Nonlinear Inertia Forces on Bodies

The theoretical influence of convective acceleration terms on the inertia force on a body is considered. The assumptions involved in using the inertia force are reviewed and an expression is derived for the inertia force acting on a body subjected to an unsteady and nonuniform flow of an inviscid fluid. Applications to a submerged sphere and to horizontal and vertical circular cylinders in waves are considered and differences between alternative predictions of the nonlinear inertia forces are compared. It is reassuring to find that the predicted forces are generally less than those calculated when convective acceleration terms are neglected.