Internal-Shear Mode Instabilities on High-Speed Liquid Jet, (I) Characteristics of Linear Solutions

The instabilities on a high-speed liquid jet, induced by amplification of perturbations in the initially-laminar shear layer underneath the free surface (internal-shear mode instabilities), are investigated theoretically and experimentally. Part I of the present paper describes the characteristics of temporally and spatially unstable modes predicted by a linear perturbation equation where the shear layer velocity profile is represented by a single straight line. The analysis focuses on simulated liquid-metal beam target flow conditions characterized by high Froude numbers Fr Δ and moderate Weber numbers We Δ, both based on the velocity difference and the thickness of the shear layer. Temporally and spatially unstable modes are predicted for We Δ >1.8, for a certain range of wave number. For these spatiotemporal modes, the temporal growth rate tends to decrease with an increase in the spatial growth rate. The instabilities predicted by the present theory are all convective, and not absolute, for We Δ ranging up to 20.