# Decomposition of the forces on a body moving in an incompressible fluid

## TL;DR

This paper proposes a new decomposition of fluid forces on a moving body in an incompressible fluid, separating inviscid and viscous effects into physically meaningful components related to flow acceleration, convection, and pressure contributions.

## Contribution

It introduces a novel split of inviscid force components into convective and accelerative parts, clarifying their physical origins and simplifying the connection to rigid-body inertia.

## Key findings

- The convective component relates to pressure in steady inviscid flow.
- The accelerative component aligns with added-mass concepts but is simpler.
- Viscous forces include pressure contributions necessary for pressure field equations.

## Abstract

In analysing fluid forces on a moving body, a natural approach is to seek a component due to viscosity and an `inviscid' remainder. It is also attractive to decompose the velocity field into irrotational and rotational parts, and apportion the force resultants accordingly. The `irrotational' resultants can then be identified as classical `added mass', but the remaining, `rotational', resultants appear not to be consistent with the physical interpretation of the rotational velocity field (as that arising from the fluid vorticity with the body stationary). The alternative presented here splits the inviscid resultants into components that are unquestionably due to independent aspects of the problem: `convective' and `accelerative'. The former are associated with the pressure field that would arise in an inviscid flow with (instantaneously) the same velocities as the real one, and with the body's velocity parameters --- angular and translational --- unchanging. The latter correspond to the pressure generated when the body accelerates from rest in quiescent fluid with its given rates of change of angular and translational velocity. They are reminiscent of the added-mass force resultants, but are simpler, and closer to the standard rigid-body inertia formulae, than the developed expressions for added-mass force and moment. Finally, the force resultants due to viscosity also include a contribution from pressure. Its presence is necessary in order to satisfy the equations governing the pressure field, and it has previously been recognised in the context of `excess' stagnation-point pressure. However, its existence does not yet seem to be widely appreciated.