On The Role of Higher-Order Terms in Local Piston Theory

The use of second- and third-order classical piston theory [1] (CPT) is commonplace, with the role of the higher-order terms being well understood [2]. The advantages of local piston theory (LPT) relative to CPT have been demonstrated previously [3]. Typically, LPT has been used to perturb a mean-steady solution obtained from the Euler equations, and recently, from the Navier-Stokes equations [4]. The applications of LPT in the literature have been limited to first-order LPT [5–7]. 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.