The sine wave at low frequency is unstable because it can create strong currents that nobody can stop them from

Bistable wave is a one-dimensional wave whose profile connects two stable equilibria asymptotically approaching one of them at minus infinity and the other one at infinity. In contrast, waves connecting one stable, one unstable equilibrium are called monostable.

It is a process known as shoaling. When waves feel the bottom they slow down and decrease their wavelength but the period of the waves does not change. The height of the wave will steadily increase until the wave becomes unstable and breaks near the beach.

unstable

Radioactive elements are unstable, and the shorter the half-life, the more unstable they are.