Large-scale flow structures and stability in shallow flows

Shallow turbulent flows occurring in wide rivers, estuaries, lakes or coastal regions, as well as the atmosphere, are readily susceptible to transverse disturbances that lead to two-dimensional coherent structures. The shallow jet, the shallow wake, and the shallow mixing layer are examples of such flow patterns. A linear stability analysis incorporating the effects of bottom friction and viscosity is applied to these flows to determine the criteria for absolute and convective instability and for stabilization of the flow. All three flow types exhibit instabilities within the range of natural flows. Three mechanisms for large-scale instability generation, namely topographic forcing, transverse velocity shear, and secondary instabilities of the base flow, are compared to the stability calculations. Based on the results, topographic forcing, and to a lesser extent, transverse shear are expected to have both absolute and convective instabilities; whereas, secondary instabilities of the base flow are expected to generate primarily convective instabilities. The resulting large-scale coherent structures greatly influence the mixing and transport of pollutants and momentum that are released into such flows. Key words: shallow flow, shallow jet, shallow wake, shallow mixing layer, linear stability analysis, bottom friction, Chebyshev polynomial method.