The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes

Abstract

The boundary between absolute and convective (linear) instability of two-dimensional inertial jets and wakes is determined as a function of the ratio of jet/wake to ambient density, as well as the ratio of mixing layer thickness to jet/wake width, the velocity ratio, and the Reynolds number. For this, a viscous, heat-conducting ideal gas is taken as the fluid, a zero Mach number, no buoyancy and a parallel basic flow are assumed, and the density variation is achieved by specifying a mean temperature profile similar to the velocity profile. Considering both ‘‘varicose’’ and ‘‘sinuous’’ disturbances, results are obtained for the inviscid top-hat jet/wake bounded by two vortex sheets, the inviscid jet with continuous velocity and density profiles, and the viscous wake. For the latter, both constant and temperature-dependent viscosity are investigated. In all the cases it is found that low density of the high-speed fluid promotes absolute instability, while low density of the low-speed fluid has the opposite effect. By comparison with experiments it is shown that the present results provide useful information about the parameter range in which flow oscillations are self-excited.

Stability analysis and breakup length calculations for steady planar liquid jets

“…We find that this leads to important qualitative differences compared with previous studies in which the density interface was assumed to lie on only one side of the shear layer (Marmottant & Villermaux 2004;Juniper 2007). Our assumption to neglect viscosity in this study is valid because Yu & Monkewitz (1990) showed that the transition to absolute instability is caused by the interaction between the two shear layers and is not a viscous effect. Lin, Lian & Creighton (1990) and Li & Tankin (1991) investigated the effect of viscosity on planar liquid jets and found that the solution contained an unstable mode with zero frequency and two convectively unstable modes, identical to those of Hagerty & Shea (1955), whose growth rates are affected by the presence of viscosity.…”

“…It is known that the density ratio has a large effect on the behaviour of absolute instabilities, in particular that low-density jets (q > 1) are almost always absolutely unstable (Sreenivasan, Raghu & Kyle 1989;Yu & Monkewitz 1990;Juniper 2006). In this work we are concerned with jets which have q < 1, but we find that absolute instabilities can occur at these density ratios for particular velocity profiles.…”

Viscous stability analysis of jets with discontinuous base profiles

“…An important example satisfying the long wavelength condition mentioned above are the columnar modes of jets, which are known to play a relevant role in their stability [8], and dominate their dynamics when self-excited by becoming locally absolutely unstable in the near field [9][10][11][12][13]. Previous viscous stability analyses of these jet flows, including planar [12] and axisymmetric [14] configurations, have made use of model base profiles with thin shear layers.…”

“…Previous viscous stability analyses of these jet flows, including planar [12] and axisymmetric [14] configurations, have made use of model base profiles with thin shear layers. Since the relevant wavelengths for the columnar modes are of the order of the jet radius, the shear-layer thickness enters in the analysis as a secondary parameter that takes small non-zero values.…”

Influence of confinement on a two-dimensional wake

“…An alternative interpretation was given by Healey (2007), based on the transverse propagation and reflection on the wall of instability waves. These last papers completed the series of variants of absolute/convective analysis of planar and axisymmetric wakes and jets, including for example the influence of the shear layer thickness (Monkewitz 1988), Reynolds number (Monkewitz 1988), density ratio (Yu & Monkewitz 1990), viscosity ratio (Sevilla, Gordillo & Martinez-Bazan 2002), surface tension (Leib & Goldstein 1986), compressibility (Lesshafft & Huerre 2007;Meliga, Sipp & Chomaz 2010) and added swirling flow component (Loiseleux, Chomaz & Huerre 1998).…”