Optimal velocity and density profiles for the onset of absolute instability in jets

International audienceThe absolute/convective character of the linear instability of axisymmetric jets is investigated for a wide range of parallel velocity and density profiles. An adjoint-based sensitivity analysis is carried out in order to maximize the absolute growth rate of jet profiles with and without density variations. It is demonstrated that jets without counterflow may display absolute instability at density ratios well above the previously assumed threshold rho(jet)/rho(infinity) = 0.72, and even in homogeneous settings. Absolute instability is promoted by a strong velocity gradient in the low-velocity region of the shear layer, as well as by a step-like density variation near the location of maximum shear. A new efficient algorithm for the computation of the absolute instability mode is presented

Linear impulse response in hot round jets

International audienceThe 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 zero group velocity is found to always be of the jet column type. Although only convectively unstable, the maximum growth rates of the shear layer modes greatly exceed those of the jet column modes in thin shear layer jets. In thick shear layer jets, axisymmetric modes of mixed jet column/shear layer type arise. The weakened maximum growth rate of mixed modes accounts for the dominance of helical modes in temporal stability studies of thick shear layer jets. © 2007 American Institute of Physics

Aerodynamic sound generation by global modes in hot jets

International audienceThe acoustic field generated by the synchronized vortex street in self-excited hot subsonic jets is investigated via direct numerical simulation of the compressible equations of motion in an axisymmetric geometry. The simulation simultaneously resolves both the aerodynamic near field and the acoustic far field. Self-sustained near-field oscillations in the present flow configurations have been described as nonlinear global modes in an earlier study. The associated acoustic far field is found to be that of a compact dipole, emanating from the location of vortex roll-up. A far-field solution of the axisymmetric Lighthill equation is derived, on the basis of the source term formulation of Lilley (AGARD-CP, vol. 131, 1974, pp. 13.1-13.12). With the near-field source distributions obtained from the direct numerical simulations, the Lighthill solution is in good agreement with the far-field simulation results. Fluctuations of the enthalpy flux within the jet are identified as the dominant aeroacoustic source. Superdirective effects are found to be negligible. © 2010 Cambridge University Press

Global linear stability of a model subsonic jet

The global stability of a subsonic jet is investigated using a model base flow designed to fit experimental results for turbulent mean flows. Eigenmodes are computed for axisymmetric perturbations in order to investigate the nature of typically observed large-scale coherent oscillations ("preferred mode"). We do not find evidence that this preferred mode corre- sponds to the least damped global mode. Non-modal stability is also considered through the computation of optimal perturbations. Although non-axisymmetric perturbations (in particular for azimuthal wavenumber m = 1) are subject to larger transient growth, these reach their peak amplitude far downstream of the potential core, and therefore they are less likely to be observed

Frequency selection in globally unstable round jets

International audienceThe 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 and maintained by the action of the baroclinic torque. © 2007 American Institute of Physics

Nonlinear global modes in hot jets

International audienceSince the experiments of Monkewitz et al. (J. Fluid Mech. vol. 213, 1990, p. 611), sufficiently hot circular jets have been known to give rise to self-sustained synchronized oscillations induced by a locally absolutely unstable region. In the present investigation, numerical simulations are carried out in order to determine if such synchronized states correspond to a nonlinear global mode of the underlying base flow, as predicted in the framework of Ginzburg - Landau model equations. Two configurations of slowly developing base flows are considered. In the presence of a pocket of absolute instability embedded within a convectively unstable jet, global oscillations are shown to be generated by a steep nonlinear front located at the upstream station of marginal absolute instability. The global frequency is given, within 10% accuracy, by the absolute frequency at the front location and, as expected on theoretical grounds, the front displays the same slope as a k--wave. For jet flows displaying absolutely unstable inlet conditions, global instability is observed to arise if the streamwise extent of the absolutely unstable region is sufficiently large: While local absolute instability sets in for ambient-to-jet temperature ratios S = 0.453, global modes only appear for S = 0.3125. In agreement with theoretical predictions, the selected frequency near the onset of global instability coincides with the absolute frequency at the inlet. For lower S, it gradually departs from this value. © 2006 Cambridge University Press

Vortex pairing in jets as a global Floquet instability: modal and transient dynamics

International audienceThe spontaneous pairing of rolled-up vortices in a laminar jet is investigated as a global secondary instability of a time-periodic spatially developing vortex street. The growth of subharmonic perturbations, associated with vortex pairing, is analysed both in terms of modal Floquet instability and in terms of transient growth dynamics. The article has the double objective to outline a toolset for global analysis of time-periodic flows, and to leverage such an analysis for a fresh view on the vortex pairing phenomenon. Axisymmetric direct numerical simulations (DNS) of jets with single-frequency inflow forcing are performed, in order to identify combinations of the Reynolds and Strouhal numbers for which vortex pairing is naturally observed. The same DNS calculations are then repeated with an added time-delay control term, which artificially suppresses pairing, so as to obtain time-periodic unpaired base flows for linear stability analysis. It is demonstrated that the natural occurrence of vortex pairing in nonlinear DNS coincides with a linear subharmonic Floquet instability of the underlying unpaired vortex street. However, DNS results suggest that the onset of pairing involves much stronger temporal growth of subharmonic perturbations than what is predicted by modal Floquet analysis, as well as a spatial distribution of these fast-growing perturbation structures that is inconsistent with the unstable Floquet mode. Singular value decomposition of the phase-shift operator (the operator that maps a given perturbation field to its state one flow period later) is performed for an analysis of optimal transient growth in the vortex street. Non-modal mechanisms near the jet inlet are thus found to provide a fast route towards the limit-cycle regime of established vortex pairing, in good agreement with DNS observations. It is concluded that modal Floquet analysis accurately predicts the parameter regime where sustained vortex pairing occurs, but that the bifurcation scenario under typical conditions is dominated by transient growth phenomena

Modal and transient dynamics of jet flows

International audienceThe linear stability dynamics of incompressible and compressible isothermal jets are investigated by means of their optimal initial perturbations and of their temporal eigenmodes. The transient growth analysis of optimal perturbations is robust and allows physical interpretation of the salient instability mechanisms. In contrast, the modal representation appears to be inadequate, as neither the computed eigenvalue spectrum nor the eigenmode shapes allow a characterization of the flow dynamics in these settings. More surprisingly, numerical issues also prevent the reconstruction of the dynamics from a basis of computed eigenmodes. An investigation of simple model problems reveals inherent problems of this modal approach in the context of a stable convection-dominated configuration. In particular, eigenmodes may exhibit an exponential growth in the streamwise direction even in regions where the flow is locally stable

Deep-water sediment wave formation: Linear stability analysis of coupled flow/bed interaction

International audienceA linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier-Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien-Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt-Val frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations. © 2011 Cambridge University Press