A numerical study of temporal shallow mixing layers using BGK-based schemes

Shallow mixing layers between non-parallel streams in a flat-bed wide channel

“…Especially for environmental fluid mechanics and geo-physical applications, where the ML develops in between a no-slip boundary and the free surface, there is interest in studying the development of the ML and of the exchange of momentum and mass between the two converging flows at large distances from the ML origin where the dynamics of the eddies generated inside the upstream part of the ML via the Kelvin–Helmholtz (KH) instability (Lesieur et al. 1988; Liu, Lam & Ghidaoui 2010; Lam, Ghidaoui & Kolyshkin 2016) is strongly affected by bed friction. In such applications, the domain width and length in which the ML develops are typically much larger than the average flow depth (e.g.…”

Near- and far-field structure of shallow mixing layers between parallel streams

“…In most cases of practical relevance for environmental and geo-physical applications, the ML develops over very large streamwise distances compared to the average flow depth, such that the ML width, δ, becomes much larger than the flow depth, H. Once this happens, bottom friction has an important effect on the dynamics of the quasi two-dimensional (2-D) coherent structures inside the ML. These eddies start as billows generated via the Kelvin-Helmholtz (KH) instability by the mean horizontal shear between the two streams (Corcos & Sherman 1984;Lesieur et al 1988;Liu, Lam & Ghidaoui 2010;Lam, Ghidaoui & Kolyshkin 2016). The growth in the size of these quasi 2-D eddies and their subsequent loss of coherence strongly influences the spatial development and structure of the ML at large distances from its origin.…”

“…These eddies start as billows generated via the Kelvin–Helmholtz (KH) instability by the mean horizontal shear between the two streams (Corcos & Sherman 1984; Lesieur et al . 1988; Liu, Lam & Ghidaoui 2010; Lam, Ghidaoui & Kolyshkin 2016). The growth in the size of these quasi 2-D eddies and their subsequent loss of coherence strongly influences the spatial development and structure of the ML at large distances from its origin.…”

Mixing layer and turbulent jet flow in a Hele--Shaw cell

“…For model I (k = 0) it follows from the first equation in (19) that v 0 = (u 0 +w 0 )/2 and from the second equation in (19) the value of q 2 0 is determined. For model II (k = 1) relations ( 19) are reduced to the quadratic equation for determining r = v 0 /u 0…”

“…Mathematical models of the plane mixing layer development based on the averaged equations of the shallow water theory were presented and verified in [2,21]. The characteristic features of the development of mixing layers in shallow water at various flow parameters were numerically studied in [19,12]. Theoretical and experimental study of quasi-two-dimensional processes of turbulent mixing in flows between rigid walls also attracts the attention of researchers.…”