Inertial Wave - Characteristics

Characteristics

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. (The opposite of a transverse wave is a longitudinal wave, where the vibrations are in the same direction as the wave travel. Sound waves, for example, are longitudinal.) 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.

Whereas a sound wave or an electromagnetic wave of any frequency is possible, inertial waves can exist only over the range of frequencies from zero to twice the rotation rate of the fluid. Moreover, the frequency of the wave is determined by its direction of travel. Waves traveling perpendicular to the axis of rotation have zero frequency and are sometimes called the geostrophic modes. Waves traveling parallel to the axis have maximum frequency (twice the rotation rate), and waves at intermediate angles have intermediate frequencies. In free space, an inertial wave can exist at any frequency between 0 and twice the rotation rate. A closed container, however, can impose restrictions on the possible frequencies of inertial waves, as it can for any kind of wave. Inertial waves in a closed container are often called inertial modes. In a sphere, for example, the inertial modes are forced to take on discrete frequencies, leaving gaps where no modes can exist.