Analytic similarity solutions of the Navier–Stokes equations for a jet in a half space with the no-slip boundary condition

Abstract

We consider steady axisymmetric no-swirl viscous flows in a half space driven by a concentrated force. A method of finding physically meaningful similarity solutions of the Navier–Stokes equations with finite values of mass and momentum fluxes satisfying the no-slip boundary condition is developed. A new one-parameter set of analytic similarity solutions that describes impinging or emerging jets depending on the value of the parameter is found. A unique emerging-jet solution can be found for an arbitrary value of the Reynolds number. The accomplished analysis of momentum balance has resulted in an algorithm to estimate the best parameter of the similarity solution corresponding to the given physical characteristics of the jet source.