Radio atmospheric km. For ELF waves (< 3 kHz), ray theory becomes invalid, and only mode theory is appropriate. Here, the zeroth mode begins to dominate and is responsible for the second window at greater distances. Resonant waves of this zeroth mode can be excited in the Earth–ionosphere waveguide cavity, mainly by the continuing current components of lightning flowing between two return strokes. Their wavelengths are integral fractions of the Earth's circumference, and their resonance frequencies can thus be approximately determined by "f" ≃ "mc"/(2π"a") ≃ 7.5 "m" Hz (with "m" = 1, 2, ...; "a" the Earth's radius and "c" the
Atmospheric wave 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