| Summary: | The extraordinary complexity of turbulence has motivated the study of some of its key features in flows with similar structure but simpler or even trivial dynamics. Recently, a novel class of such flows has been developed in the laboratory by applying multiscale electromagnetic forcing to a thin layer of conducting fluid. In spite of being stationary, planar, and laminar these flows have been shown to resemble turbulent ones in terms of energy spectra and particle dispersion. In this thesis, some extensions of these flows are investigated through simulations of a layer-averaged model carried out using a bespoke semi-Lagrangian spline code. The selected forcings generalise the experimental ones by allowing for various kinds of self-similarity and planetary motion of the multiple scales. The spatiotemporal structure of the forcings is largely reflected on the flows, since they mainly arise from a linear balance between forcing and bottom friction. The exponents of the approximate power laws found in the wavenumber spectra can thus be related to the scaling and geometrical forcing parameters. The Eulerian frequency spectra of the unsteady flows exhibit similar power laws originating from the sweeping of the multiple flow scales by the forcing motions. The disparity between fluid and sweeping velocities makes it possible to justify likewise the observed Lagrangian power laws, but precludes a proper analogy with turbulence. In the steady case, the absolute dispersion of tracer particles presents ballistic and diffusive stages, while relative dispersion shows a superquadratic intermediate stage dominated by separation bursts due to the various scales. In the unsteady case, the absence of trapping by fixed streamlines leads to appreciable enhancement of relative dispersion at low and moderate rotation frequency. However, the periodic reversals of the large scale give rise to subdiffusive absolute dispersion and severely impede relative dispersion at high frequency.
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