ABSTRACT
ABSTRACT: Large scale coherent structures are prominent in free surface flows including estuaries, oceans, lakes and rivers. The structures are in the form of vortices with vertical axis which extend from the bed to the water surface and possess diameters that are far larger than the water depth. Understanding of such coherent structures is important for the mixing and transport of mass (e.g., pollutants and sediments), momentum and energy in surface water flows. The life of the structures involves birth, growth with downstream distance for part of the flow domain followed by decay and ultimately full disappearance. The mechanisms leading to birth and growth are believed to involve flow instabilities which, because of the near twodimensionality of the flow, evolve under the constraint of enstrophy and energy cascade. The energy and enstrophy constraint – a result of the suppression of vortex stretching due to the vertical confinement by the bed and free surface – promotes growth via vortex merging. On the other hand, the bottom friction, which represents the effect of the background three-dimensional turbulence on the large scale quasi-two dimensional turbulence, suppresses the large scale instabilities, limits their growth and causes them to eventually disappear with distance downstream. In this paper, the role of linear, weakly nonlinear and nonlinear hydrodynamic stability theories in illuminating the mechanisms of formation, growth and then decay of large scale structures in free shear flows is explained. For illustration purpose, the shallow mixing layer is used.
