Abstract
We study a steady 3D flow of the ideal gas. In the flow between the bow shock wave and the nose part of the body streamlined by the uniform supersonic flow, we consider isoentropic stream surfaces that originate at closed lines on the shock and envelope its leading point. We show that each vortex line is closed and once envelopes the isoentropic stream surface. We obtain the integral invariant of isoentropic stream surfaces, namely, the circulation of the scaled (in a certain way) vorticity vector over (closed) vortex lines. This result is a 3D generalization of the streamline invariant obtained by L. Crocco for axisymmetric flows.
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 12, pp. 52–56.
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Golubkin, V.N., Sizykh, G.B. Generalization of the Crocco Invariant for 3D Gas Flows Behind Detached Bow Shock Wave. Russ Math. 63, 45–48 (2019). https://doi.org/10.3103/S1066369X19120053
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DOI: https://doi.org/10.3103/S1066369X19120053