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Erschienen in:
07.04.2020
Vorticity and other properties associated with an unsteady, three-dimensional shock
Erschienen in: Journal of Engineering Mathematics | Ausgabe 1/2020
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Abstract
In accord with the analysis by Emanuel [J Eng Math, 117:79–105, 2019], the upstream and downstream vorticities are provided for an unsteady, three-dimensional shock, where the upstream flow may be non-uniform. The transformation for the upstream velocity Taylor series coefficients, \(e_{ij}^{*}\rightarrow e_{ij}\), is also provided. The analytic approach is illustrated for the vorticity with a simplified flow model. Additionally, the intrinsic coordinate basis, on the downstream side of the shock, is obtained. The analytical representation of the vorticities is in a shock-based, flow-plane coordinate system, whereas the intrinsic coordinate basis is associated with a shock-based, osculating plane. In all cases, results are exact, explicit, and simplified as much as possible.