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
