THESIS
2015
xiv, 159 pages : illustrations (some color) ; 30 cm
Abstract
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...[
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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.
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