Minimal-energy perturbations rapidly approaching the edge state in Couette flow
Article dans une revue avec comité de lecture
Transition to turbulence in shear flows is often subcritical, thus the dynamics of the flow strongly depends on the shape and amplitude of the perturbation of the laminar state. In the state space, initial perturbations which directly relaminarize are separated from those that go through a chaotic trajectory by a hypersurface having a very small number of unstable dimensions, known as the edge of chaos. Even for the simple case of plane Couette flow in a small domain, the edge of chaos is characterized by a fractal, folded structure. Thus, the problem of determining the threshold energy to trigger subcritical transition consists in finding the states on this complex hypersurface with minimal distance (in the energy norm) from the laminar state. In this work we have investigated the minimal-energy regions of the edge of chaos, by developing a minimization method looking for the minimal-energy perturbations capable of approaching the edge state (within a prescribed tolerance) in a finite target time T. For sufficiently small target times, the value of the minimal energy has been found to vary with T following a power law, whose best fit is given by E T-1.75. For large values of T, the minimal energy achieves a constant value which corresponds to the energy of the minimal seed, namely the perturbation of minimal energy asymptotically approaching the edge state (Rabin etÂ al., J. Fluid Mech., vol. 738, 2012, R1). For T\geqslant 40, all of the symmetries of the edge state are broken and the minimal perturbation appears to be localized in space with a basic structure composed of scattered patches of streamwise velocity with inclined streamwise vortices on their flanks. Finally, we have found that minimal perturbations originate in a small low-energy zone of the state space and follow very fast similar trajectories towards the edge state. Such trajectories are very different from those of linear optimal disturbances, which need much higher initial amplitudes to approach the edge state. The time evolution of these minimal perturbations represents the most efficient path to subcritical transition for Couette flow.
Showing items related by title, author, creator and subject.
Article dans une revue avec comité de lectureCHERUBINI, Stefania; DE TULLIO, Marco; DE PALMA, Pietro; PASCAZIO, Giuseppe (American Society of Mechanical Engineers, 2013)This work provides a three-dimensional energy optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of roughness elements. The immersed ...
Article dans une revue avec comité de lectureCHERUBINI, Stefania; DE TULLIO, Marco; DE PALMA, Pietro; PASCAZIO, Giuseppe (Cambridge University Press (CUP), 2013)This work provides a global optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of smooth three-dimensional roughness elements. ...
Article dans une revue avec comité de lectureFARANO, Mirko; CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro (Springer Verlag, 2017)Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded ﬂows. In this work, a nonlinear energy optimization strategy is employed ...
Article dans une revue avec comité de lectureCHERUBINI, Stefania; DE PALMA, Pietro (IOP Publishing, 2014)This paper provides an investigation of the structure of the stable manifold of the lower branch steady state for the plane Couette flow. Minimal energy perturbations to the laminar state are computed, which approach within ...
Article dans une revue avec comité de lectureFARANO, Mirko; CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro (Cambridge University Press (CUP), 2015)In this work it is shown that hairpin vortex structures can be the outcome of a nonlinear optimal growth process, in a similar way as streaky structures can be the result of a linear optimal growth mechanism. With this ...