  Waves patterns in the Faraday instability have been studied for decades.
Besides the rich dynamics that can be observed on the waves at the interface,
Faraday waves hide beneath them an elusive range of flow patterns --or
streaming patterns-- which have not been studied in detail until now. The
streaming patterns are responsible for a net circulation in the flow which are
reminiscent of convection cells. In this article, we analyse these streaming
flows by conducting experiments in a Faraday-wave setup. To visualize the
flows, tracers are used to generate both trajectory maps and to probe the
streaming velocity field via Particle Image Velocimetry (PIV). We identify
three types of patterns and experimentally show that identical Faraday waves
can mask streaming patterns that are qualitatively very different. Next we
propose a three-dimensional model that explains streaming flows in
quasi-inviscid fluids. We show that the streaming inside the fluid arises from
a complex coupling between the bulk and the boundary layers. This coupling can
be taken into account by applying modified boundary conditions in a
three-dimensional Navier-Stokes formulation for the streaming in the bulk.
Numerical simulations based on this theoretical framework show good qualitative
and quantitative agreement with experimental results. They also highlight the
relevance of three-dimensional effects in the streaming patterns. Our
simulations reveal that the variety of experimental patterns is deeply linked
to the boundary condition at the top interface, which may be strongly affected
by the presence of contaminants along the surface.

Fluid Dynamics