Patrick Huerre

Inviscid instability of the Batchelor vortex: Absolute-convective transition and spatial branches

The main objective of the study is to examine the spatio-temporal instability properties of the Batchelor q-vortex, as a function of swirl ratio q and external axial flow parameter a. The inviscid dispersion relation between complex axial wave number and frequency is determined by numerical integration of the Howard–Gupta ordinary differential equation. The absolute-convective nature of the instability is then ascertained by application of the Briggs–Bers zero-group-velocity criterion. A moderate amount of swirl is found to promote the onset of absolute instability. In the case of wakes, transition from convective to absolute instability always takes place via the helical mode of azimuthal wave number m=−1. For sufficiently large swirl, co-flowing wakes become absolutely unstable. In the case of jets, transition from absolute to convective instability occurs through various helical modes, the transitional azimuthal wave number m being negative but sensitive to increasing swirl. For sufficiently large swir...

Steep nonlinear global modes in spatially developing media

A lubrication pump with a stroking action of a delivery piston and with regulatable metering of the amount of lubricant delivered with each stroke of the pump, wherein the delivery piston is actuated by the pump and aspirates the lubricant into a suction space whose volume is adjustable, wherein furthermore the lubrication is fed from the suction space through an intermediate storage space to the lubricant outlet or to the lubrication circulation circuit and wherein a check valve is provided in the above-mentioned delivery path of the lubricant, so that, when viewed in the delivery direction of the lubricant, the check valve is located following the receiving space and upstream of the intermediate storage space.

Linear impulse response in hot round jets

The linear impulse response of axisymmetric jets is examined for a family of variable-temperature profiles typical of the potential core. The influence of jet heating, shear layer thickness, and Reynolds and Mach numbers on the spatiotemporal stability of both axisymmetric and helical modes is investigated. The linear impulse response is retrieved from a numerical solution of the spatial eigenvalue problem, which is derived from the fully compressible equations of motion. Changes in the spatiotemporal stability of heated versus isothermal jets are shown to arise solely from the effect of the baroclinic torque. By considering the full linear impulse response, the competition between jet column modes and shear layer modes is characterized. Jet column modes are only found to occur for axisymmetric disturbances. In thin shear layer jets, the jet column mode is shown to prevail at low group velocities, whereas axisymmetric and helical shear layer modes dominate at high group velocities. The absolute mode of ze...

Frequency selection in globally unstable round jets

The self-sustained formation of synchronized ring vortices in hot subsonic jets is investigated by direct numerical simulation of the axisymmetric equations of motion. The onset of global instability and the global frequency of synchronized oscillations are examined as functions of the ambient-to-jet temperature ratio and the initial jet shear layer thickness. The numerical results are found to follow the predictions from nonlinear global instability theory; global instability sets in as the unperturbed flow is absolutely unstable over a region of finite streamwise extent at the inlet, and the global frequency near the global instability threshold corresponds to the absolute frequency of the inlet profile. In strongly supercritical thin shear layer jets, however, the simulations display global frequencies well above the absolute frequency, in agreement with experimental results. The inner structure of rolled-up vortices in hot jets displays fine layers of positive and negative vorticity that are produced ...

Absolute and convective instabilities of a swirling jet/wake shear layer

The absolute (AI)/convective (CI) nature of the instability is determined in the family of swirling jet/wake shear layers considered by Martin and Meiburg [Phys. Fluids 6, 424 (1994)] and Lim and Redekopp [Eur. J. Mech. B/Fluids 17, 165 (1998)]. This idealized model includes as essential ingredients both the centrifugal instability associated with the swirl difference and the Kelvin–Helmholtz instability associated with the swirl and axial velocity differences between the core and the outer flow. Centrifugally stabilizing or destabilizing swirl differences are found to promote AI, but a centrifugally destabilizing configuration is more effective in triggering such a transition. For sufficiently large swirl differences, both co-flowing jets and wakes may become AI. In the case of jets, a centrifugally destabilizing swirl difference first brings about AI via the axisymmetric mode m=0 in a large range of mean swirl values. By contrast, a centrifugally stabilizing swirl difference triggers AI via the helical mode m=−∞. In the case of wakes, a centrifugally destabilizing swirl difference leads to AI via the bending mode m=1 whereas a centrifugally stabilizing swirl difference triggers AI via various negative helical modes m=−1,−2, etc.