Inertial wave

Most commonly they are observed in atmospheres, oceans, lakes, and laboratory experiments.

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.

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.

One peculiar geometrical characteristic of inertial waves is that their phase velocity, which describes the movement of the crests and troughs of the wave, is perpendicular to their group velocity, which is a measure of the propagation of energy.

Waves traveling perpendicular to the axis of rotation have zero frequency and are sometimes called the geostrophic modes.

In free space, an inertial wave can exist at any frequency between 0 and twice the rotation rate.

Any kind of fluid can support inertial waves: water, oil, liquid metals, air, and other gases.

Inertial waves are observed most commonly in planetary atmospheres (Rossby waves, geostrophic winds) and in oceans and lakes (geostrophic currents), where they are responsible for much of the mixing that takes place.

Inertial waves can be observed in laboratory experiments or in industrial flows where a fluid is rotating.

Inertial waves are also likely to exist in the liquid outer core of the Earth, and at least one group [1] has claimed evidence of them.

Similarly, inertial waves are likely in rotating astronomical flows like stars, accretion disks, planetary rings, and galaxies.

In the equation above, the centrifugal force is included as a part of the generalized pressure

Taking a curl of both sides and applying a few vector identities, the result is One class of solutions to this equation are waves that satisfy two conditions.

The dispersion relation looks much like the Coriolis term in the momentum equation—notice the rotation rate and the factor of two.