Spectral and particle dispersion properties of steady two-dimensional multiscale flows

Abstract

The spectral and particle dispersion characteristics of steady multiscale laminar thin-layer flows are investigated through numerical simulations of a two-dimensional layer-averaged model. The model assumes a semiparabolic velocity profile and is solved using a semi-Lagrangian spline method. The main features of the flows are turbulentlike and consistent with previous experimental studies. The Eulerian wavenumber spectra and the Lagrangian frequency spectra oscillate around power laws that reflect the self-similarity of the forcing. In the weak forcing regime, the exponents of these power laws can be related to the multiscale geometry and the intensity scaling of the forcing. The Lagrangian spectra also show low-frequency plateaus, which arise from the slow motions far away from the applied forces. The absolute dispersion of tracer particles in these steady planar flows presents a ballistic stage followed by a diffusive regime, which results from the decorrelated motions of particles lying on streamlines of different periods. Relative dispersion shows an additional intermediate stage consisting of several separation bursts, which originate from the intense strain regions imposed by the different forcing scales. While these bursts can cause locally superquadratic mean square separation, the trapping by steady recirculation regions rules out an intermediate relative dispersion power law regardless of the number of scales in the flow.