This study provides a detailed exploration of the near-field shear-layer instabilities associated with a gaseous jet injected normally into crossflow, also known as the transverse jet. Jet injection from nozzles which are flush as well as elevated with respect to the tunnel wall are explored experimentally in this study, for jet-to-crossflow velocity ratiosRin the range 1 ≲R≤ 10 and with jet Reynolds numbers of 2000 and 3000. The results indicate that the nature of the transverse jet instability is significantly different from that of the free jet, and that the instability changes in character as the crossflow velocity is increased. Dominant instability modes are observed to be strengthened, to move closer to the jet orifice, and to increase in frequency as crossflow velocity increases for the regime 3.5 <R≤ 10. The instabilities also exhibit mode shifting downstream along the jet shear layer for either nozzle configuration at these moderately high values ofR. WhenRis reduced below 3.5 in the flush injection experiments, single-mode instabilities are dramatically strengthened, forming almost immediately within the shear layer in addition to harmonic and subharmonic modes, without any evidence of mode shifting. Under these conditions, the dominant and initial mode frequencies tend to decrease with increasing crossflow. In contrast, the instabilities in the elevated jet experiments are weakened as R is reduced below about 4, probably owing to an increase in the vertical coflow magnitude exterior to the elevated nozzle, untilRfalls below 1.25, at which point the elevated jet instabilities become remarkably similar to those for the flush injected jet. Low-level jet forcing has no appreciable influence on the shear-layer response when these strong modes are present, in contrast to the significant influence of low-level forcing otherwise. These studies suggest profound differences in transverse-jet shear-layer instabilities, depending on the flow regime, and help to explain differences previously observed in transverse jets controlled by strong forcing.

The dominant non-dimensional parameter for isodensity transverse jet flow is the mean jet-to-crossflow velocity ratio,R. In Part 1 (Megerianet al.,J. Fluid Mech., vol. 593, 2007, p. 93), experimental results are presented for the behaviour of transverse-jet near-field shear-layer instabilities for velocity ratios in the range 1 <R≤ 10. A local linear stability analysis is presented in this paper for the subrangeR>4, using two different base flows for the transverse jet. The first analysis assumes the flow field to be described by a modified version of the potential flow solution of Coelho & Hunt (J. Fluid Mech., vol. 200, 1989, p. 95), in which the jet is enclosed by a vortex sheet. The second analysis assumes a continuous velocity model based on the same inviscid base flow; this analysis is valid for the larger values of Strouhal number expected to be typical of the most unstable disturbances, and allows prediction of a maximum spatial growth rate for the disturbances. In both approaches, results are obtained by expanding in inverse powers ofRso that the free-jet results are obtained asR→∞. The results from both approaches agree in the moderately low-frequency regime. Maximum spatial growth rates and associated Strouhal numbers extracted from the second approach both increase with decreasing velocity ratioR, in agreement with the experimental results from Part 1 in the range 4<R≤10. The nominally axisymmetric mode is found to be the most unstable mode in the transverse-jet shear-layer near-field region, upstream of the end of the potential core. The overall agreement of theoretical and experimental results suggests that convective instability occurs in the transverse-jet shear layer for jet-to-crossflow velocity ratios above 4, and that the instability is strengthened asRis decreased.

The convective and absolute nature of instabilities in Rayleigh–Bénard–Poiseuille (RBP) mixed convection for viscoelastic fluids is examined numerically with a shooting method as well as analytically with a one-mode Galerkin expansion. The viscoelastic fluid is modelled by means of a general constitutive equation that encompasses the Maxwell model and the Oldroyd-B model. In comparison to Newtonian fluids, two more dimensionless parameters are introduced, namely the elasticity number ${\it\lambda}_{1}$ and the ratio ${\it\Gamma}$ between retardation and relaxation times. Temporal stability analysis of the basic state showed that the three-dimensional thermoconvective problem can be Squire-transformed. Therefore, one must distinguish mainly between two principal roll orientations: transverse rolls TRs (rolls with axes perpendicular to the Poiseuille flow direction) and longitudinal rolls LRs (rolls with axes parallel to the Poiseuille flow direction). The critical Rayleigh number for the appearance of LRs is found to be independent of the Reynolds number ( $\mathit{Re}$ ). Depending on ${\it\lambda}_{1}$ and ${\it\Gamma}$ , two different regimes can be distinguished. In the weakly elastic regime, the emerging LRs are stationary, while they are oscillatory in the strongly elastic regime. For TRs, it is found that in the weakly elastic regime, the stabilization effect of $\mathit{Re}$ is more important than in Newtonian fluids. Moreover, for sufficiently elastic fluids a jump is observed in the oscillation frequencies and wavenumbers for moderate $\mathit{Re}$ . In the strongly elastic regime, the effect of the imposed throughflow is to promote the appearance of the upstream moving TRs for low values of $\mathit{Re}$ , which are replaced by downstream moving TRs for higher values of $\mathit{Re}$ . Moreover, the results proved that, contrary to the case where $\mathit{Re}=0$ , the elasticity number ${\it\lambda}_{1}$ (the ratio ${\it\Gamma}$ ) has a strongly stabilizing (destabilizing) effect when the throughflow is added. The influence of the rheological parameters on the transition curves from convective to absolute instability in the Reynolds–Rayleigh number plane is also determined. We show that the viscoelastic character of the fluid hastens the transition to absolute instability and even may suppress the convective/absolute transition. Throughout this paper, similarities and differences with the corresponding problem for Newtonian fluids are highlighted.

Laminar separation bubbles on airfoils and low-pressure turbines are generally expected to be dominated by convective inflectional instability. However, absolute instability is possible under certain circumstances, which may lead to important changes in the laminar-turbulent transition, reattachment processes, and their impact on the aerodynamics. This paper revisits the absolute/convective instability properties of different families of boundary-layer velocity profiles with a reversed flow region. A new methodology is employed in the analysis, which incorporates an additional equation to the classic Rayleigh’s equation governing inviscid instability. This allows for the direct recovery of the zero-group-velocity disturbance waves that govern the absolute/convective behavior, at an unprecedented low computational cost that enabled the large parametric study performed here. Present results show that while the peak reversed flow or wall-normal extent of the reversed flow impact the instability character, criteria based on any of them are generally not valid. A new criterion is proposed, based on the relative position of the inflection point: inviscid inflectional instability becomes of an absolute kind when the inflection point is located inside of the recirculation region. Absolutely unstable velocity profiles are identified with peak reversed flow as low as 10% of the free-stream velocity, a value substantially smaller than thresholds previously proposed in the literature.