Direct and Large Eddy Simulation of Turbulence: Proceedings by N. Gilbert, L. Kleiser (auth.), Ulrich Schumann, Rainer

By N. Gilbert, L. Kleiser (auth.), Ulrich Schumann, Rainer Friedrich (eds.)

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31J Wortmann, F. X. 1981 Boundary-layer waves and transition, in: Advances in Fluid Mechanics (ed. E. Krause), Lecture Notes in Physics 148, 268-279, Springer-Verlag. [32J May, C. L. & Kleiser, 1. 1985 Numerical simulation of subharmonic transition in plane Poiseuille flow, Bull. Amer. Phys. Soc. 30, 1748. 36 SUBGRID SCALE MODELS FOR HOMOGENEOUS ANISOTROPIC' TURBULENCE B. AUPOIX ONERA/CERT Department of Aerothermodynamics 2 avenue Edouard Belin - 31055 TOULOUSE Cedex (FRANCE) SUMMARY A statistical model is used to study the subgrid scale modelling problem for homogeneous turbulence.

It must be stressed again that these pressure terms are trace-free and redistribute the energy at each wavenumber. For the transfer term. the k4 beating term injects some energy in an isotropic way and also redistributes energy in a return to isotropy way. The effective viscosity term drains all the components of the Reynolds stress spectra in an isotropic viscosity way. But the most surprising contribution comes from the last k 2 E(k) term. As the energy spectrum decreases. o[E(p) Hij(P)]/op can be assumed negative and the integral has the sign of the anisotropy.

Beyond the growth rates (eigenvalues), our analysis provides the disturbance velocity distributions (eigenvectors/functions). Figure 7 shows the comparison of experimental and theoretical results for the principal fundamental mode in Poiseuille flow [27]. Figure 8 gives analogue results for the subharmonic mode in the Blasius flow [7]. Similar agreement extends to the phase distribution and to other measured quantities. The streamwise rms fluctuation in figures 7, 8 assumes a pronounced maximum near the critical layer at Yc' where uo(Yc) = cr' Figure 8 also shows that the secondary disturbance velocity is confined in a narrow region within the boundary layer (see also [24] for fundamental modes).

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