Certain conservation properties in gas dynamics

A vortex-line invariant of the steady barotropic flow of an ideal gas is found, and an analog of this invariant and several other invariants of streamlines and vortex lines is obtained for the more general case of nonbarotropic flow. An equation is obtained which describes the change in the vorticity projection on the velocity direction in the three-dimensional flow of an ideal gas. Attention is given to cases of vorticity conservation along the streamlines which yields an additional integral of the gasdynamic equations. The hypersonic flow past a wing of medium aspect ratio at high angle of attack is considered as an example.