Flow field induced by sea waves over brick-pattern ripples

This paper examines the oscillatory flow induced by progressive gravity waves near a sea bottom covered with three-dimensional ripples. Previous works on the subject, in which only two-dimensional bottom waviness were considered, are thus extended. By assuming small values of the ratio between ripple amplitude and the thickness of the bottom boundary layer, the solution is given analytically by means of a perturbation approach. Arbitrary values of the ratio r between fluid displacement and ripple wavelength are considered. For vanishing values of r an asymptotic solution is also determined as an independent check for the previous one. Even though the solution can provide the flow field over arbitrary bottom topographies, detailed results are presented only for the profile of brick-pattern ripples, which is characterized by transverse crests joined by longitudinal bridges. Finally, relevance of the results to understanding the mechanism of three-dimensional ripple formation (brick-pattern ripples, tile ripples) is discussed.