Inertial waves

Inertial waves, also known as inertial oscillations, are a type of mechanical wave possible in rotating fluids. Unlike surface gravity waves commonly seen at the beach or in the bathtub, inertial waves flow through the interior of the fluid, not at the surface. Like any other kind of wave, an inertial wave is caused by a restoring force and characterized by its wavelength and frequency. Because the restoring force for inertial waves is the Coriolis force, their wavelengths and frequencies are related in a peculiar way. Inertial waves are transverse. Most commonly they are observed in atmospheres, oceans, lakes, and laboratory experiments. Rossby waves, geostrophic currents, and geostrophic winds are examples of inertial waves. Inertial waves are also likely to exist in the molten core of the rotating Earth.

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.

Inertial waves are possible only when a fluid is rotating, and exist in the bulk of the fluid, not at its surface. Like light waves, inertial waves are transverse, which means that their vibrations occur perpendicular to the direction of wave travel. One peculiar geometrical characteristic of inertial waves is that their phase velocity, which tells about the movement of the crests and troughs of the wave, is perpendicular to their group velocity, which tells about the propagation of energy.

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