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An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

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Abstract

An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral.

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Authors
  1. G. Ya. Dynnikova
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Additional information

Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–41, January–February, 2000.

The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00156 and project No. 96-15-9603 for the support of leading science schools).

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Dynnikova, G.Y. An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid. Fluid Dyn 35, 24–32 (2000). https://doi.org/10.1007/BF02698782

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  • DOI: https://doi.org/10.1007/BF02698782

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