Nonlinear dynamics of an ice plate overlaying deep water under supercritical compression

• Flexural-gravity waves in a compressed ice plate • Buckling phenomenon and plate distortion • Nonstationary regimes of plate behaviour under supercritical compression • Ice plate instability and stabilisation • 2D and 3D stationary formations on a compressed ice plate We investigate a supercritical regime of a compressed ice plate floating on infinitely deep water. Our derived governing equations describe wave amplitude dynamics when compression exceeds a critical threshold in 2D and 3D cases. Results show that small deviations in the ice plate initially grow exponentially, leading to either complete structural failure (at high supercriticality) or oscillations around equilibrium states. We provide quantitative estimates of wave amplitudes, oscillation periods in stable regimes, and instability growth rates using realistic ice plate parameters. This research offers valuable insights for ice-working researchers and engineers regarding hazardous compression conditions and the relationship between compression supercriticality and resulting ice dynamics.