Stability of an accelerated hydrodynamic discontinuity*

While looking from a far field, we analyze the evolution of an accelerated discontinuity separating ideal incompressible fluids of different densities. We develop and apply a general matrix method and identify a new hydrodynamic instability that occurs when the acceleration magnitude exceeds a critical threshold value. The flow dynamics conserves mass, momentum and energy in the fluid bulk and at the interface, has potential velocity fields in the fluid bulk, and is shear-free at the interface. The interface stability is set by the interplay of inertia and buoyancy. Surface tension also stabilizes the dynamics by a distinct mechanism. The growth rate and the flow fields’ structure of the unstable dynamics depart substantially from those of other interfacial hydrodynamic instabilities, thus suggesting new opportunities for stabilization, diagnostics, and control of the interfacial dynamics.