Due to the high Reynolds numbers many important inverse problems of high-speed hydromechanics (in particular, supercavitating flows, [1]) can be solved with the use of the ideal fluid approach. The axisymmetric shapes of elongated cavities or bodies with the prescribed pressure distribution were calculated with the use of asymptotical series for flow potential and exact solutions of Euler equations, [2]. To avoid separation of the boundary layer and reduce the drag, axisymmetric and 2D shapes with negative pressure gradients on their surfaces were calculated, [2]. On some bodies, the absence of separation was confirmed by experiments in the wind tunnels [2, 3]. Special attention was paid to the axisymmetric shapes similar to the bodies of aquatic animals [4-6]. It was shown that shapes with sharp concave noses (similar to the rostrum of the fastest fish) have no stagnation points and corresponding pressure and temperature peaks [4]. These special shaped bodies moving near the water surface cause much lower vertical velocities on its surface [5] and can have a low wave resistance. These facts open prospects of using corresponding hulls for underwater and floating vehicles [6]. In supersonic flows, they can reduce overheating of the noses [4].

1. I. Nesteruk, ed. Supercavitation. Advances and Perspectives, Springer, 2012. DOI: 10.1007/978-3-642-23656-3

2. I. Nesteruk Rigid Bodies without Boundary-Layer Separation// International Journal of Fluid Mechanics Research, Vol. 41, No. 3, 2014, pp. 260-281. DOI: 10.1615/InterJFluidMechRes.v41.i3.50

3. I. Nesteruk, M. Brühl, Th. Möller. Testing a special shaped body of revolution similar to dolphins trunk, KPI Science News, No. 2, 2018, pp.44-53. https://doi.org/10.20535/1810-0546.2018.2.129140

4. I. Nesteruk. Fastest fish shapes and optimal supercavitating and supersonic bodies of revolution. Innov Biosyst Bioeng, 2020, vol. 4, no. 4, 169–178. doi: 10.20535/ibb.2020.4.4.215578 5. I Nesteruk. Shapes of the fastest fish and optimal underwater and floating hulls. Theoretical and Applied Mechanics Letters, September 2022, DOI: 10.1016/j.taml.2022.100378

6. Nesteruk, I.; Krile, S.; Möller, T. Improved Low-Drag Pontoons for Water Bikes. J. Mar. Sci. Eng. 2023, 11, 1754. https://doi.org/10.3390/jmse11091754