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We investigate the effect of three-dimensionality on the synchronisation characteristics of the wake behind an oscillating circular cylinder at$${\textit {Re}} = 300$$. Cylinder oscillations in rotation, transverse translation and streamwise translation are considered. We utilise phase-reduction analysis, which quantifies the phase-sensitivity function of periodic flows, to examine the synchronisation properties. Here, we present an ensemble-based framework for phase-reduction analysis to handle three-dimensional wakes that are not perfectly time-periodic. Based on the phase-sensitivity functions, synchronisability to three types of cylinder oscillations is evaluated. In spite of similar trends, we find that phase-sensitivity functions involving three-dimensional wakes are lower in magnitude compared with those of two-dimensional wakes, which leads to narrower conditions for synchronisation to weak cylinder oscillations. We unveil that the difference between the phase-sensitivity functions of two- and three-dimensional flows is strongly correlated to the amplitude variation of the three-dimensional flow by the cylinder motions. This finding reveals that the cylinder motion modifies the three-dimensionality of the wake as well as the phase of vortex shedding, which leads to reduced phase modulation. The synchronisation conditions of three-dimensional wakes, predicted by phase-reduction analysis, agree with the identification by parametric studies using direct numerical simulations for forced oscillations with small amplitudes. This study presents the potential capability of phase-reduction to study synchronisation characteristics of complex flows. 

We obtain an optimal actuation waveform for fast synchronization of periodic airfoil wakes through the phase reduction approach. Using the phase reduction approach for periodic wake flows, the spatial sensitivity fields with respect to the phase of the vortex shedding are obtained. The phase sensitivity fields can uncover the synchronization properties in the presence of periodic actuation. This study seeks a periodic actuation waveform using phase-based analysis to minimize the time for synchronization to modify the wake shedding frequency of NACA0012 airfoil wakes. This fast synchronization waveform is obtained theoretically from the phase sensitivity function by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. Actuation based on the obtained waveform achieves rapid synchronization within as low as two vortex shedding cycles irrespective of the forcing frequency, whereas traditional sinusoidal actuation requires$${O}(10)$$shedding cycles. Further, we analyse the influence of actuation frequency on the vortex shedding and the aerodynamic coefficients using force-element analysis. The present analysis provides an efficient way to modify the vortex lock-on properties in a transient manner with applications to fluid–structure interactions and unsteady flow control. 

Network theory is used to formulate an atomistic material network. Spectral sparsification is applied to the network as a method for approximating the interatomic forces. Local molecu- lar forces and the total force balance is quantified when the inter- nal forces are approximated. In particular, we compare spectral sparsification to conventional thresholding (radial cut-off dis- tance) of molecular forces for a Lennard–Jones potential and a Coulomb potential. The spectral sparsification for the Lennard– Jones potential yields comparable results while spectral sparsi- fication of the Coulomb potential outperforms the thresholding approach. The results show promising opportunities which may accelerate molecular simulations containing long-range electri- cal interactions which are relevant to many multifunctional ma- terials. 

We numerically examine the use of Gurney flap to modify the two-dimensional wake dynamics for lift enhancement on NACA 0000 (flat plate), 0006, 0012 and 0018 airfoils. Incompressible flows over the airfoils at different angles of attack are considered at Re = 1000. It is observed that the attachment of the Gurney flap at the trailing edge is able to enhance the lift force experienced by the airfoil appreciably with increase in Gurney flap height. The lift-to-drag ratio of the airfoils is also observed to increase at lower angles of attack. The lift spectra and airfoil wake are examined to reveal the effect of the Gurney flap on the formation of different characteristic wake modes and the associated change in the aerodynamic forces exerted on the airfoils. Based on the observations, we classify the resulting wakes into four distinct modes. The emergence of these modes (steady, 2S, P and 2P) are mapped over a wide range of angles of attack and Gurney flap heights for all four airfoils in consideration.