The full impulse response of two-dimensional jet/wake flows and implications for confinement

Abstract

In this theoretical study, a linear spatio-temporal analysis is performed on unconfined and confined inviscid jet/wake flows in order to determine whether they are absolutely or convectively unstable. The impulse response is evaluated in the entire outer fluid, rather than just at the point of impulse, over a wide range of density ratios. This confirms that the dominant saddle point can validly migrate into the plane of diverging eigenfunctions. This reveals that, at certain density ratios and shear numbers, the response can grow upstream in some directions with a cross-stream component, even though it decays directly upstream of, and at, the point of impulse. This type of flow is convectively unstable when unconfined, but becomes absolutely unstable when confined. Other effects of confinement are described in a previous paper. Together, these articles have important implications for the design of fuel injectors, which often employ confined shear flows at high Reynolds number and large density ratios to generate strong mixing in combustion chambers.