Abstract
The complete system of hydrodynamic equations that describe the free surface of an inviscid fluid, a tangential discontinuity, and the development of the hydrodynamic instability of a reaction front is reduced to a closed system of surface equations using Lagrangian variables, special integrals of motion, and their analogues. The vorticity is shown to play a fundamental role in the pattern of motion of hydrodynamic discontinuities, imparting a differential form to the equations. In the isentropic approximation, it is demonstrated how to take into account the fluid density oscillations caused by this motion. The derived system of equations is consistent with the previously known analytical solutions obtained in special cases.
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Original Russian Text © M.L. Zaytsev, V.B. Akkerman, 2009, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 135, No. 4, pp. 800–819.
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Zaytsev, M.L., Akkerman, V.B. A nonlinear theory for the motion of hydrodynamic discontinuity surfaces. J. Exp. Theor. Phys. 108, 699–717 (2009). https://doi.org/10.1134/S1063776109040177
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DOI: https://doi.org/10.1134/S1063776109040177