The coherent structures and wake dynamics of a two-degree-of-freedom vibrating cylinder with a low mass ratio at Re=5300 are investigated by means of proper orthogonal decomposition (POD) of a numerical database generated using large-eddy simulations. Two different reduced velocities of U*=3.0 and U*=5.5, which correspond with the initial and super-upper branches, are considered. This is the first time that this kind of analysis is performed in this kind of system in order to understand the role of large coherent motions on the amplification of the forces. In both branches of response, almost 1000 non-correlated in-time velocity fields have been decomposed using the snapshot method. It is seen that a large number of modes is required to represent 95% of the turbulent kinetic energy of the flow, but the first two modes contain a large percentage of the energy as they represent the wake large-scale vortex tubes. The energy dispersion of the high-order modes is attributed to the cylinder movement in the inline and cross-stream directions. Substantially different POD modes have been found in the two branches. While the first six modes resemble those observed in the static cylinder or in the initial branch of a one-degree of freedom cylinder in the initial branch, the modes not only contain information about the wake vortexes in the super-upper branch but also about the formation of the 2T vortex pattern and the Taylor–Görtler structures. It is shown that the 2T vortex pattern is formed by the interplay between the Taylor–Görtler stream-wise vortical structures and the cylinder movement and is responsible for the increase in the lift force and larger elongation in the super-upper branch.

A direct numerical simulation of a three dimensional diffuser at Reynoldsnumber Re = 10, 000 (based on inlet bulk velocity) has been per-formed using a low-dissipation finite element code. The geometry chosenfor this work is the Stanford diffuser, introduced by Cherry et al.(Int.J. Heat Fluid Fl. 29, 2008, pp. 803-811). Results have been exhaus-tively compared with the published data with a quite good agreement.A proper orthogonal decomposition and a dynamic mode decompositionanalysis of the main flow variables have been performed to identify themain characteristics of the large-scale motions. A combined motion of thelarge-scales has been found to originate in the top-right expansion cornerwith two clear features. A low-frequency diagonal cross-stream beatingfeature first reported by Malm et al. (J. Fluid Mech. 699, 2012, pp.320-351), has been clearly identified in the spatial modes of the stream-wise velocity components and the pressure, associated with the narrowband frequency of St ∈ [0.083, 0.01]. This feature has been found tobe more compacted near the expansion corner and elongates inside the diffuser section. A second low-frequency feature has been identified asso-ciated with the secondary flows and acting as a back and forth globalaccelerating-decelerating motion on the diffuser. The frequencies associ-ated to this motion are of St < 0.005, while the smallest observed inthis work has been St = 0.0013. This low-frequency motion observedin the Stanford diffuser point out the need for longer simulations.