Development of laminar jet flows with zero excess impulse

Abstract

The problem of the development of a laminar jet of viscous incompressible fluid with zero excess impulse (the wake of a hydrodynamic motor) was investigated for the first time by Birkhoff and Zarantonello [1], who found a self-similar solution to the dynamical problem for the case of a two-dimensional laminar wake. The problem of the development of turbulent wakes of hydrodynamic motors in the near and far flow regions was solved by Ginevskii [2] on the basis of an integral method. In the present paper, the method of asymptotic expansions is used on the basis of the boundary layer equations to solve nonself-similar problems of the development of laminar jet flows of a viscous incompressible fluid with zero excess impulse. The obtained solution takes into account the influence of the details of the source (finite size of the body and its geometry) and the value of the Prandtl number on the velocity and temperature distribution. In the case of a laminar axi-symmetric wake, a self-similar solution is obtained to the thermal problem, the solution being valid in a wide range of Prandtl numbers.