Shallow mixing layers are flows formed at the confluence of two parallel streams with different velocities in fluid domains having horizontal dimensions far greater than the water depth. Shallow mixing layers are omnipresent in natural and man-made hydraulic systems, e.g. longshore currents, compound and composite channels and the interface region between a groyne field and the main river reach. One striking feature of shallow mixing layers is the presence of large-scale two dimensional coherent structures (2DCS). 2DCS are vortices with vorticity aligned with the gravitational axis and are largely two-dimensional, having horizontal dimensions greatly exceeding the water depth. 2DCS have a decisive role in mass and momentum transport in hydraulic systems, so the understanding of...[ Read more ]

Shallow mixing layers are flows formed at the confluence of two parallel streams with different velocities in fluid domains having horizontal dimensions far greater than the water depth. Shallow mixing layers are omnipresent in natural and man-made hydraulic systems, e.g. longshore currents, compound and composite channels and the interface region between a groyne field and the main river reach. One striking feature of shallow mixing layers is the presence of large-scale two dimensional coherent structures (2DCS). 2DCS are vortices with vorticity aligned with the gravitational axis and are largely two-dimensional, having horizontal dimensions greatly exceeding the water depth. 2DCS have a decisive role in mass and momentum transport in hydraulic systems, so the understanding of 2DCS is important for the prediction of flows and pollutant transport in hydraulic systems. The life of 2DCS involves birth, growth with downstream distance followed by decay and eventually full disappearance. The birth and growth of 2DCS are believed to involve flow instabilities. The current work seeks to map the appropriate stability theory to the appropriate stage of development of 2DCS. To this end, shallow water equation-based numerical simulations and stability analyses are performed. The birth of 2DCS is shown to be the result of linear stability theory and the nonlinear mean-field theory. The growth of 2DCS in shallow mixing layers after their birth is shown to be due to the secondary instability of the 2DCS, which causes separate 2DCS to merge, resulting in larger 2DCS. The physical picture suggests that the roll-up and merging of 2DCS in shallow mixing layers are nonlinear, but the previous success of linear theory with local parallel assumption gives an illusion that the entire birth, growth and decay process of 2DCS is linear. Results also show that the merging of 2DCS in shallow mixing layers are sensitive to the phase angle difference between the most unstable mode of the velocity profile at the upstream and its subharmonic mode. Such sensitivity implies that the phase angles of instability modes are important to the modelling of 2DCS in shallow mixing layers.