Abstract:
The use of second- and third-order classical piston theory (CPT) is commonplace, with the
role of the higher-order terms being well understood. The advantages of local piston theory
(LPT) relative to CPT have been demonstrated previously. Typically, LPT has been used to
perturb a mean-steady solution obtained from the Euler equations, and recently, from the NavierStokes
equations. The applications of LPT in the literature have been limited to first-order
LPT. The reasoning behind this has been that the dynamic linearization used assumes small
perturbations. The present note clarifies the role of higher-order terms in LPT. It is shown that
second-order LPT makes a non-zero contribution to the normal-force prediction, in contrast to
second-order CPT
