Abstract
Fluid dynamics studies the motion of continuous media with fluidity.
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Notes
- 1.
- 2.
This theory is also applicable to all other vector fields to be encountered in our study. Before moving on, the reader is strongly recommended to get a full familiarity of the materials in Appendix as a necessary preparation.
- 3.
In this book the two pair of names will be used alternatively.
- 4.
Whenever written in component form, throughout this book we use the convention that the (i, j)th component of \(\nabla {\varvec{{u}}}\) is \(\nabla _iu_j =\partial _iu_j = u_{j,i}\).
- 5.
Since only material line element \(\delta {\varvec{{x}}}\) is involved, operator D / Dt can be replaced by d / dt, see (1.1.4).
- 6.
See, e.g. Aris (1962), Zhuang et al. (2009), and Panton (2013).
- 7.
Some authors use the term “kinematics” more restrictively, only to the spatial relations of the relevant quantities at a single time instance.
- 8.
A surface element is a vector consisting of its normal direction \({\varvec{{n}}}\) and area dS.
- 9.
See, e.g. Lighthill (1956).
- 10.
The postulation (1.2.5) holds for most common fluids but is not universally true. In those exceptional cases the angular-momentum balance is an independent law and stress tensor is no longer symmetric.
- 11.
In general, \(\mu \) and k are at most functions of \(\rho \) and T as the physical properties of a fluid; but \(\zeta \) has been found to depend on not only \(\rho , T\) but also frequency of the gas motion, and can be enhanced enormously at very high frequencies (cf. Landau and Lifshitz 1959).
- 12.
For unsteady flow without characteristic frequency, one may use L and U to define the dimensionless time \(t^* =Ut/L\), which corresponds to setting \(St =1\).
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Wu, JZ., Ma, HY., Zhou, MD. (2015). Fundamentals of Fluid Dynamics. In: Vortical Flows. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47061-9_1
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DOI: https://doi.org/10.1007/978-3-662-47061-9_1
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