Experimental and numerical analysis of flow instabilities in rectangular shallow basins

Free surface flows in several shallow rectangular basins have been analyzed
experimentally, numerically and theoretically. Different geometries, characterized by different
widths and lengths, are considered as well as different hydraulic conditions. First, the
results of a series of experimental tests are briefly depicted. They reveal that, under clearly
identified hydraulic and geometrical conditions, the flow pattern is found to become nonsymmetric,
in spite of the symmetrical inflow conditions, outflow conditions and geometry of
the basin. This non-symmetric motion results from the growth of small disturbances actually
present in the experimental initial and boundary conditions. Second, numerical simulations
are conducted based on a depth-averaged approach and a finite volume scheme. The simulation
results reproduce the global pattern of the flow observed experimentally and succeed in
predicting the stability or instability of a symmetric flow pattern for all tested configurations.
Finally, an analytical study provides mathematical insights into the conditions under which
the symmetric flow pattern becomes unstable and clarifies the governing physical processes.