The breaking of waves is studied by fluid dynamics, a sub-discipline of physics that studies the science behind liquids and gases.
Scientists have concluded that waves break when their amplitude reaches a critical level that causes large amounts of wave energy to be transformed into turbulent kinetic energy, like a ball rolling down the hill.
In other words, when waves reach shallow waters – usually near coastlines – they increase in height, and their crests meet the Law of Gravitation. The waves break. That is what wave shoaling tells us.