Surface Jet at Small Richardson Numbers

The spreading of a jet discharged horizontally at the surface of an initially quiescent water of larger density is treated analytically. The equations of continuity and of mass conservation are derived as well as a momentum equation for the longitudinal and for the transverse direction. The entrainment of ambient water into the jet is included in the analysis. The four partial differential equations thus obtained are then transformed into ordinary differential equations by assuming similarity of the velocity profiles and of the density profiles, respectively. An exact solution of the equations is obtained for the case of small Richardson numbers. From this the following conclusions are drawn: the jet thickness is proportional to the distance from the outlet. The velocity profiles, as well as the density profiles, follow a Gaussian distribution.