Fig. 1

Variable types of hyperpycnal flows. a Single-layer hyperpycnal flow, Yellow River, China. Color concentration = Suspended sediment concentration; h = Flow thickness; τt = Upper surface; τb = Bed shear stress. From Gao et al. (2015); b Double-layer hyperpycnal flow with density and velocity stratification (i.e., debris flow with hydroplaning, red arrow added in this article, see Mohrig et al. 1998), Yellow River, China. Uw = Wave orbital velocity; Uc = Along shelf current magnitude; Ug = Velocity of gravity current; NWIW = Normal wind-induced wave velocity; TIW = Typhoon-induced wave. The red line represents the downslope variation trend of the bottom-turbid layer. From Gao et al. (2015) with additional labels; c Multi-layer hyperpycnal flow in numerical modeling (Morales de Luna et al. 2017). Note that multi-layer numerical modeling was also applied to hypopycnal flows. h = Height of a fluid layer; u = Velocity; ɸ = Particle concentration; ρ = Density. See Morales de Luna et al. (2017) for details of various parameters and related equations; d Tide-modulated hyperpycnal flow, Yellow River (Wang et al. 2010; modified after Wright et al. 1988). Color labels by G. Shanmugam. Note internal waves. Internal waves occur only along pycnoclines (Shanmugam 2014a, 2014b), but there is no indication of pycnoclines in this diagram. From Shanmugam (2018a)