On the sensitivity of planar jets

Highlights: • The CMM is adapted to the stability analysis of planar jets. • An explanation is given for the high sensitivity of planar jets close to the orifice. • Necessary conditions are given for the occurrence of varicose modes. - Abstract: Planar jets are widely researched flows. Many aspects of their instability have been well-known for a long time. One of them is the observation that the jet is more sensitive to disturbances near the orifice than elsewhere. This paper aims at giving an explanation to this hitherto unexplained phenomenon. To this end, linear stability investigations on various velocity profiles were carried out using the Orr–Sommerfeld (OS) equation. The velocity profiles were provided by analytical approximations and numerical computational fluid dynamics (CFD) simulations. A special method called compound matrix method (CMM) was used for solving the OS equation to obtain sufficiently accurate results. The adaptation of the method for symmetric jets was briefly derived. The stability of various velocity profiles was compared based on the local spatial growth rate. The results of the comparison clearly show that velocity profiles near the orifice are more unstable than the downstream ones. The outcomes also show that the velocity profile close to the orifice and the wall thickness of the nozzle have impact on the stability properties of the flow there.