Modeling the Motion of an Elongated Contour under Free Surface of a Heavy Fluid under Large Froude Numbers

The flow around an elongated smooth contour under the free surface of a fluid is considered. The fluid is perfect, incompressible, and heavy. The critical flow branching and flow shedding points are located on the contour. The depth of the contour immersion and its length are given. It is assumed that the velocity magnitude on the free surface is close to its value in the undisturbed flow. A nonlinear approximation of the Bernoulli integral on the free surface associated with logarithm is used. Two auxiliary planes in which the flow domain is a half-plane with an excluded circle and an annular region are used. The complex potential is determined in the first parametric plane using a conformal mapping onto the annular region. A system of equations is derived for finding the defining parameters. This system is solved using the minimization of a functional and an iteration method over two sets of parameters. An algorithm and computer program for solving this system are developed. The hydrodynamic characteristics of a specific hydrofoil are computed. Results for the coefficients of wave drag, lift force, moment, and position of the contour center are analyzed depending on the Froude number and circulation of different signs. Examples of computations of nonlinear waves formed on the free surface at significant Froude numbers are given.