253 research outputs found

    Transient growth of secondary instabilities in parallel wakes: Anti lift-up mechanism and hyperbolic instability

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    International audienceThis paper investigates the three-dimensional temporal instabilities and the transient growth of perturbations on a Von Kármán vortex street, issuing from the development of the primary instability of a parallel Bickley velocity profile typical of a wake forming behind a thin flat plate. By solving iteratively the linearized direct Navier Stokes equations and its adjoint equations, we compute the optimal perturbations that exhibit the largest transient growth of energy between the initial instant and different time horizons. At short time horizons, optimal initial perturbations are concentrated on the points of maximal strain of the base flow. The optimal gain of energy and the mechanism of instability are well predicted by local theories that describe the lagrangian evolution of a perturbation wave packet. At time of order unity, hyperbolic region leads the dynamics. Only at large time (t ? 20), the growth is led by the most amplified eigenmode. This eigenmode evolves, when the wavenumber increases, from perturbation centred in the core of the vortices, to perturbations localised on the stretching manifold of the hyperbolic points. At finite and large time, the gain in energy is initially associated with a mechanism reminiscent to the anti lift-up mechanism described by Antkowiak and Brancher [J. Fluid Mech. 578, 295 (2007)] in the context of an axisymmetric vortex. Presently, the optimal initial condition (the adjoint modes at large time) corresponding to streamwise streaks localised on the contracting manifold of the hyperbolic point induces streamwise vortices aligned with the stretching manifold of the hyperbolic point (the direct modes). The localisation on distinct manifolds of direct and adjoint eigenmodes is more pronounced when the Reynolds number is increased. An interpretation is proposed based on a balance between diffusion and stretching effects that predicts the thickness of the energy containing region for the adjoint and the direct mode decreasing as 1/?Re. The extra gain of energy due to non normal effects grows, since direct and adjoint modes are localised in different regions of space, i.e., the stretching and contracting manifold, a novel effect of the so called convective non normality associated with the transport of the perturbation by the base flow. © 2011 American Institute of Physics

    Necessary and sufficient stability conditions for integral delay systems

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    A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at initial conditions depending on the fundamental matrix we are able to present necessary and sufficient stability conditions expressed exclusively in terms of the delay Lyapunov matrix for integral delay systems. Some examples illustrate and validate the stability conditions.Comment: This paper has been submitted to International Journal of Robust and Nonlinear Contro

    Spatial Holmboe instability

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    International audienceIn mixing-layers between two parallel streams of different densities, shear and gravity effects interplay; buoyancy acts as a restoring force and the Kelvin-Helmholtz mode is known to be stabilized by the stratification. If the density interface is sharp enough, two new instability modes, known as Holmboe modes, appear, propagating in opposite directions. This mechanism has been studied in the temporal instability framework. The present paper analyzes the associated spatial instability problem. It considers, in the Boussinesq approximation, two immiscible inviscid fluids with a piecewise linear broken-line velocity profile. We show how the classical scenario for transition between absolute and convective instability should be modified due to the presence of propagating waves. In the convective region, the spatial theory is relevant and the slowest propagating wave is shown to be the most spatially amplified, as suggested by intuition. Predictions of spatial linear theory are compared with mixing-layer [C.G. Koop and F.K. Browand, J. Fluid Mech. 93, 135 (1979)] and exchange flow [G. Pawlak and L. Armi, J. Fluid Mech. 376, 1 (1999)] experiments. The physical mechanism for Holmboe mode destabilization is analyzed via an asymptotic expansion that predicts the absolute instability domain at large Richardson number. © 2002 American Institute of Physics

    Three-dimensional instabilities and optimal perturbations of a counter-rotating vortex pair in stratified flows

