## 1 Introduction
[10] published a review on fluid dynamics of flapping foils, providing a summary of both experimental and numerical investigations of flapping foils which comprises effects of relevant parameters, such as Reynolds and Strouhal number, amplitudes of oscillations, three-dimensionality, wake structures and energy harvesting efficiency. Based on statistics of publishing activity in the field, the review states that starting from 2000, the number of papers on flapping foils shows an unprecedented growth. Widely discussed in recent years is a possibility to use flapping wings for ship propulsion and wave energy extraction which is exemplified by the above-mentioned wave gliders (WG)--a two module marine robots converting wave induced motions of the upper displacement hull into thrust of winged lower module resulting in forward motion of the vehicle. Quite a number of studies have been dedicated to elastic foils which can help to considerably increase both thrust and propulsion efficiency of flapping foils. It was also discussed that the efficient use of flapping foils implies optimal superposition of heaving and pitching oscillations of the same frequency albeit shifted in phase. The authors conclude that prevailing are the studies of two-dimensional flapping wing flows whereas 3D case is not yet sufficiently covered. Also underlined are prospects of using multiple foils for thrust generation and power extraction. [PERSON] and [PERSON] [11] developed a mathematical model of a ship with energy-saving wings fixed on the ship in the plane of the keel at the extremities. The equations of ship motions comprise coupled heaving and pitching motions, and take into account the inertial and damping effects of the wings. The resulting motions of the wings then allow to calculate additional thrust due to the action of waves. Based on the results obtained both for regular and irregular waves the authors state that use of the wings leads to a noticeable moderation of ship motions, a decrease in the additional wave resistance and, eventually, to a reduction in the energy efficiency design index (EEDI), i.e., lowering of carbon dioxide emissions. The subject of using flapping wings for ship propulsion was also studied by [PERSON] and [PERSON] [12] and [PERSON] and [PERSON] [13]. [PERSON] et al. [14] analyzed pressure distributions on a flapping wing near a wall with account of the influence of the time-averaged ground clearance, Reynolds number, effective angle of attack and oscillation frequency upon power extraction efficiency. They underlined that the impact of the ground wall on the power extraction efficiency of the foil becomes increasingly obvious when the oscillation frequency and the angle of attack are increased simultaneously. Numerical and experimental investigation of flapping wing propulsion in ground effect was undertaken in [PERSON], [PERSON], [PERSON] and [PERSON], [15]. Flying in ground effect was shown to have substantial performance advantages in thrust and efficiency. The authors used bi-plane configuration and employed high-aspect ratio experimental model with direct measurement of thrust. Numerically they used 2D unsteady inviscid flow model with deforming wake and 2D incompressible Navier-Stokes solver. [PERSON], [PERSON] and [PERSON] [16] noted that flapping wing devices have attracted considerable attention as a new means of power extraction. Applying transient numerical calculations based on the dynamic mesh technique, the authors explored the influence of the leading edge, trailing edge and that of overall circular arc airfoil deformations on the power extraction capability under condition of the constant arc length of the foil camber line, concluding that deformations can improve the power extraction efficiency of the flapping wing devices. [PERSON] et al. [17] studied power extraction of a flexible hydrofoil in swing arm mode.