Inertial Wave - Restoring Force

Restoring Force

To understand the idea of a restoring force, imagine a guitar string. In equilibrium, the string is taut and straight, held stationary between its ends. Plucking the string moves it away from this equilibrium position. The tension in the string immediately pulls it back toward equilibrium, but soon overshoots, so that the string bows in the opposite direction. Next, tension again pulls the string back toward equilibrium, but again overshoots, and the cycle continues until the string finally comes to rest. Since tension restores the string to equilibrium (overshooting many times along the way), it is called the restoring force. Without it, the string would not vibrate, and no wave could exist.

Likewise, the open ocean is in equilibrium when it is level and at rest. If something (like wind) causes part of the ocean to rise and form a crest, the crest is immediately pulled back toward equilibrium by gravity. Soon gravity overshoots, and the crest becomes a trough, displacing water and forming other crests nearby. They, in turn, are pulled back toward equilibrium by gravity, and the cycle continues. So gravity is the restoring force for wind waves on the open ocean, often called gravity waves.

Inertial waves are restored to equilibrium by the Coriolis force, a result of rotation. To be precise, the Coriolis force arises (along with the centrifugal force) in a rotating frame to account for the fact that such a frame is always accelerating. Inertial waves, therefore, cannot exist without rotation. More complicated than tension on a string, the Coriolis force acts at a 90° angle to the direction of motion, and its strength depends on the rotation rate of the fluid. These two properties lead to the peculiar characteristics of inertial waves.