The preferred mode of incompressible jets: linear frequency response analysis

Abstract

International audienceThe linear amplification of axisymmetric external forcing in incompressible jet flows is investigated within a fully non-parallel framework. Experimental and numerical studies have shown that isothermal jets preferably amplify external perturbations for Strouhal numbers in the range 0.25 ≤ StD ≤ 0.5, depending on the operating conditions. In the present study, the optimal forcing of an incompressible jet is computed as a function of the excitation frequency. This analysis characterizes the preferred amplification as a pseudo-resonance with a dominant Strouhal number of around 0.45. The flow response at this frequency takes the form of a vortical wavepacket that peaks inside the potential core. Its global structure is characterized by the cooperation of local shear-layer and jet-column modes

Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

“…for inlet forcing on Γ in (Garnaud et al 2013). We write formally (2.2) as u vol = R vol (ω)f vol and (2.3) as u in = R in (ω)f in , where in both cases R(ω) is the resolvent operator.…”

“…those specific structures associated with maximal transient growth or harmonic gain. Extensive literature exists about the calculation of transient growth (Butler & Farrell 1992;Corbett & Bottaro 2000;Blackburn et al 2008) and harmonic gain (Åkervik et al 2008;Alizard et al 2009;Garnaud et al 2013;Sipp & Marquet 2013;Dergham et al 2013).…”

Open-loop control of a separated boundary layer

“…In this study, optimal gains are computed using the same procedure as Garnaud et al [8]. The linear dynamical system (4) is spatially discretized (with the same mesh and same elements as for base flow calculation), and G 2 opt (ω) is recast as the leading eigenvalue of an Hermitian eigenvalue problem, solved with an implicitly restarted Arnoldi method.…”

“…For example, non-normality leads to large transient growth in parallel shear flows through the twodimensional (2D) Orr mechanism and, more importantly, the three-dimensional (3D) lift-up effect [3]; in non-parallel flows, large transient growth is observed because of convective nonnormality [4]. Today, transient growth is a well-established notion, and most attempts to control convectively unstable flows naturally focus on reducing the largest possible transient growth, or "optimal growth" [5], but recently optimal response to harmonic forcing, or "optimal gain", has drawn increasing attention too [6,7,8]. Brandt et al [9] introduced a method to quantify the sensitivity of the largest asymptotic amplification to steady control, and applied it to a flat plate boundary layer.…”

Saturation of the response to stochastic forcing in two-dimensional backward-facing step flow: A self-consistent approximation

“…Optimal forcing/response structures have been assessed in plane Couette [13] as well as in spatially developing open flows [8,10,11,14] and particularly in the backward-facing step [15][16][17][18][19]. A slightly different approach is undertaken by Garnaud, Lesshaftt, Schmid, and Huerre [14] where, in an attempt to describe more precisely the actual physics involved in the strong noise amplification exhibited in turbulent jets, they apply the optimal gain analysis on a model mean flow instead of the stable steady solution of the Navier-Stokes equations (NSEs) as in the previously mentioned studies. In general, both time and frequency approaches describe the most energetic instability mechanisms at play.…”