On the crest factor and its relevance in detecting turbulent behaviour in solutions of partial differential equations

In this work we investigate the connection between two fundamental features of solutions of partial differential equations (PDEs), namely the crest factor and the length scale associated to each solution. We illustrate how the crest factor of solutions of some linear and non-linear PDEs, including the incompressible two-dimensional Navier-Stokes equations, has the capability for detecting turbulent and non-turbulent behaviour.