Histeretical behaviour of two-dimensional vortex shedding past the NACA0012 airfoil at ultra-low Reynolds number

We unfold the complex transition route from steady to chaotic dynamics of the two-dimensional flow past the NACA0012 airfoil upon increasing the angle of attack a at the ultra-low Reynolds number Re = 5300. Hopf, forward and backward period-doubling cascades, Neimark-Sacker and saddlenode bifurcations are found along the way, the latter producing hysteretical regions where two distinct two-dimensional vortex-shedding modes coexist. Although the advent of three-dimensionality obliterates the two-dimensional path here addressed and deteriorates aerodynamic performances shortly after the advent of time-dependence at the first Hopf bifurcation, active flow control might assist in postponing the disruption of spanwise invariance to some extent, thus partially recovering the two-dimensional scenario.Peer ReviewedPostprint (published version

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.Peer ReviewedPostprint (published version

Symmetry-breaking waves and space-time modulation mechanisms in two-dimensional plane Poiseuille flow

We investigate two distinct scenarios of spatial modulation that are candidate mechanisms for streamwise localization of waves in two-dimensional plane Poiseuille flow. The first one stems from a symmetry-breaking bifurcation that disrupts the half-shift and reflect equivariance of Tollmien-Schlichting waves (TSW). A new state, an asymmetric TSW (ATSW), emerges from unstable lower-branch TSWs at subcritical Reynolds number and undergoes subharmonic Hopf bifurcations that lead to branches of asymmetric time-periodic space-modulated waves (MATSW). Streamwise modulation does not evolve into localization within the range of parameters explored. In breaking the last standing remnants of the reflectional symmetry about the channel midplane, ATSW and MATSW admit a bias toward either one of the channel walls, thus bearing a potential for explaining near-wall structures that are typical of developed turbulence. The second scenario follows the fate of a branch of time-periodic space-modulated TSWs (MTSW) initially discovered by Mellibovsky and Meseguer [J. Fluid Mech. 779, R1 (2015)]. We find that these waves can lead to localization but the mechanism is not new, as they do so through their connection, by means of a codimension-2 bifurcation point, with other known localizing MTSWs. The codimension-2 point is, however, responsible for the appearance of MTSWs that exclusively bridge upper-branch TSW-trains of different number of replicas. In this respect, these MTSWs possess all required properties that single them out as possible constituents of the strange saddle that governs domain-filling turbulent dynamics at high Reynolds numbers.Postprint (author's final draft

El problema de Reynolds: transició subcrítica a la turbulència

Fa 125 anys, Osborne Reynolds, matemàtic i professor d’enginyeria de la Universitat de Manchester, va publicar el seu treball experimental i teòric sobre la transició a la turbulència de fluids en moviment dins de canonades. Els experiments publicats per Reynolds van plantejar moltes qüestions i van introduir nous conceptes com ara el nombre de Reynolds adimensional, la criticitat i la intermitència turbulenta. L’article de Reynolds va suposar un gran salt a la comprensió del fenomen de transició de fluids en moviment. Després d’aquests 125 anys, encara es desconeixen els mecanismes físics responsables de la transició a la turbulència a l’interior d’una canonada. La simplicitat del problema contrasta notablement amb l’enorme dificultat que suposa entendre’n la dinàmica, desafiant físics, matemàtics i enginyers del segle passat i del present. Algunes de les qëstions més fonamentals han començat a veure la llum fa quatre o cinc anys, gràcies a la col.laboració de grups de recerca britànics, alemanys i catalans.Postprint (published version

Fold-pitchfork bifurcation for maps with Z(2) symmetry in pipe flow

This study aims to provide a better understanding of recently identified transition scenarios exhibited by traveling wave solutions in pipe flow. This particular family of solutions are invariant under certain reflectional symmetry transformations and they emerge from saddle-node bifurcations within a two-dimensional parameter space characterized by the length of the pipe and the Reynolds number. The present work precisely provides a detailed analysis of a codimension-two saddle-node bifurcation arising in discrete dynamical systems (maps) with Z2 symmetry. Normal form standard techniques are applied in order to obtain the reduced map up to cubic order. All possible bifurcation scenarios exhibited by this normal form are analyzed in detail. Finally, a qualitative comparison of these scenarios with the ones observed in the aforementioned hydrodynamic problem is provided.Postprint (published version

