Author(s): Shooka Karimpour Ghannadi; Vincent H. Chu
Linked Author(s): Vincent H. Chu
Keywords: Shear instabilities; Open-channel flow; Flux limiting; Numerical simulations; Grid refinement
Abstract: Direct numerical simulations (DNS) of the traverse shear instabilities in open-channel flow are conducted using the shallow-water equations for the convective Froude numbers of Frc = 0. 01, 0. 1 and 0. 8. The simulations determine the evolution of a small disturbance with time in the transverse shear flow for a range of wave number. It also produces the nonlinear development that leads to the formation of eddies at the low convective Froude numbers of Frc= 0. 01 and the shocklets at the higher convective Froude number of Frc = 0. 8. The exchanges across the shocklets are characterized by the radiation of gravity wave and reduced rate of the shear instabilities. Five different flux limiting schemes are employed for the DNS. Four stages of the grid refinement determine the order of convergence toward the true solution for each of the computational schemes. The results for the initial exponential growth are in agreement with the linear stability analysis using the normal mode approach. The gravity-wave radiation from the open channel flow has the similar effect on the shear instabilities as the radiation of the sound from the shear flow in compressible gas. The dependence on the convective Froude number for the transverse shear flow in open channel is shown to be analogous to the shear instability in compressible gas and is consistent with the shear instability calculation results obtained for the ideal gas by Sandham & Reynolds (1990).
Year: 2013