This study focuses on numerically investigating the impact of fluid viscoelasticity on the flow dynamics around a transversely forced oscillating cylinder operating in the laminar vortex shedding regime at a fixed Reynolds number of $Re = 100$. Specifically, we explore how fluid viscoelasticity affects the boundary between the lock-in and no lock-in regions and the corresponding wake characteristics compared with a simple Newtonian fluid. Our findings reveal that fluid viscoelasticity enables the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than those required for a Newtonian fluid. Consequently, the lock-in region boundary for a viscoelastic fluid differs from that of a Newtonian fluid and expands in the non-dimensional cylinder oscillation amplitude and frequency parameter space. In the primary synchronization region, the wake of a Newtonian fluid exhibits ‘2S’ (two single vortices) and ‘P+S’ (a pair of vortices and a single vortex) shedding modes. In contrast, a ‘2P’ (two pairs of vortices) vortex mode is observed for a viscoelastic fluid within the same region. To gain a deeper understanding of the differences in the coherent flow structures and their associated frequencies between the two fluids, we employ the data-driven reduced-order modelling technique, known as the dynamic mode decomposition (DMD) technique. Utilizing this technique, we successfully extract and visualize the two competing fundamental frequencies (cylinder oscillation and natural vortex shedding frequencies) and their associated flow structures in the case of the no lock-in state, whereas only the dominant cylinder oscillation frequency and associated flow structure in the case of the lock-in state. Furthermore, we propose that the presence of excess strain resulting from the stretching of polymer molecules in viscoelastic fluids leads to a distinct difference in the wake structure compared with Newtonian fluids. This observation aligns with the findings obtained from the $Q$-criterion and vorticity transport analysis of the wake.

Quasistatic magnetoconvection of a fluid with low Prandtl number (${\textit {Pr}}=0.025$) with a vertical magnetic field is considered in a unit-aspect-ratio box with no-slip boundaries. At high relative magnetic field strengths, given by the Hartmann number ${\textit {Ha}}$, the onset of convection is known to result from a sidewall instability giving rise to the wall-mode regime. Here, we carry out three-dimensional direct numerical simulations of unprecedented length to map out the parameter space at ${\textit {Ha}} = 200, 500, 1000$, varying the Rayleigh number (${\textit {Ra}}$) over the range $6\times 10^5 \lesssim {\textit {Ra}} \lesssim 5\times 10^8$. We track the development of stable equilibria produced by this primary instability, identifying bifurcations leading to limit cycles and eventually to chaotic dynamics. At ${\textit {Ha}}=200$, the steady wall-mode solution undergoes a symmetry-breaking bifurcation producing a state that features a coexistence between wall modes and a large-scale roll in the centre of the domain, which persists to higher ${\textit {Ra}}$. However, under a stronger magnetic field at ${\textit {Ha}}=1000$, the steady wall-mode solution undergoes a Hopf bifurcation producing a limit cycle which further develops to solutions that shadow an orbit homoclinic to a saddle point. Upon a further increase in ${\textit {Ra}}$, the system undergoes a subsequent symmetry break producing a coexistence between wall modes and a large-scale roll, although the large-scale roll exists only for a small range of ${\textit {Ra}}$, and chaotic dynamics primarily arise from a mixture of chaotic wall-mode dynamics and arrays of cellular structures.

