Recent Advances in Boundary Layer Theory by Alfred Kluwick (eds.)

By Alfred Kluwick (eds.)

Recent advances in boundary-layer conception have proven how sleek analytical and computational concepts can and will be mixed to deepen the certainty of excessive Reynolds quantity flows and to layout powerful calculation thoughts. this is often the unifying subject of the current quantity which addresses laminar in addition to turbulent flows.

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_.!. 5) u:,. (b) For Pr ~ 00: Ve• = - . 0T - - . 0T Oy W O Internal energy is convected downstream by the near wall velocity boundary layer protile. This can be represented by the tirst non-zero term of a Taylor series expansion at Oy·)w can be replaced by the the wall. For order of magnitude considerations (Ou· / characteristic quantities u:, /o· . 6) 34 H. 13). 5) after the boundary layer transformation y~N in the limit Re~oo. For boundary layers it is more convenient to use since often there is a well detined temperature difference AT: which can be used as a reference quantity.

This, however, means that for finite Reynolds numbers there must be a certain overlap region in which both solutions are valid! This is an important feature in the theory of matched asymptotic expansions. 23) one could equally well introduce a so-called intermediate variable which is of order one in this overlap region, rewrite both expansions in this variable and equate terms of equal asymptotic magnitude as a matching procedure. Once the solutions in the two regions are found (in different coordinates, however) they can be combined by rewriting them in one common coordinate.

Two types of transition are generally considered. , sound, freestream turbulence, etc. , vibrations, roughness, etc. are strong enough that vortex stretching and other nonlinear mechanisms directly lead to turbulence without going through the known stability mechanisms. The second type is the so-called 'quiet' environment transition which evolves gradually, as has been experimentally documented, and can be foIlowed by theory and numerical computations (see Reshotko [1] and Mack [2]). In this review we shall be concerned with this latter type of process.

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