Stability of an accelerated hydrodynamic discontinuity*

While looking from a far field at the accelerated interface separating ideal fluids of different densities, we identify, for the first time to our knowledge, a new type of hydrodynamic instability that develops when the acceleration magnitude exceeds a critical value. The flow dynamics conserves the fluxes of mass, momentum and energy at the interface, has potential velocity fields in the fluid bulk, and is shear-free at the interface. The growth rate and the flow fields' structure of this unstable dynamics depart substantially from those of other interfacial hydrodynamic instabilities, thus suggesting new opportunities for stabilization, diagnostics, and control of the interfacial dynamics.