Stability Balloon for Two-Dimensional Vortex Ripple Patterns

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude $a$ or frequency $f$. A sufficient decrease of $f$ leads to a “freezing” of the pattern, while a sufficient increase of $f$ leads to a supercritical secondary “pearling” instability. Sufficient changes in the amplitude $a$ lead to subcritical secondary “doubling” and “bulging” instabilities. Our findings are summarized in a “stability balloon” for vortex ripple pattern formation.