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The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio $R = \Delta U/2\overline{U}$, where ΔU is the velocity difference between the two streams and $\overline{U}$ their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.

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The goal of this study is to characterize the various breakdown states taking place in a swirling water jet as the swirl ratio S and Reynolds number Re are varied. A pressure-driven water jet discharges into a large tank, swirl being imparted by means of a motor which sets into rotation a honeycomb within a settling chamber. The experiments are conducted for two distinct jet diameters by varying the swirl ratio S while maintaining the Reynolds number Re fixed in the range 300<Re<1200. Breakdown is observed to occur when S reaches a well defined threshold Sc≈1.3–1.4 which is independent of Re and nozzle diameter used. This critical value is found to be in good agreement with a simple criterion derived in the same spirit as the first stage of Escudier & Keller's (1983) theory. Four distinct forms of vortex breakdown are identified: the well documented bubble state, a new cone configuration in which the vortex takes the form of an open conical sheet, and two associated asymmetric bubble and asymmetric cone states, which are only observed at large Reynolds numbers. The two latter configurations differ from the former by the precession of the stagnation point around the jet axis in a co-rotating direction with respect to the upstream vortex flow. The two flow configurations, bubble or cone, are observed to coexist above the threshold Sc at the same values of the Reynolds number Re and swirl parameter S. The selection of breakdown state is extremely sensitive to small temperature inhomogeneities present in the apparatus. When S reaches Sc, breakdown gradually sets in, a stagnation point appearing in the downstream turbulent region of the flow and slowly moving upstream until it reaches an equilibrium location. In an intermediate range of Reynolds numbers, the breakdown threshold displays hysteresis lying in the ability of the breakdown state to remain stable for S<Sc once it has taken place. Below the onset of breakdown, i.e. when 0<S<Sc, the swirling jet is highly asymmetric and takes the shape of a steady helix. By contrast above breakdown onset, cross-section visualizations indicate that the cone and the bubble are axisymmetric. The cone is observed to undergo slow oscillations induced by secondary recirculating motions that are independent of confinement effects.

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The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e. that its streamwise development is slow on the scale of a typical instability wavelength. This implies the general study of the temporal evolution of global modes, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. Flow domains of both doubly infinite and semi-infinite streamwise extent are considered and complete solutions are obtained within the framework of asymptotically matched WKBJ approximations. In both cases the global eigenfrequency is given, to leading order in the WKBJ parameter, by the absolute frequency ω0(Xt) at the dominant turning pointXtof the WKBJ approximation, while its quantization is provided by the connection of solutions acrossXt. Within the context of the present analysis, global modes can therefore only become time-amplified or self-excited if the basic flow contains a region of absolute instability.

The possible existence of global modes or self‐excited linear resonances in spatially developing systems is explored within the framework of the WKBJ approximation. It is shown that the existence and properties of the dominant global mode may be deduced from the variations of the local absolute frequency ω0 with distance X. The main results are summarized in two theorems: (1) A system with no region of absolute instability does not sustain temporally growing global modes with an O(1) growth rate. (2) If the singularity X, closest to the real X‐axis of the complex function ω0(X) is a saddle point, the most unstable global mode has, to leading order in the WKBJ approximation, a complex frequency ω0(Xs). Thus, it will be temporally growing only if ω0(Xs) is positive.