Abstract
After the development of a general background on fundamental processes in fluid motion in Chap. 2 and basic theory of vorticity dynamics in Chap. 3, we now move onto vortex dynamics, i.e., the dynamics of vortices observed at large Reynolds numbers, which by definition are shear flow structures with highly concentrated vorticity.
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Notes
- 1.
In general, the spatial-temporal integral of the nonlinear term \(\nabla \times ({\varvec{\omega }}\times {{\varvec{u}}})\) has an additional contribution to the \({\varvec{\omega }}\)-field and \({\varvec{\omega }}_B\).
- 2.
This may also be explained in terms of pressure gradient and acceleration, e.g., Batchelor (1967).
- 3.
It is of interest to compare this estimate for shear layer with that for a shock layer of thickness \(\delta \), where the advection and diffusion both along the streamwise direction are balanced, so there is \(\rho u^2/\delta \sim \mu u/\delta ^2\), yielding \(\delta /L \sim Re^{-1}_L\), much smaller than \(Re^{-1/2}\).
- 4.
Mao and Xuan (2010), private communications.
- 5.
See Sect. 11.1.2 for the concept of buffer layer in turbulent boundary layers.
- 6.
Mao and Xuan (2010), private communications.
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Wu, JZ., Ma, HY., Zhou, MD. (2015). Attached and Free Vortex Layers. In: Vortical Flows. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47061-9_4
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DOI: https://doi.org/10.1007/978-3-662-47061-9_4
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