Using clusters of instantaneous vortices to quantify secondary circulation sub-cells in open channel bends with and without a submerged transverse jet

Large eddy simulations of an open channel bend with and without a submerged transverse jet upstream of the bend are conducted. Sub-cells of secondary circulation are identified using clusters of instantaneous vortices, which allows for better resolution of sub-cell development than can be achieved with mean flow alone. The method allows us to pinpoint the development location of sub-cells to positions at the outer bank, which can be understood using conceptual models of vorticity production based on flow acceleration at wall boundaries. The sub-cell circulation quantification allows for interactions between developing sub-cells and established circulation cells to become clear. This is demonstrated through the interaction of developing sub-cells and jet vortices, by introducing a transverse jet from the outer bank wall upstream of the channel bend. The presence of the jet counter-rotating vortex pair at the beginning of the bend redistributes the bend secondary circulation between sub-cells but does not change the total amount of secondary circulation. The principle of using clusters of instantaneous vortices to track developing cells and their interactions with already-established cells has many further applications, from studying secondary circulation development in channels with previous bends to identifying locations where circulation first develops in bends with bathymetry.