Eulerian-Lagrangian aspects of a steady multiscale laminar flow

One key feature for the understanding and control of turbulent flows is the relation between Eulerian and Lagrangian statistics. This Brief Communication investigates such a relation for a laminar quasi-two-dimensional multiscale flow generated by a multiscale (fractal) forcing, which reproduces some aspects of turbulent flows in the laboratory, e.g., broadband power-law energy spectrum and Richardson’s diffusion. We show that these multiscale flows abide with Corrsin’s estimation of the Lagrangian integral time scale, TL, as proportional to the Eulerian (integral) time scale, LE∕urms, even though Corrsin’s approach was originally constructed for high Reynolds number turbulence. We check and explain why this relation is verified in our flows. The Lagrangian energy spectrum, Φ(w), presents a plateau at low frequencies followed by a power-law energy spectrum Φ(w)∼w−α at higher ones, similarly to turbulent flows. Furthermore, Φ(ω) scales with LE and urms with α>1. These are the key elements to obtain such a ...