## Abstract

Among the three ways to compute turbulent flows, namely O. Reynolds’ statistical approach, the large-eddy (LES) and the direct simulation (DS) approaches, the latter is the most attractive because it dispenses with models and solves the unfiltered Navier-Stokes equations for suitable initial and boundary conditions. Since in a DS all turbulent length and time scales are resolved — from the largest down to the smallest scales, which decrease rapidly with increasing Reynolds number — its application is limited to low Reynolds number flow. There is at present only one possibility to study the instantaneous structure of a high Reynolds number flow, namely through large-eddy simulation. Its basic idea is to compute the large scale turbulence directly and to model the small-scale (sub-grid scale, SGS) part, which is supposed to behave universally, so that a small number of parameters are sufficient to describe its dynamics. Sophisticated SGS models have been proposed in the past, based on modern statistical theory of isotropic turbulence; however, simple models of the gradient- diffusion type were used and tested more extensively. The review articles of Ferziger (1983), Rogallo and Moin (1984) and the monograph of Lesieur (1987) provide comprehensive and deep insight into the state of the art and the theoretical background of SGS modeling. Reynolds’ statistical approach, on the other hand, which defines and calculates only mean values, involves a complete loss of information on turbulence spectra and provides therefore the most serious closure problem.

### Keywords

Vortex Convection Stratification Vorticity## Preview

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### References

- Brown, G. L., Roshko, A. (1974): On density effects and large structure in turbulent mixing layers. J. Fluid Mech.
**64**, 775–816ADSCrossRefGoogle Scholar - Ferziger, J. H. (1983): “Higher Level Simulations of Turbulent Flow,” in
*Computational methods for Turbulent, Transonic, and Viscous Flows*, ed. by J.-A. Essers (Hemisphere Publ., New York)Google Scholar - Ferziger, J. H. (1987): Simulation of incompressible turbulent flows. J. Comp. Phys.
**69**, 1–48MathSciNetADSMATHCrossRefGoogle Scholar - Hino, M., Kashiwayanagi, M., Nakayama, A., Hara, T. (1983): Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech.
**131**, 363–400ADSCrossRefGoogle Scholar - Horiuti, K. (1987): Comparison of conservative and rotational forms in large eddy simulation of turbulent channel flow. J. Comp. Phys.
**71**, 343–370ADSMATHCrossRefGoogle Scholar - J. Mécan. Théor. Appl. (Numéro spéciale, 1983) (Gauthier-Villars, Paris) pp. 775–816Google Scholar
- Kim, J. (1987): “Evolution of a Vortical Structure Associated with the Bursting Event in a Channel Flow,” in
*Turbulent Shear Flows 5*, ed. by F. Durst, B. E. Launder, J. L. Lumley, F. W. Schmidt, J. H. Whitelaw (Springer, Berlin, Heidelberg) pp. 221CrossRefGoogle Scholar - Kline, S. J., Reynolds, W. C., Schraub, F. A., Runstadler, P. W. (1967): The structure of turbulent boundary layers. J. Fluid Mech.
**30**, 741–773ADSCrossRefGoogle Scholar - Kraichnan, R. H. (1967): Inertial ranges in two-dimensional turbulence. Phys. Fluids
**10**, 1417–1423ADSCrossRefGoogle Scholar - Lesieur, M. (1987):
*Turbulence in Fluids*(Martinus Nijhoff Publ., Boston)MATHCrossRefGoogle Scholar - Mansour, N. N., Kim, J., Moin, P. (1987): “Near-wall
*k*—*ε*-Turbulence Modeling,” 6th Symposium on Turbulent Shear Flows, Toulouse, 17–4Google Scholar - Moffat, H. K. (1986): “Geophysical and Astrophysical Turbulence,” in
*Advances in Turbulence*, ed. by G. Comte-Bellot and J. Mathieu (Springer, Berlin, Heidelberg) pp. 228–244Google Scholar - Mumford, J. C. (1982): The structure of the large eddies in fully developed turbulent shear flows. Part 1. The plane jet. J. Fluid Mech.
**118**, 241–268ADSCrossRefGoogle Scholar - Peitgen, H.-O. (1984): “A Mechanism for Spurious Solutions of Nonlinear Boundary Value Problems,” in
*Stochastic Phenomena and Chaotic Behavior in Complex Systems*, ed by P. Schuster (Springer, Berlin, Heidelberg) p. 38CrossRefGoogle Scholar - Prüfer, M. (1985): Turbulence in multistep methods for initial value problems. SIAM J. Appl. Math.
**45**, 32–69MathSciNetADSMATHCrossRefGoogle Scholar - Rogallo, R. S., Moin, P. (1984): Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech.
**16**, 99–137ADSCrossRefGoogle Scholar - Saffman, P. G. (1971): Studies in Appl. Math. 50, pp. 377Google Scholar
- Stewart, R. W. (1969): Turbulence. NCFMF FilmGoogle Scholar
- Tennekes, H., Lumley, J. L. (1972):
*A First Course in Turbulence*. (The MIT Press, Cambridge, Massachusetts)Google Scholar