Shallow turbulent mixing layers in open-channel flows

A mixing layer (ML) forms when two streams of different speeds or densities merge. MLs are ubiquitous in nature and can be often observed in the atmosphere, ocean, rivers, canals, lakes and reservoirs. This review paper focuses on the turbulent MLs developing in open-channel flows when the vertical size of the ML is smaller than its streamwise and spanwise dimensions. Such MLs are referred to as shallow MLs (SMLs). The SMLs often involve large-scale features such as quasi-two-dimensional coherent structures with a bed-normal axis, streamwise-oriented vortices, secondary currents, gravity currents, and bed-induced turbulent structures such as large- and very-large-scale motions. Considering various types of SMLs, we distinguish SMLs driven by (i) spanwise inhomogeneity of hydrodynamic parameters, (ii) lateral changes in flow resistance, and (iii) spanwise heterogeneity in fluid density. As SMLs and associated flow structures largely control transverse exchanges of various substances (e.g., sediments, pollutants, nutrients) and heat, the mixing of substances and thermal mixing are also addressed. Then, commonalities and differences among the various types of SMLs are identified. The paper is concluded with suggestions on future research efforts for advancing the knowledge on SMLs and capabilities for their predictions and control.