We demonstrate that gravity acting alone at large length scales (compared to the capillary length) can produce a jet from a sufficiently steep, axisymmetric surface deformation imposed on a quiescent, deep pool of liquid. Mechanistically, the jet owes it origin to the focusing of a concentric, surface wave towards the axis of symmetry, quite analogous to such focusing of capillary waves and resultant jet formation observed during bubble collapse at small scales. A weakly nonlinear theory based on the method of multiple scales in the potential flow limit is presented for a modal (single-mode) initial condition representing the solution to the primary Cauchy–Poisson problem. A pair of novel, coupled, amplitude equations are derived governing the modulation of the primary mode. For moderate values of the perturbation parameter $\epsilon$ (a measure of the initial perturbation steepness), our second-order theory captures the overshoot (incipient jet) at the axis of symmetry quite well, demonstrating good agreement with numerical simulation of the incompressible, Euler equation with gravity (Popinet 2014, Basilisk. http://basilisk.fr) and no surface tension. We demonstrate that the underlying wave focusing mechanism may be understood in terms of radially inward motion of nodal points of a linearised, axisymmetric, standing wave. This explanation rationalises the ubiquitous observation of such jets accompanying cavity collapse phenomena, spanning length scales from microns to several metres. Expectedly, our theory becomes inaccurate as $\epsilon$ approaches unity. In this strongly nonlinear regime, slender jets form with surface accelerations exceeding gravity by more than an order of magnitude. In this inertial regime, we compare the jets in our simulations with the inertial, self-similar, analytical solution by Longuet-Higgins (J. Fluid Mech., 1983, vol. 127, pp. 103–121) and find qualitative agreement with the same. This analysis demonstrates, from first principles, an example of a jet created purely under gravity from a smooth initial perturbation and provides support to the analytical model of Longuet-Higgins (J. Fluid Mech., 1983, vol. 127, pp. 103–121).

In this study, the effects of antagonistic muscle actuation on the propulsion of a bilaminar-structure fish fin ray were investigated using a two-dimensional computational flow–structure interaction (FSI) model. The structure and material properties of the model were based on the realistic biological data of the sunfish fin. The effect of muscle actuation was modelled using root displacement offset between the two hemitrichs. Parametric FSI simulations were conducted by assuming a sinusoidal function of the offset over a cycle and varying the amplitude and phase difference between the actuations and pitching/plunging motions. The results show that the phase of muscle actuation is a critical factor affecting its effects. Three performance regions can be identified with different phase ranges, including a thrust-favour region, an efficiency-favour region and a thrust-efficiency-unfavour region. In each region, the relationships among the root actuations, fin-ray kinematics, vortex dynamics and resulting performance are studied and discussed. Furthermore, a strong positive correlation between the trailing–leading amplitude ratio and thrust coefficient as well as a negative relationship between the efficiency and angle of attack at the centre of mass of the fin ray are observed.

We investigate the effects of fluid elasticity on the flow forces and the wake structure when a rigid cylinder is placed in a viscoelastic flow and is forced to oscillate sinusoidally in the transverse direction. We consider a two-dimensional, uniform, incompressible flow of viscoelastic fluid at $Re=100$, and use the FENE-P model to represent the viscoelastic fluid. We study how the flow forces and the wake patterns change as the amplitude of oscillations, $A^*$, the frequency of oscillations (inversely proportional to a reduced velocity, $U^*$), the Weissenberg number, $Wi$, the square of maximum polymer extensibility, $L^2$, and the viscosity ratio, $\beta$, change individually. We calculate the lift coefficient in phase with cylinder velocity to determine the range of different system parameters where self-excited oscillations might occur if the cylinder is allowed to oscillate freely. We also study the effect of fluid elasticity on the added mass coefficient as these parameters change. The maximum elastic stress of the fluid occurs in between the vortices that are observed in the wake. We observe a new mode of shedding in the wake of the cylinder: in addition to the primary vortices that are also observed in the Newtonian flows, secondary vortices that are caused entirely by the viscoelasticity of the fluid are observed in between the primary vortices. We also show that, for a constant $Wi$, the strength of the polymeric stresses increases with increasing reduced velocity or with decreasing amplitude of oscillations.

Insights gained from modal analysis are invoked for predictive large-eddy simulation (LES) wall modelling. Specifically, we augment the law of the wall (LoW) by an additional mode based on a one-dimensional proper orthogonal decomposition (POD) applied to a two-dimensional turbulent channel. The constructed wall model contains two modes, i.e. the LoW-based mode and the POD-based mode, and the model matches with the LES at two, instead of one, off-wall locations. To show that the proposed model captures non-equilibrium effects, we perform a priori and a posteriori tests in the context of both equilibrium and non-equilibrium flows. The a priori tests show that the proposed wall model captures extreme wall-shear stress events better than the equilibrium wall model. The model also captures non-equilibrium effects due to adverse pressure gradients. The a posteriori tests show that the wall model captures the rapid decrease and the initial decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients, respectively, both of which are missed by currently available wall models. These results show promise in applying modal analysis for turbulence wall modelling. In particular, the results show that employing multiple modes helps in the modelling of non-equilibrium flows.