The mechanics of the formation region of vortices behind bluff bodies

TLDR

The characteristic lengths of oscillating wakes behind bluff bodies are discussed, focusing on those used in universal non‑dimensional frequencies proposed by Roshko (1954) and Goldburg, Washburn & Florsheim (1965). The developed ideas are applied to analyze the effects of splitter plates on the wake. At high Reynolds numbers, the two characteristic lengths—the formation‑region scale and the shear‑layer diffusion width—are equivalent, providing a physical basis for the wake frequency and suggesting that a symmetrical formation region explains the very small lift values observed without free‑stream disturbances.

Abstract

The characteristic lengths of the oscillating wakes of bluff bodies is discussed; in particular, those used in the universal non-dimensional frequencies proposed by Roshko (1954 b ) and Goldburg, Washburn & Florsheim (1965). It is concluded that these are equivalent at high Reynolds number. A closer examination leads to the conclusion that there are two simultaneous characteristic lengths; the scale of the formation region, and the width to which the free shear layers diffuse. Discussion of the mechanics of the formation region results in a physical basis for the determination of the frequency by these two characteristic lengths. The ideas developed are applied to the effects of splitter plates in the wake. The possibility of a high-Reynolds-number symmetrical formation region is suggested as an explanation of the very small lift values observed in the absence of free-stream disturbances.