What Are Atmospheric Waves?

Atmospheric waves are organized oscillations of pressure, temperature, and wind within Earth's atmosphere that arise from the interplay of buoyancy, rotation, gravity, and large-scale flow. They span an enormous range of spatial and temporal scales, from internal gravity waves with horizontal wavelengths of a few kilometers and periods of minutes, to planetary Rossby waves with scales of thousands of kilometers and periods of days to weeks. These waves are fundamental to atmospheric dynamics because they transport energy and momentum across latitude and altitude, connecting weather systems at the surface to processes in the stratosphere and mesosphere.

The study of atmospheric waves draws from fluid dynamics, geophysical fluid dynamics, and wave mechanics. Their mathematical treatment rests on linearized perturbation theory applied to the governing equations of atmospheric motion, in which small disturbances are superimposed on a background flow and analyzed for their propagation, dispersion, and energy transport properties.

Gravity Waves

Atmospheric gravity waves are buoyancy-driven oscillations that arise when air is displaced vertically from its equilibrium position in a stably stratified atmosphere. Restoring buoyancy forces produce oscillations at the Brunt-Vaisala frequency, which depends on the vertical temperature gradient. Common sources include flow over mountain ranges (orographic gravity waves), convective outflows, and shear instabilities in the jet stream. Gravity waves propagate both horizontally and vertically, carrying energy from the troposphere into the middle atmosphere where they eventually break and deposit momentum, driving the quasi-biennial oscillation and the mesospheric circulation. As reviewed in ECMWF's meteorological training lecture series on atmospheric waves, gravity wave drag is a dominant term in the middle atmosphere momentum budget and must be parameterized in models because the generating waves are too small to resolve on global grids. Clear air turbulence encountered by aircraft is frequently associated with breaking gravity waves in the upper troposphere and lower stratosphere.

Rossby Waves

Rossby waves, first identified by Carl Gustaf Rossby in the 1930s, are large-scale meanders of the atmospheric flow driven by the variation of the Coriolis parameter with latitude (the beta effect). They exist in the westerly jet streams of the mid-latitudes as troughs and ridges in the geopotential height field with horizontal scales of 3,000 to 10,000 kilometers. As noted by NOAA's Ocean Service explanation of Rossby waves, these waves transfer heat poleward and cold air equatorward, contributing to the balance of the general circulation. Stationary Rossby waves, forced by orography and land-sea heating contrasts, establish the climatological pattern of troughs and ridges that shapes regional climate and precipitation. Transient Rossby waves propagate westward relative to the mean flow and are associated with the amplification of extratropical cyclones along storm tracks. NOAA's Geophysical Fluid Dynamics Laboratory analysis of Rossby wave teleconnections documents how tropical heating anomalies, such as those associated with El Nino, excite Rossby wave trains that alter weather patterns in remote regions.

Acoustic and Lamb Waves

Acoustic waves in the atmosphere are compressional oscillations in which pressure and density fluctuations propagate at the speed of sound, approximately 340 m/s at sea level. While pure acoustic waves are rapidly damped and of limited meteorological importance, their low-frequency limiting case, the Lamb wave, is a horizontally propagating acoustic mode trapped near the surface by the atmosphere's thermal structure. Lamb waves are generated by explosive volcanic eruptions and large surface detonations and can propagate globally. Infrasound networks, operated by the Comprehensive Nuclear-Test-Ban Treaty Organization, detect Lamb waves to monitor large explosive events anywhere on Earth.

Applications

Atmospheric waves have applications across a wide range of scientific and engineering fields, including:

• Aviation safety: identifying regions of clear air turbulence associated with jet stream gravity wave breaking for flight route optimization
• Numerical weather prediction: parameterizing sub-grid gravity wave drag to correctly represent middle atmosphere circulation in global models
• Climate research: understanding Rossby wave teleconnections that link tropical variability to mid-latitude weather extremes
• Space and upper atmosphere science: tracking gravity wave energy flux into the ionosphere and its coupling to space weather
• Nuclear monitoring: using infrasound networks to detect atmospheric Lamb waves from underground and surface explosive events