Laminar Jets: Physical Sensitivity and Instability Theory

Abstract

A laminar jet of fluid is “sensitive” if disturbances from ordinary sound waves are amplified to a macroscopic scale. Relevant hydrodynamic instability theories concern spatial disturbances of hypothetical nonspreading laminar jets. The neutral stability curve by Curle has a ⊂-shape on a Reynolds number-wave-number plot. Difficulties arise in quantitative applications to the real jet, mainly from (a) the essentially temporal disturbances, (b) varying local Reynolds and Strouhal numbers due to jet spread (especially at low values), and (c) transitional velocity profiles. The last two appear to promote increasing stability away from the orifice (except at very small Strouhal numbers). The phenomenon is nonlinear (or quasi-linear at best), fundamentally depending upon (i) Reynolds number, (ii) Strouhal number, (iii) nondimensional disturbance amplitude, (iv) initial velocity profile. In recent experiments by L. D. Miller, R. C. Chanaud, and the author, which are discussed in detail,. (iv) was made invariable; the remaining three parameters were used to establish dynamical similarity for the verge of sensitivity corresponding to the important upper ⊂-limb. Expectedly, parameter (iii) is significant. Further developments will concern the lowest Reynolds number limit and the lower ⊂-limb, where the phenomenon is a little more obtuse. (This work has been partially supported by the Office of Naval Research, U. S. Navy.)