Bridging the gap
12.1 Non-linear versus linear – or both
This Chapter pursues the search for a realistic gas process model to supersede the arbitrary driving function resorted to in pulse-tube studies to date. The obvious analytical tool is wave mechanics – linear (LWA) or non-linear (MoC). The former takes multiple wave reflections in its stride, but is compromised by temperature gradient. The latter has no problem with temperature gradient but becomes unwieldy when more than a handful of reflection sites are involved.
The ideal would be a hybrid scheme combining the strengths of both. This Chapter takes a first step in that direction: the defining equations of LWA are explored for characteristic directions, allowing solution to proceed graphically as for the MoC. The process promises to be a formality, the characteristic directions ± c being a foregone conclusion. A minor revelation will nevertheless emerge to justify going through the motions.
Starting from the opposite end of the divide, the MoC may be modified so as to follow the characteristic directions (dx/dtI, II = ± c) inherent in LWA. The feature whereby LWA deals with unlimited wave reflections is analytical, and cannot be embodied into the workings of the MoC as traditionally implemented.
Sufficient common ground between LWA and the MoC is identified to raise the hope that some competent intellect will eventually bridge the gap completely.
Chapter 10 has already introduced LWA – but on the basis of a perfunctory ...