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    International audienceThis paper investigates the three-dimensional instabilities and the optimal perturbations on a pair of horizontal counter-rotating Lamb-Oseen vortices in a vertically stably stratified flow. Two-dimensional (2D) simulations are first performed, showing that while the dipole moves vertically against the stratification the vortex parameters: the radius a ∗, the separation distance b ∗, and the circulation Γ∗ are solely function of the time rescaled by the Brunt-Väisälä frequency N, independently of the Froude number, when the Reynolds number is large enough. Here, the Froude number is Fr = W 0/Nb 0 with W 0 the initial advection velocity of the dipole and b 0 the initial separation distance between the two vortices. For weak and moderate stratifications (large Fr), the stratification acts on a long time scale compared to the advection time of the dipole implying that the 2D flow can be considered as quasi-steady. In that case, when three dimensional instabilities are added, a linear stability analysis of this 2D flow at different instants retrieves the instability peaks corresponding to the Crow instability for the long wavelengths and to the elliptic instability for the short wavelengths showing that the dynamics is almost unaffected by buoyancy effects. The Crow and elliptic instabilities scale with the instantaneous dipole parameters showing in particular that stratification promotes instability by reducing the distance b ∗ between vortices [K. K. Nomura et al., “Short-wavelength instability and decay of a vortex pair in stratified fluid,” J. Fluid Mech. 553, 283-322 (2006)]. For strong stratifications (Froude numbers of order unity or smaller), the quasi-steady approximation is not valid, and the question of stability should be formulated in a different way, by, for example, searching for the transient growth of the energy of perturbation that may be computed for steady or unsteady base flow. Then, for each time horizon τ, we should determine the critical perturbation leading to the largest energy growth by the time τ. Presently, we compute the optimal perturbations at two time horizons τ = 4 and τ = 10 dimensionalized by with a direct-adjoint technique which takes into account the evolution of the base flow. In the homogeneous case, this technique allows to investigate the effect of the weak unsteadiness of the flow due to viscous diffusion which induces a growth of the vortex core radius a ∗. Both Crow and elliptic instabilities are retrieved in the optimal response and in the energy gain curves. Even if very slow, the viscous diffusion is found to increase the gain of the antisymmetric elliptic perturbation compared to the symmetric one. When the fluid is stratified, peaks at small wavenumber and at wavenumber of the order of the vortex core size are found for all Froude numbers with optimal responses strongly resembling, respectively, the Crow and the elliptic modes with optimal gains corresponding to mean growth rates larger than in the homogeneous case for both modes. However, as the strength of stratification increases (Froude numbers smaller than 2), optimal perturbations start departing from their homogeneous counterpart with large perturbation in the wake of the dipole associated with density effects.2πb20/Γ0© 2015 AIP Publishing LL

    Three-dimensional instabilities and transient growth of a counter-rotating vortex pair

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    International audienceThis paper investigates the three-dimensional instabilities and the transient growth of perturbations on a counter-rotating vortex pair. The two dimensional base flow is obtained by a direct numerical simulation initialized by two Lamb-Oseen vortices that quickly adjust to a flow with elliptic vortices. In the present study, the Reynolds number,ReΓ=Γ/ν, with Γ the circulation of one vortex and ν the kinematic viscosity, is taken large enough for the quasi steady assumption to be valid. Both the direct linearized Navier-Stokes equation and its adjoint are solved numerically and used to investigate transient and long time dynamics. The transient dynamics is led by different regions of the flow, depending on the optimal time considered. At very short times compared to the advection time of the dipole, the dynamics is concentrated on the points of maximal strain of the base flow, located at the periphery of the vortex core. At intermediate times, depending on the symmetry of the perturbation, one of the hyperbolic stagnation points provides the optimal amplification by stretching of the perturbation vorticity as in the classical hyperbolic instability. The growth of both short time and intermediate time transient perturbations are non- or weakly dependent of the axial wavenumber whereas the long time behavior strongly selects narrow bands of wavenumbers. We show that, for all unstable spanwise wavenumbers, the transient dynamics last until the nondimensional time t=2, during which the dipole has traveled twice the separation distance between vorticesb. During that time, all the wavenumbers exhibit a transient growth of energy by a factor of 50, for the Reynolds numberReΓ=2000. For time larger than t=2, energy starts growing at a rate given by the standard temporal stability theory. For all wavenumbers and two Reynolds numbers,ReΓ=2000 and ReΓ=105, different instability branches have been computed using a high resolution Krylov method. At large Reynolds number, the computed Crow and elliptic instability branches are in excellent agreement with the inviscid theory [S. C. Crow, AIAA J.8, 2172 (1970); S. Le Dizes and F. Laporte, J. Fluid Mech.471, 120 (2002)] and numerical analysis [D. Sipp and L. Jacquin, Phys. Fluids15, 1861 (2003)]. A novel oscillatory elliptic instability involving Kelvin waves with azimuthal wavenumbers m=0 and |m|=2, that was missed in previous numerical analysis [D. Sipp and L. Jacquin, Phys. Fluids15, 1861 (2003)] is found. For the stationary elliptic instability, we show that viscous effect may be estimated using the large Reynolds number direct and adjoint eigenmodes. This asymptotically exact estimate of the viscous damping of elliptic instability mode agrees with our direct numerical computation of instability branches at moderate Reynolds number and demonstrates that formula proposed by Le Dizes and Laporte [J. Fluid Mech.471, 120 (2002)] strongly over estimated the viscous correction

