Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures

The effect of the shallowness on meandering jets in a shallow rectangular reservoir is
investigated. Four meandering flows were investigated in an experimental shallow
rectangular reservoir. Their boundary conditions were chosen to cover a large range of
friction numbers (defined with the sudden expansion width). Due to the unsteady
characteristics of the flows, a Proper Orthogonal Decomposition of the fluctu-ating part
of the surface velocity fields measured using LSPIV was used for discriminating the
flow struc-tures responsible for the meandering of the jet. Less than 1 % of the
calculated POD modes significantly contribute to the meandering of the jet and two
types of instability are in competition in such a flow con-figuration. The sinuous mode is
the dominant mode in the flow and it induces the meandering of the flow, while the
varicose mode is a source of local mixing and weakly participates to the flow. The
fluctuating velocity fields were then reconstructed using the POD modes corresponding
to 80% of the total mean fluctuating kinetic energy and the coherent structures were
identified using the residual vorticity, their centres being localised using a topology
algorithm. The trajectories of the structures centres emphasize that at high friction
number the coherent structures are small and laterally paired in the near, middle and
far fields of the jet, while with decreasing friction number the structures merge into
large horizontal vortices in the far-field of the jet, their trajectories showing more
variability in space and time. The analysis of the stability regime finally reveals that the
sinuous mode is convectively unstable and may become absolutely unstable at the end
of the reservoir when the friction number is small.