## 1 Introduction
Varying the swing arm length and amplitude, as well as pitching amplitude, reduced frequency and flexure amplitude, the authors found considerable efficiency gains for a flexible hydrofoil as compared to the rigid one. Note that hydrodynamics of an elastic wing propulsor was first investigated by [PERSON] and [PERSON] [18]. [PERSON] et al. [19] explored possibilities of efficient power extraction with proper tuning of a tandem oscillating foil system. Notably, one of the first studies of thrust generating tandem of oscillating wings was carried out by [PERSON] [20]. [PERSON] and [PERSON] [21] numerically examined aerodynamic behavior of a heaving inverted airfoil in ground effect as function of reduced frequency and mean clearance. The authors attempted to categorize different modes of the flow by the magnitude of the lag of the aerodynamic coefficients with respect to the vertical motion. In the following paper on aerodynamics of inverted airfoils, [PERSON], [PERSON] and [PERSON] [22] considered both pure pitching and combined pitching-heaving motion, and found that pure pitching increases separation on the suction side and results in a larger hysteresis. For combined oscillations, when the character of interactions is determined by the phase shift between them, the pitch mode was found to control the flow at small frequencies with heave mode prevailing at high frequencies. [PERSON] and [PERSON] [23] emphasized the significance of accounting for the dynamic heaving motion in aerodynamics of multi-element wings, which is supposed to improve correlation of the results between computational fluid dynamics, wind tunnel and track testing in race cars applications. The comparisons with static wing data furnishes evidence that dynamic motion of the race car wing can be beneficial in terms of performance. The authors investigated the relationship between time-dependent aerodynamic forces, the vortex shedding and unsteady pressure fields using 2D URANS approach and overset mesh method for modelling of the two-element moving wing. It was also revealed that addition of the flap considerably changes the frequency of the shed vortices in the wake and maintains the generation of the downforce for longer time in ground proximity. [PERSON] et al. [24] presented experimental and computational results for an airfoil pitching close to a solid boundary, and demonstrated that as the mean distance of the foil from the ground decreases the time-averaged thrust monotonically increases whereas the propulsive efficiency stays almost constant. The paper also singles out two distinct regimes: (1) the foil being pulled downward when mean position of the pitching foil is between 0.4 and 1.0 chord lengths from the ground plane and (2) the foil is pushed from the ground for relative clearances in the range of 0.25-0.4 chord lengths. [PERSON] et al. [25] considered the scaling laws for thrust generation and power expenditure of a purely pitching hydrofoil in ground effect for a range of biologically relevant Strouhal numbers. The authors claim to have introduced physics-driven modifications to the added mass and circulatory forces versus ground clearance variation. Aiming to understand the role of the unsteady ground effect in control strategies of near-boundary fish and fish inspired robots, [PERSON] et al. [26]presented experimental and computational results for a foil pitching around its leading edge near a flat wall. Examined were the cases when the foil is constrained in space and when it is unconstrained (or freely swimming) in cross-stream direction. The paper by [PERSON] et al. [27] studied the effects of non-sinusoidal heaving and pitching trajectories of the flapping foil with use of a commercial Star CCM+ solver based on the finite volume method.