= Quasistatic bed stability with suspended sediment
{title2=$\sigma=-4\kappa^2/(1+\kappa^2)-i\kappa[3\beta+4/(1+\kappa^2)]$}
A leading fixed-discharge, level-surface approximation to a shallow erodible-bed flow gives perturbation <equations> $C_x=4U-C$ and $U_t+3\beta U_x=-4U+C$. The displayed Fourier growth rate has negative <real part> for every nonzero <wave number>, independently of bedload parameter $\beta$. Bedload changes the propagation <speed> but not this damping. The zero-wave-number mode is neutral, so absence of growing modes should not be confused with strict asymptotic decay of every spatially uniform perturbation.
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