
Lighthill, M. J. 1955 In Gas Dynamics of Cosmic Clouds, IAU Symposium n 2 (ed. H. C. van de Hulst & J. M. Burgers), p. 121. North Holland.
Lighthill, M. J. 1956 In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies), p. 250. Cambridge University Press.
L'Vov, V. S. & Mikhailov, A. V.1978a Sov. Phys., J. Exp. Theor. Phys. 47, 756.
L'Vov, V. S. & Mikhailov, A. V.1978b Sov. Phys., J. Exp. Theor. Phys. 48, 840.
Moiseev, S. S., Sagdeev, R. Z., Tur, A. V. & Yanovsky, V. V. 1977 Sov. Phys. Dokl. 22, 582.
Moiseev, S. S., Petviashvili, V. I., Tur, A. V. & Yanovsky, V. V. 1981 Physica 2D, 218.
Moiseev, S. S., Sagdeev, R. Z., Tur, A. V., Khomenko, G. A. & Yanovsky, V. V. 1983 Sov. Phys., J. Exp. Theor. Phys. 58, 1149.
Passot, T. 1987 Simulations numériques d’écoulements compressibles homogènes en régime turbulent: application aux nuages moléculairs. Thésis, Université de Paris VII, 14 Mai.
Passot, T. & Pouquet, A. 1986 DRET-ONERA Colloquium, Poitiers, Ecole Nationale Supérieure de Mécanique et Aérotechnique.
Passot, T. & Pouquet, A. 1987 Hyperviscosity for compressible flows using spectral methods. J. Comp. Phys. (to appear).Google Scholar
Pelletier, G. 1980 J. Plasma Phys. 24, 421.
Pouquet, A. 1984 In Statistical Methods in Turbulence. Langley Research Workshop, Applied Math. Sc., vol. 58, p. 209. Springer.
Pouquet, A., Sulem, P.-L. & Meneguzzi, M. 1987 Influence of velocity—magnetic field correlations on decaying MHD turbulence with neutral X-points. Submitted to Phys. Fluids.
Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa.
Saffman, P. G. 1971 Stud. Appl. Maths 50, 377.
Streett, C. L., Zang, T. A. & Hussaini, M. Y. 1983 Spectral Multigrid Methods with applications to transonic potential flow. ICASE Rep. 83–111.
Sulem, P.-L., Fournier, J.-D. & Pouquet, A. 1979 In Dynamic Critical Phenomena and Related Topics. Lecture Notes in Physics, vol. 104, p. 321. Springer.
Sulem, P.-L., Frisch, U., Pouquet, A. & Meneguzzi, M. 1985 J. Plasma Phys. 33, 191.
Tatsumi, T. & Tokunaga, H. 1974 J. Fluid Mech. 65, 581.
Tokunaga, H. 1976 J. Phys. Soc. Japan 41, 328.
Tokunaga, H. & Tatsumi, T. 1975 J. Phys. Soc. Japan 38, 1167.
Weiss, J. 1979 A class of compressible partial differential equations related to the incompressible Navier—Stokes equation. Ph.D. thesis, New York University.
Wolibner, W. 1933 Math Z. 37, 668.
Yates, J. E. 1978 NASA Contractor Rep. 2987, Langley Research Center.
Zakharov, V. E. & Sagdeev, R. Z. 1970 Sov. Phys. Dokl. 15, 439.