Nonlocal conservation law in a free submerged jet

A free axisymmetric nonswirling submerged jet of viscous incompressible fluid is considered. For large Reynolds numbers, the unknown constant in the asymptotic Landau–Rumer–Gol'dshtik–Yavorsky solution to the Navier–Stokes equations that describes the far jet field is determined. A similar constant in Loitsyanskii’s solution in the boundary layer approximation is found. These constants are expressed in terms of the distribution of velocity in the jet source using a nonlocal conservation law.