Gaining and understanding flow dynamics have much importance in a wide range of disciplines, e.g., astrophysics, geophysics, biology, mechanical engineering, and biomedical engineering. For turbulent flows, local flow information such as velocity and its statistics, can be measured experimentally. Due to the poor fidelity or experimental limitations, some information may not be resolved in a region of interest. On the other hand, detailed flow features are described by the governing equations, e.g., the Navier–Stokes equations for viscous fluid, and can be resolved numerically, which is heavily dependent on the capability of either computing resources or modeling. Alternatively, we address this problem by employing the physics-informed deep learning and treat the governing equations as a parameterized constraint to recover the missing flow dynamics. We demonstrate that with limited data, no matter from experiment or others, the flow dynamics in the region where the required data are missing or not measured, can be reconstructed with the parameterized governing equations. Meanwhile, a richer dataset, with spatial distribution of the control parameter (e.g., eddy viscosity of turbulence modelings), can be obtained. The method provided in this paper may shed light on the data-driven scale-adaptive turbulent structure recovering and understanding of complex fluid physics and can be extended to other parameterized governing systems beyond fluid mechanics.

The active synchronous deformation in the arc length of an airfoil employed in a flapping wing can improve its energy extraction efficiency. The present study seeks to understand the underlying physics of this energy extraction by conducting transient numerical simulations of a novel arc-deformable flapping foil design based on dynamic mesh technology and a relative heaving motion reference system. The influence of the flapping frequency and the pitching amplitude on the energy extraction efficiency of the flapping foil modeled under a constant arc length is investigated. The effects of the deformation magnitude β and the position of the deformation center on the energy extraction efficiency are also examined at a constant flapping frequency and pitching amplitude. The results show that active synchronous arc deformation can greatly improve the energy extraction efficiency of a flapping foil compared to the efficiency of a conventional non-deformable flapping foil design. In addition, the results provide sets of optimal flapping frequencies and pitching amplitudes for the deformable flapping foil design with fixed deformation parameters and the non-deformable foil design that obtains the highest energy extraction efficiencies. A single high efficiency zone is obtained for the deformable foil design at a relatively high flapping frequency. In contrast, relatively high efficiency zones are obtained for the non-deformable foil design at both a relatively low flapping frequency and a high flapping frequency. The energy extraction efficiency of the deformable flapping foil first increases with increasing β up to a maximum value of β = 0.25 and then decreases with a further increase in β. The energy extraction efficiency of the deformable flapping foil is also demonstrated to increase as the deformation center moves from the leading edge of the foil to the trailing edge, attaining a maximum value when the deformation center coincides with the center of the pitching axis, and then decreases.

A global stability analysis is performed for the flip-flopping wake pattern behind two side-by-side cylinders with emphasis on the unstable vorticity field. The combination of direct numerical simulation with the state-of-art lattice Boltzmann method and dynamic mode decomposition is used to analyse such wake pattern for the first time. The vorticity mode of the secondary instability is extracted from the flow. Such mode is found to be symmetrical with respect to the geometric axis of symmetry. Furthermore, a new scenario is found for the high order harmonics that there is a pair of two tertiary modes as a result of nonlinear interaction between the mode related to the secondary instability and the global mode of the in-phase synchronized vortex shedding base flow. Besides, the reason for the Fourier spectra of the lift on the two cylinders being the same is also illustrated for this case.