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Periodic disturbance in atmospheres

An atmospheric wave is a periodic disturbance in the fields of atmospheric variables (like surface pressure or geopotential height, temperature, or wind velocity) which may either propagate (traveling wave) or be stationary (standing wave). Atmospheric waves range in spatial and temporal scale from large scale planetary waves (Rossby waves) to minute sound waves. Atmospheric waves with periods which are harmonics of 1 solar day (e. g. 24 hours, 12 hours, 8 hours etc.) are known as atmospheric tides.

The mechanism for the forcing of the wave, for example, the generation of the initial or prolonged disturbance in the atmospheric variables, can vary. Generally, waves are either excited by heating or dynamic effects, for example the obstruction of the flow by mountain ranges like the Rocky Mountains in the U. S. or the Alps in Europe. Heating effects can be small scale (like the generation of gravity waves by convection) or large scale (the formation of Rossby waves by the temperature contrasts between continents and oceans in the Northern hemisphere winter). Atmospheric waves transport momentum, which is fed back into the background flow as the wave dissipates. This wave forcing of the flow is particularly important in the stratosphere, where this momentum deposition by planetary scale Rossby waves gives rise to sudden stratospheric warmings and the deposition by gravity waves gives rise to the quasi biennial oscillation. In the mathematical description of atmospheric waves, spherical harmonics are used. When considering a section of a wave along a latitude circle, this is equivalent to a sinusoidal shape. Spherical harmonics, representing individual Rossby Haurwitz planetary wave modes, can have any orientation with respect to the axis of rotation of the planet. Remarkably while the very existence of these planetary wave modes requires the rotation of the planet around its polar axis the phase velocity of the individual wave modes does not depend on the relative orientation of the spherically harmonic wave mode with respect to the axis of the planet. This can be shown to be a consequence of the underlying (approximate) spherical symmetry of the planet, even though this symmetry is broken by the planet's rotation.