Energy of acceleration of a perfect unbounded fluid surrounding an arbitrary moving rigid body

Abstract

This paper introduces the Gibbs–Appell formalism into fluids. It devises the energy of acceleration of a perfect fluid surrounding a moving impermeable rigid body and the hydrodynamic forces acting on the body. The fluid is considered infinite, and the rigid body may have any closed tridimensional form. Therefore, the velocity field is non-divergent and irrotational; the density field is homogeneous in space and non-dependent on time, and all viscous effects are neglected. Under these assumptions, an explicit formulation for the hydrodynamic forces acting on the body is known as a-priori, and it is recovered in this text following an approach based on generalized quasi-velocities and the Gibss–Appell formalism, that may handle a vaster class of mechanical problems in comparison to Newtonian mechanics, especially non-holonomic constrained systems. The devised formulation is applied to the two-dimensional case study of a disc in unsteady rectilinear motion: the analytical form for the generalized hydrodynamic forces acting on the disc is evaluated, as well as the explicit formulae for the hydrodynamic coefficients of the body and the total energy of acceleration of the surrounding fluid.