Sand ripples under sea waves Part 3. Brick-pattern ripple formation

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Abstract
An oscillatory flow over a cohesionless bottom can produce regular three-dimensional bedforms known as brick-pattern ripples characterized by crests perpendicular to the direction of fluid oscillations joined by equally spaced bridges shifted by half a wavelength between adjacent sequences (a photo of brick-pattern ripples is shown in Sleath 1984, p. 141). In the present paper brick-pattern ripple formation is explained on the basis of a weakly nonlinear stability analysis of a flat cohesionless bottom subject to an oscillatory flow in which three-dimensional perturbations are considered. It is shown that brick-pattern ripples are generated by the simultaneous growth of two-dimensional and three-dimensional perturbations which interact with each other, according to a mechanism similar to that described by Craik (1971) in a different context, forming a resonant triad. A comparison between the present theoretical finding and experimental data by Sleath & Ellis (1978), concerning the region of existence of brick-pattern ripples in the parameter space and their geometrical characteristics, supports the validity of the present approach.

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