    Pyrolytic temperature evaluation of macauba biochar for uranium adsorption from aqueous solutions

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    Macauba (Acrocomia aculeata) is a palm tree native to the tropical regions of America. In Brazil, it is prevalent in the savannah, known as “cerrado”. A valuable natural and renewable source of vegetable oil for food and cosmetic industries (nut oil) and for biodiesel (mesocarp oil), macauba has the potential to become the new “green gold” of Brazil, not only for its oil quality, but because it could solely be destined for commercial purposes, since it doesn’t compete with food market industry such as soybean and sugar cane. The dark stiff part that protects the nut, called “endocarp”, is generated as a residue in a considerable amount after the processing of the nut oil. Please click on the file below for full content of the abstract

    Dynamical modes of sheared confined microscale matter

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    Based on (overdamped) Stokesian dynamics simulations and video microscopy experiments, we study the non equilibrium dynamics of a sheared colloidal cluster, which is confined to a two-dimensional disk. The experimental system is composed of a mixture of paramagnetic and non magnetic polystyrene particles, which are held in the disk by time shared optical tweezers. The paramagnetic particles are located at the center of the disk and are actuated by an external, rotating magnetic field that induces a magnetic torque. We identify two different steady states by monitoring the mean angular velocities per ring. The first one is characterized by rare slip events, where the inner rings momentarily depin from the outer ring, which is kept static by the set of optical traps. For the second state, we find a bistability of the mean angular velocities, which can be understood from the analysis of the slip events in the particle trajectories. We calculate the particle waiting- and jumping time distributions and estimate a time scale between slips, which is also reflected by a plateau in the mean squared azimuthal displacement. The dynamical transition is further reflected by the components of the stress tensor, revealing a shear-thinning behavior as well as shear stress overshoots. Finally, we briefly discuss the observed transition in the context of stochastic thermodynamics and how it may open future directions in this field

    Precise radial velocities of giant stars IX. HD 59686 Ab: a massive circumstellar planet orbiting a giant star in a ~13.6 au eccentric binary system

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    Context: For over 12 yr, we have carried out a precise radial velocity survey of a sample of 373 G and K giant stars using the Hamilton \'Echelle Spectrograph at Lick Observatory. There are, among others, a number of multiple planetary systems in our sample as well as several planetary candidates in stellar binaries. Aims: We aim at detecting and characterizing substellar+stellar companions to the giant star HD 59686 A (HR 2877, HIP 36616). Methods: We obtained high precision radial velocity (RV) measurements of the star HD 59686 A. By fitting a Keplerian model to the periodic changes in the RVs, we can assess the nature of companions in the system. In order to discriminate between RV variations due to non-radial pulsation or stellar spots we used infrared RVs taken with the CRIRES spectrograph at the Very Large Telescope. Additionally, to further characterize the system, we obtain high-resolution images with LMIRCam at the Large Binocular Telescope. Results: We report the likely discovery of a giant planet with a mass of mp sini=6.920.24+0.18 MJupm_{p}~\sin i=6.92_{-0.24}^{+0.18}~M_{Jup} orbiting at ap=1.08600.0007+0.0006a_{p}=1.0860_{-0.0007}^{+0.0006} au from the giant star HD 59686 A. Besides the planetary signal, we discover an eccentric (eB=0.7290.003+0.004e_{B}=0.729_{-0.003}^{+0.004}) binary companion with a mass of mB sini=0.52960.0008+0.0011 MSunm_{B}~\sin i=0.5296_{-0.0008}^{+0.0011}~M_{Sun} orbiting at a semi-major axis of just aB=13.560.14+0.18a_{B}=13.56_{-0.14}^{+0.18} au. Conclusions: The existence of the planet HD 59686 Ab in a tight eccentric binary system severely challenges standard giant planet formation theories and requires substantial improvements to such theories in tight binaries. Otherwise, alternative planet formation scenarios such as second generation planets or dynamical interactions in an early phase of the system's lifetime should be seriously considered in order to better understand the origin of this enigmatic planet.Comment: 14 pages, 11 figures, 2 tables. Accepted for publication in A&A. Updated version to match the published pape
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