LINEAR STABILITY ANALYSIS OF UPPER-REGIME BED WAVES INCLUDING THE EFFECT OF DENSITY STRATIFICATION

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Abstract

 Linear stability analysis (LSA) is performed in order to investigate the bed stability of open channel flow. The bed is assumed to be covered with sediment. The governing equations are the Reynolds averaged Navier Stokes equation (RANS) and the dispersion/diffusion equation of suspended sediment c. In addition, as a turbulent closure model, we employ the standard k-ε model which includes the transport equation of turbulent kinetic energy k, and the transport equation of the dissipation rate ε. Asymptotic expansions of the variables are then introduced into the governing equations to obtain the perturbation equations. The perturbation equations are solved with the use of the spectral collocation method incorporated with the Chebyshev polynomials. It is found that density stratification increases the velocity and suspended sediment concentration at the region near to the bed in the base state condition. The unstable region of antidune is shifted to the range of smaller wavenumber around the critical Froude number due to the effect of density stratification.

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