Hydrodynamic interaction between bodies in a perfect incompressible fluid and their motion in nonuniform streams: PMM vol. 37, n≗4, 1973, pp. 680–689

Abstract

A general method based on the use of Lagrangian equations for determining hydrodynamic interaction between bodies in a fluid is presented. Formulas for the kinetic energy and the Lagrangian function are reduced to a form which permits an effective application of the method of small parameter. Additive components of kinetic energy and of the Lagrangian function, which determine the hydrodynamic interaction between two bodies, one of which is small in comparison with the distance between the two, are calculated. The method is used for considering the case of several bodies. The results are expressed in terms of coefficients of apparent mass of individual bodies in a boundless fluid. General formulas are derived for forces and moments acting on a body in a nonuniform stream. The feasibility of expressing hydrodynamic reactions on a body in a nonuniform stream in terms of apparent mass coefficients has not been, so far, established. Solutions were sought for bodies of particular form, while in the three-dimensional case no solution was found even for a small sphere. The description of a solid body in a perfect incompressible fluid by Lagrangian equations was first given in [1]. The forces and moments acting on such body moving in a boundless fluid were determined in [2]. The most rigorous proof of equations of motion of a solid body in a boundless fluid appears in [3]. The problem of a body in an arbitrary stream of fluid was apparently first formulated by Zhukovskii [4]. The motion of a body in a uniform accelerated stream was investigated in [5]. Formulas for forces and moments acting on a stationary elliptical cylinder in an arbitrary plane potential flow were derived in [6], while in [7] the force acting on an expanding circular cylinder moving in an arbitrary stream with constant vorticity was calculated. As survey of publications on the hydrodynamic interaction between bodies in a fluid appears in [8].