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Non-stationary rotational surface waves are considered, where the underlyingcurrent has constant vorticity. A study is presented on the robustness of acritical layer in the presence of a bottom topography, as well as on itsspontaneous formation for waves generated from rest. The restriction, fromprevious studies, to a traveling-wave formulation is removed leading to anon-stationary set of equations. In this setting streamlines are notnecessarily pathlines. Particle-trajectories are found evolving the respectivesubmarine dynamical system with a cloud of tracers. Pathlines are thenvisualized and the respective submarine structures identified. Robustness isillustrated through surface waves interacting with topographic undulations. Therespective Kelvin cat eye structure dynamically adjusts itself over the bottomtopography without loosing its integrity. On the spontaneous formation of aKelvin cat eye structure, the surface is initially undisturbed and waves aregenerated from either the current-topography interaction or by a surfacepressure distribution suddenly imposed. Under the pressure forcing, an isolatedKelvin cat eye spontaneously forms. The two extreme critical points of the cateye structure are connected with a stagnation segment, thus exhibiting a newform of a critical layer.

Spontaneous critical layer formation and robustness beneath rotational waves