Temporally quasi-periodic data, propagating in the laboratory frame, can be rendered periodic by Galilean transformation

Velocity, temperature, pressure, or concentration data are usually acquired in the laboratory frame, but when a preferred direction exists (e.g., due to mean flow), the question arises as to whether one can gain additional insight or simplify data analysis, by considering the data in a different reference frame. For a broad class of velocity, temperature, pressure, or concentration distributions propagating rectilinearly, we show that temporally quasi-periodic behavior in the laboratory frame can be rendered periodic by appropriate Galilean transformation. The approach is illustrated analytically and numerically using as an example a closed-form model distribution generated from a one-dimensional partial differential equation describing a pressure-driven diffusion process. A detailed procedure is developed to determine appropriate frame speeds for more general quasi-periodic, one-dimensional data, either continuous in space and time, or temporally- and spatially-discretized. The approach is extended to two- and three-dimensional rectilinear (and some nonrectilinear) propagation, and implications for interpreting noise-corrupted data are also discussed.