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13. Savchenko YuN, Semenenko VN, Serebryakov VV. Experimental verification of asymptotic formulas for axisymmetric cavities at s ! 0 (in Russian). Problems in high speed hydrodynamics. Cheboksary: Chuvash University; 1993. p. 225–30. 14. Savchenko YuN, Vlasenko YuD, Semenenko VN. Experimental investigations of high-speed cavity flows (in Russian). Gidromekhanika. 1998;72:103–11. 15. Vlasenko YuD. Experimental investigations of high-speed unsteady supercavitating flows. Proceedingsof the Third International Symposium on Cavitation.

The numerical model in these works is based on the two dimensional linear theory of cavity flow behind wedge under solid horizontal flat wall. The calculation results are compared with experiment which was obtained in a hydrodynamic channel for a cavity under a flat plate with side discs. The description of Butuzov’s method can be found in books [13, 14]. Later this method was also used by K. Matveev, see, for example, [15]. Butuzov has spread his idea of solution method for the problem with a cavity under wall to the modeling cavity on planing surface behind step [11, 12].

The general approach to the study of system of planing surfaces is presented in work [17]. The present work consists of two logical parts united by common mathematical theory. The theory is based on reduction of original problem for velocity potential with linear boundary conditions to the singular integral equations. In the first part the two dimensional theory of the planing hull with a cavity behind a step under the bottom is presented. The examples of numerical results that show the model possibilities are given.