Transition to periodic behaviour of flow past a circular cylinder under the action of fluidic actuation in the transitional regime

This study focuses on the numerical investigation of the underlying mechanism of transition from chaotic to periodic dynamics of circular cylinder wake under the action of time-dependent fluidic actuation at the Reynolds number = 2000. The forcing is realized by blowing and suction from the slits located at ±90° on the top and bottom surfaces of the cylinder. The inverse period-doubling cascade is the underlying physical mechanism underpinning the wake transition from mild chaos to perfectly periodic dynamics in the spanwise-independent, time-dependent forcing at twice the natural vortex-shedding frequency.This work has been financed by the Spanish and Catalan Governments under grants FIS2016-77849-R and 2017-SGR-00785, respectively. The authors also thankfully acknowledge the computer resources at MareNostrum and Calendula accessed through grants RES-FI-2017-2-0020 and RES-FI-2017-3-0009, respectivelyPostprint (published version

A mechanism for streamwise localisation of nonlinear waves in shear flows

We present the complete unfolding of streamwise localisation in a paradigm of extended shear flows, namely two-dimensional plane Poiseuille flow. Exact solutions of the Navier-Stokes equations are computed numerically and tracked in the streamwise wavenumber-Reynolds number parameter space to identify and describe the fundamental mechanism behind streamwise localisation, a ubiquitous feature of shear flow turbulence. Unlike shear flow spanwise localisation, streamwise localisation does not follow the snaking mechanism demonstrated for plane Couette flow.Peer ReviewedPostprint (author's final draft

Edge state in pipe flow experiments

Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border.Postprint (published version

Large eddy simulation of optimal synthetic jet actuation on a SD7003 airfoil in post-stall conditions

Aerodynamic performances may be optimised by the appropriate tuning of Active Flow Control (AFC) parameters. For the first time, we couple Genetic Algorithms (GA) with an unsteady Reynolds-Averaged Navier-Stokes (RANS) solver using the Spalart-Allmaras (SA) turbulence model to maximise lift and aerodynamic efficiency of an airfoil in stall conditions [1], and then validate the resulting set of optimal Synthetic Jet Actuator (SJA) parameters against well-resolved three-dimensional Large Eddy Simulation (LES). The airfoil considered is the SD7003, at the Reynolds number and the post-stall angle of attack . We find that, although SA-RANS is not quite as accurate as LES, it can still predict macroscopic aggregates such as lift and drag coefficients, provided the free-stream turbulence is prescribed to reasonable values. The sensitivity to free-stream turbulence is found to be particularly critical for SJA cases. Baseline LES simulation agrees well with literature results, while RANS-SA would seem to remain a valid model to a certain degree. For optimally actuated cases, our LES simulation predicts far better performances than obtained by suboptimal SJA LES computations as reported by other authors [2] for the same airfoil, Re and a, which illustrates the applicability and effectiveness of the SJA optimisation technique applied, despite using the less accurate yet computationally faster SA-RANS. The flow topology and wake dynamics of baseline and SJA cases are thoroughly compared to elucidate the mechanism whereby aerodynamic performances are enhancedThis work was supported by the Spanish Government under grants FIS2016-77849-R and PID2020-114043GB-I00 and by the Catalan Government under grant 2017-SGR-00785. Computations were performed in the Red Española de Supercomputación (RES), Spanish supercomputer network, under the grants IM-2019-3-0002 and IM-2020-1-0001. F. M. is a Serra-Húnter fellowPostprint (published version

Otterboard hydrodynamic performance testing in flume tank and wind tunnel facilities

© 2017 Elsevier LtdTwo pelagic otterboards, previously tested in a wind tunnel, have been tested in a flume tank prior to their analysis in real working conditions in sea trials. This intermediate step aims at providing guidance for sea trial planning and a basis for otter board performance analysis from real campaign data. The doors were rigged in working-like conditions in the flume tank, with onboard-mounted attitude sensors to provide at the same time a noisy environment as expected in sea trials and accurate measurement of all quantities relevant to precise determination of hydrodynamic angles and forces. The trends found in flume tank experiments closely match wind tunnel results, although systematic offset has been observed that can be ascribed to deviations between nominal and real water velocity, due to inhomogeneous velocity distribution in the cross-section.Peer ReviewedPostprint (author's final draft