The round laminar jet: the development of the flow field

Abstract

The development of the flow field of a jet emanating from a point source of momentum in an infinite incompressible fluid of density σ is considered. The flow field is assumed to be due to the application of a constant force F₀ at the origin. The problem is formulated in terms of the dimensionless variable λ = (vt)^½/r, where v is the kinematic viscosity of the fluid, t the time from the application of the force and r the distance from the origin. At a station r the flow field is dipolar, with the dipole axis in the direction of F₀, for all t satisfying the inequalities vt Lt; r² and F₀t² [Lt ] 4πρr⁴. Also, at a given time t the streamlines of the developing flow field in a section through the axis of symmetry of the problem form closed loops about a stagnation point. If this occurs at λ = λ_m, the stagnation point propagates to infinity, along a straight line emanating from the origin, with speed v^½/2λ_mt^½, where λ_m = λ_m(F₀) decreases as F₀ increases. The larger F₀ is the faster the steady state is established.