This study is to develop an asymptotic theory for the profile of a thin layer of mud on the bottom of a waterway under the combined effects of surface waves and density current. By virtue of the sharply different time scales (wave periodic excitation being effective at fast scales, while gravity and streaming currents at slow scales), a multiple-scale perturbation analysis is conducted. Evolution equations are deduced for the mud layer by solving a boundary-value problem. When reflected waves are present, the balance between gravity and streaming will result, on a time scale one order longer than the wave period, in the formation of a ripple on the water/mud interface whose displacement amplitude is one order smaller than the thickness of the mud layer itself.
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