Abstract
As stated at the end of Chap. 5, if at large Reynolds numbers a moving body is dressed in fully attached boundary layers, the flow can be solved by potential-flow theory with good accuracy, and then a boundary-layer correction yields the friction force to the body.
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Notes
- 1.
An attached boundary layer will eventually leave the trailing edge of a finite body, which in a broad sense is also a separation.
- 2.
Here, we say a fixed point is “stable” if all neighboring vector lines point toward it, and “unstable” if some of neighboring vector lines point out of it. This stability concept is not to be confused with either the stability of topological structures outlined in Sect. 8.4.4, or the flow stability addressed in Chap. 10.
- 3.
The true curvature of a \({{\varvec{\tau }}}\)-line in space involves not only the projection of \(\partial _1{{\varvec{e}}}_1\) onto \({{\varvec{e}}}_2\) but also that onto \({{\varvec{e}}}_3\), the latter being an effect of wall curvature.
- 4.
But, for unsteady flow this identification itself may not be an easy job. Besides, although some examples will be presented in Sects. 8.4.4 and 8.5.3 on the topology analysis of unsteady streamline patterns, caution is necessary regarding the role of these streamline patterns in interpreting the evolution of unsteady vortical structures. See relevant observation of Sect. 8.5.2.
- 5.
The times for the 6 plots in the original figure of Haller have been modified to be consistence with (8.5.2). The plots display the instant positions of the released particles at each individual time.
- 6.
\(Cp_b \) is the pressure coefficient at the downstream end b of the body, which reflects the sensitivity of the flow pattern to Re more adequately than that of \(C_D\).
- 7.
The concept of Reynolds stress is mainly introduced in the study of averaged flow behavior, see Sect. 11.1.2. This concept can equally applied to unsteady laminar flows, where the time average of products of fluctuating velocities can also be viewed as a Reynolds stress.
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Wu, JZ., Ma, HY., Zhou, MD. (2015). Flow Separation and Separated Flows. In: Vortical Flows. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47061-9_8
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DOI: https://doi.org/10.1007/978-3-662-47061-9_8
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