Spontaneous "wave ripples" through sequential wrinkling interference

The coupling between fluid motion, both unidirectional and periodic, and sediment transport, gives rise to the familiar yet fascinating, self-organisation processes responsible for the formation of `ripples' in sand beds and beach dunes. Analogous patterns are found in folded, layered rock formations, developing a range of orthogonal to non-orthogonal interference patterns. Striking periodic and aperiodic structures also emerge in biological morphogenesis, for instance in the epicuticular topography of certain insect wings, such as dragonflies or cicadae, modulating appearance and function, such as structural colour and superhydrophobicity. Here, we report the formation of `sand ripple' patterns by the sequential superposition of non-orthogonal surface waves excited by the spontaneous buckling of polymeric bilayers. A PDMS slab is uni-axially stretched and then subjected to plasma oxidation, forming a thin glassy skin. Upon strain release, a first wrinkling generation is formed, with prescribed wavelength and amplitude. Interference is achieved by superposing the second wrinkling generation at a prescribed angle, termed `compression angle'. This sequential wrinkling approach provides a facile and scalable framework to induce tunable undulated and checkerboard patterns, by varying layer skin and strain parameters. Albeit of a different nature and micronscale compared to the familiar sedimentary ripples caused by gentle wave oscillations, we find commonalities in their topography, defects and bifurcations. The patterns are rationalised in terms of a defect density that depends on the relative angle between generations, and a constant in-plane bending angle that depends on skin thickness. A minimal wave summation model enables the design of ripple and checkerboard surfaces by tuning material properties and fabrication process, guiding surface fabrication, mimicking naturally-occurring patterns, with potential practical applications.