Rossby waves

Rossby waves owe their existence to the conservation of potential vorticity, a quantity that combines the spin of the Earth with the relative spin of the fluid. As an air or water parcel moves poleward, the planetary vorticity (the Coriolis parameter) increases, so the parcel must acquire negative relative vorticity, causing it to turn equatorward. This restoring mechanism produces a wave that propagates westward relative to the mean flow, with a phase speed that depends on the wavelength and the latitudinal gradient of the Coriolis parameter.

In the atmosphere, these waves are most prominent in the mid-latitude jet stream, where they appear as meanders that can become cut-off lows or highs. In the ocean, they are generated by wind stress and propagate westward across ocean basins, influencing sea surface height and the thermocline depth.¹

Atmospheric Rossby waves are a primary driver of day-to-day weather variability in the mid-latitudes. They transport heat and momentum, and their breaking can lead to blocking patterns that cause persistent heatwaves or cold spells. They also connect tropical and polar regions through teleconnections, such as the Pacific–North American pattern.

Oceanic Rossby waves, though slower, are crucial for adjusting the ocean to changes in wind forcing. They transmit signals across ocean basins over years to decades, affecting the Gulf Stream and the El Niño–Southern Oscillation. Satellite altimetry has revealed their global presence, with wavelengths of hundreds of kilometers and speeds of a few centimeters per second.²

The theoretical foundation was laid by Carl-Gustaf Rossby in 1939, who derived the dispersion relation for these waves in a barotropic atmosphere. His work built on earlier observations of westerly wind belts and was motivated by the need to understand long-range weather forecasting. Rossby's model simplified the atmosphere to a single layer, yet it captured the essential restoring mechanism.

Later, the concept was extended to stratified and baroclinic atmospheres, and to the oceans, where the slower propagation was first predicted in the 1950s. The advent of satellite altimetry in the 1990s allowed direct observation of oceanic Rossby waves, confirming their existence and speeds.²

Rossby waves also occur in other planetary atmospheres, such as Jupiter's visible cloud bands, where they manifest as slow-moving meanders. In the Earth's oceans, they are not only generated by wind but also by changes in buoyancy forcing, and they can be reflected at coastlines, leading to boundary-trapped waves.³

In the atmosphere, Rossby waves can be forced by large-scale topography like the Rocky Mountains and by diabatic heating in the tropics. They also interact with the stratospheric polar vortex, and their breaking can influence the timing of sudden stratospheric warmings. A niche application is in the study of Martian dust storms, where similar wave dynamics affect atmospheric circulation.

Coriolis effect

The apparent deflection of moving objects due to Earth's rotation.

Potential vorticity

A conserved quantity combining the spin of the Earth and the relative spin of a fluid parcel.

Barotropic

A state where density depends only on pressure, simplifying wave dynamics.

Teleconnection

A recurring and persistent large-scale pattern of pressure and temperature anomalies spanning vast areas.