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ISSN Imprimir: 1099-2391
ISSN En Línea: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

# Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v1.i3.10
31 pages

## ON KAPLUN LIMITS AND THE MULTILAYERED ASYMPTOTIC STRUCTURE OF THE TURBULENT BOUNDARY LAYER

Atila P. Silva Freire
Mechanical Engineering Department, Federal University of Rio de Janeiro, Av. Moniz de Aragao 420, 21945-972 Rio de Janeiro, Brazil

### SINOPSIS

In the present work, some formal properties of singular perturbation equations are studied through the concept of "equivalent in the limit" of Kaplun, so that a proposition for the principal equations is derived. The proposition shows that if there is a principal equation at a point (η, 1) of the (Ξ × Σ) product space, Ξ space of all positive continuous functions in (0, 1], Σ = (0, 1], then there is also a principal equation at a point (η, ε) of (Ξ × Σ), ε = first critical order. The converse is also true. The proposition is of great implication because it ensures that the asymptotic structure of a singular perturbation problem can be determined by a first-order analysis of the formal domains of validity. The turbulent boundary layer asymptotic structure is then studied by application of Kaplun limits to three test cases: the zero-pressure boundary layer, the separating boundary layer and the shock-wave interacting boundary layer. As it turns out, different asymptotic structures are found, depending on the test cases considered. However, before we consider the real turbulent boundary layer problem, the basics of the theory are illustrated by the study of a model equation that mimics turbulent flow passed over a flat surface. The model equation was chosen for being relatively simple while retaining most of the features of the real problem. This allows one to easily grasp the main concepts and ideas wthout being hampered by unnecessary details. Results show that a two-layered structure is derived, which, however, is different from the classic structure commonly found in the literature, and hence is capable of explaining the flow separation phenomenon. A skin-friction equation resulting from a matching process, and universal laws resulting from local approximated equations are carefully interpreted and evaluated.

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