The vortex dynamics of leading-edge vortices on plunging high-aspect-ratio (AR = 10) wings and airfoils were investigated by means of volumetric velocity measurements, numerical simulations and stability analysis to understand the deformation of the leading-edge vortex filament and spanwise instabilities. The vortex filaments on both the wing and airfoil exhibit spanwise waves, but with different origins. The presence of a wing-tip causes the leg of the vortex to remain attached to the wing upper surface, while the initial deformation of the filament near the wing tip resembles a helical vortex. The essential features can be modelled as the deformation of an initially L-shaped semi-infinite vortex column. In contrast, the instability of the vortices is well captured by the instability of counter-rotating vortex pairs, which are formed either by the trailing-edge vortices or the secondary vortices rolled-up from the wing surface. The wavelengths observed in the experiments and simulations are in agreement with the stability analysis of counter-rotating vortex pairs of unequal strength.

The thrust generated by heaving airfoil in incompressible flow is studied both numerically and theoretically. It is found that the behaviors of leading-edge vortex (LEV) under different airfoil’s transverse velocities have an important influence on the thrust. When this velocity is small, the LEV is advected downstream regularly; however, as transverse velocity increases, the LEV can be pushed back to the leading edge again and pass over it to the opposite side of the airfoil. In cases with the LEV passing over the leading edge, the maximum transient thrust can be enhanced by several times compared with that in the single-stroke motion. The reason and critical condition for the occurrence of passing-over leading-edge vortex (PO-LEV) are found. Based on the source of the pressure Poisson equation, a near-field force theory is developed and used together with the boundary vorticity flux (BVF) theory to clarify the thrust enhancement mechanisms.

The propulsive performance and vortex dynamics of a two-dimensional model for the jellyfish-like propulsion with burst-and-coast strategy are investigated using a penalty-immersed boundary method. The simplified model comprises a pair of pitching flexible plates with their leading edges connected. The effects of two key parameters are considered, i.e., the duty cycle (DC, the ratio of the closing phase to the whole period) and the bending stiffness (K). Three different wake patterns, i.e., periodic symmetric, periodic asymmetric, and chaotic wakes, are identified in the DC–K plane. Numerical results indicate that a significant fast-close-slow-open motion is more likely to achieve higher speed, efficiency, and stability than a slow-close-fast-open motion, and proper higher bending stiffness is conducive to improving efficiency. A force decomposition based on the weighted integral of the second invariant of the velocity gradient tensor is performed to gain physics insight into the self-propulsive mechanism. It is found that the repulsive force induced by the strain-rate field between the body and the previous vortex pair is the main driving force of the jellyfish-like motion and that capturing the previous vortex pair during the closing phase can significantly enhance the strain rate as well as the thrust. This clarifies why the jellyfish can achieve thrust by pushing back vortex pairs. This study provides inspiration for the design and control of flexible jet propulsion devices.

The three-dimensional (3-D) transition of the leading-edge vortex (LEV) and the force characteristics of the plunging airfoil are investigated in the chord-based Strouhal number $St_c$ range of 0.10 to 1.0 by means of experimental measurements, numerical simulations and linear stability analysis in order to understand the spanwise instabilities and the effects on the force. We find that the interaction pattern of the LEV, the LEV from a previous cycle (pLEV) and the trailing-edge vortex (TEV) is the primary mechanism that affects the 3-D transition and associated force characteristics. For $St_c \leq 0.16$ , the 3-D transition is dominated by the LEV–TEV interaction. For $0.16 < St_c \leq 0.44$ , the TEV lies in the middle of the LEV and the pLEV and therefore vortex interaction between them is relatively weak; as a result, the LEV remains two-dimensional up to a relatively high Reynolds number of $Re = 4000$ at $St_c = 0.32$ . For $0.44 < St_{c} \leq 0.54$ , and at relatively low Reynolds numbers, the pLEV and the TEV tend to form a clockwise vortex pair, which is beneficial for the high lift and stability of the LEV. For $0.49 \leq St_c$ , the pLEV and TEV tend to form an anticlockwise vortex pair, which is detrimental to the lift and flow stability. In the last $St_c$ range, vortex interaction involving the LEV, the TEV and the pLEV results in an unstable period-doubling mode which has a wavelength of about two chord-lengths and the 3-D transition enhances the lift.

The hydrodynamics of a two-dimensional self-propelled flexible plate in a uniform shear flow is explored using a penalty-immersed boundary method. The leading edge of the plate is enforced into a prescribed harmonic oscillation in the vertical direction but free to move in the horizontal direction. It is found that as the shear rate increases, the input power, the propulsive velocity, and the efficiency increase. This finding means that the plate enables to get substantial hydrodynamic benefits from the shear flow. Using the force decomposition method based on the weighted integral of the second invariant of the velocity gradient tensor, the hydrodynamic force exerted on the plate is decomposed into a body-acceleration force, a vortex-induced force, and forces due to viscous effects. The results show that the body-acceleration force is the main driving force of the self-propelled motion, and that it is almost invariant with the shear rate. The vortex-induced force offers a significant contribution to the drag, and it decreases with the shear rate. The viscous friction force provides a pure drag, and it increases with the propulsion velocity. Further investigation on the vortex evolution and the vortex-induced force shows that the incoming shear flow destroys the trailing-edge vortex that sheds during the downward half period and, therefore, reduces the vortex-induced drag, which is the reason for the enhanced propulsive performance in the shear flow. The result obtained in this study provides new insight into the self-propulsion mechanism in complex incoming flows.

This numerical study focuses on the coherent structures and bypass transition mechanism of the Stokes boundary layer in the intermittently turbulent regime. In particular, the initial disturbance is produced by a temporary roughness element that is removed immediately after triggering a two-dimensional vortex tube under an inflection-point instability. The present study reveals a complete scenario of self-induced motion of a vortex tube after rollup from the boundary layer. The trajectory of the vortex tube is reasonably described based on the Helmholtz point-vortex equation. The three-dimensional transition of the vortex tube is attributed to the Crow instability, which leads to a sinusoidal disturbance that eventually evolves into a ring-like structure, especially for the weaker vortex. Further investigation demonstrates that three-dimensional or quasi-three-dimensional vortex perturbations in the free stream play a critical role in the boundary layer transition through a bypass mechanism, which is featured by the non-modal and explosive transient growth of the subsequent boundary layer instabilities. This transition scenario is found to be analogous to the oblique transition in the steady boundary layer, both of which are characterised by the formation of streaks, rollup of hairpin-like vortices and burst into turbulent spots. In addition, the streamwise propagation of turbulent spots is discussed in detail. To shed more light on the nature of the intermittently turbulent Stokes boundary layer, a conceptual model is proposed for the periodically self-sustaining mechanism of the turbulent spots based on the present numerical results and experimental evidence reported in the literature.