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The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented.Formulas for components of vorticity behind a steady-state shock wave for flows with constant parameters in the general case were obtained in [1] under the assumption of an infinite shock-wave intensity. Formulas for components of vorticity behind a shock wave of an arbitrary intensity for a uniform incoming flow were derived in [2,3]. The vorticity behind a curvilinear steady-state detonation wave in a supersonic vortex flow is obtained in the present paper. Calculation of Vorticity behind a Steady-State Detonation Wave.Let there be a detonation wave in a steady-state supersonic axisymmetric vortex flow of a combustible gas. The detonation wave is considered as a strong discontinuity surface on which combustion of a unit mass of the gas releases an amount of heat Q, which may be a variable function. For Q = 0, there is a usual shock wave. In this case, the gas motion is described by the following system of equations:Here u(x, r), v(x, r), and w(x, r) are the components of velocity V in a cylindrical coordinate system (x, r, ϕ) and ρ and p are the density and pressure of the gas, respectively. The vorticity 2ω = rot V has the components 2ω r = − ∂w ∂x , 2ω x = 1 r ∂rw ∂r , 2ω ϕ = ∂v ∂x − ∂u ∂r .(2)

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