Hydrodynamic wrinkling of an elastic loop in transient radial flow

When the compression exerted on a thin elastic structure is sufficient to cause buckling instability, a regular wrinkle pattern emerges. The formation of wrinkles can be achieved and mechanically guided by transient external loading. As a novel dynamic wrinkling mechanism, we introduce the hydrodynamic coupling between elasticity and pressure induced by transient flow. A circular elastic loop immersed in an expanding fluid-filled gap undergoes buckling due to the net hydrodynamic pressure between its inner and outer surfaces, yielding a time-dependent wrinkle pattern. Because of the transient features of the hydrodynamic pressure, the apparent mode of the wrinkles reaches the maximum mode number immediately after the instant of peak pressure, followed by a cascade to lower modes. The maximum mode number of the wrinkles is determined by the magnitude of the peak pressure. In contrast to an elastic loop of uniform thickness, varying the thickness distribution of the loop and facilitating buckling at specific local points produce a distinct wrinkle pattern with a specific low mode consistently over time.