ИСТИНА

By non-viscous fluid is meant a limiting case of a viscous fluid with a Reynolds number tending to infinity. The Navier-Stokes equations are the basis of the model. The hypothesis that viscosity is significant only in a thin layer on the surface of the body, beyond which the fluid is ideal (no viscosity), is supposed in the same way as in the classical theory of the boundary layer. The hypothesis that the vorticity is orthogonal to its rotor in the boundary layer is also assumed. This is consistent with traditional estimates for the velocity field in the boundary layer. The Navier-Stokes equations in the boundary layer are written using the concept of diffusion velocity on the grounds of these hypotheses. Next the integral equation for the flux of vorticity from the surface of the body into the fluid domain is obtained. This equation, together with the equations for the motion of fluid points, the vorticity equations at these points, the integral representation for the velocity field in the form of a Bio-Savart law, and initial conditions, constitutes a closed mathematical problem for fluid flow within the Lagrangian approach.