It has been proposed that a number of regional weather extremes in the Northern Hemisphere associated with blocked atmospheric circulation patterns may have been caused by quasiresonant amplification of Rossby waves. Examples include the 2013 European floods, the 2012 China floods, the 2010 Russian heat wave, the 2010 Pakistan floods and the 2003 European heat wave. Even taking global warming into account, the 2003 heat wave would have been highly unlikely without such a mechanism.

Normally freely travelling synoptic-scale Rossby waves and quasistationary planetary-scale Rossby waves exist in the mid-latitudes with only weak interactions. The hypothesis, proposed by Vladimir Petoukhov, Stefan Rahmstorf, Stefan Petri, and Hans Joachim Schellnhuber, is that under some circumstances these waves interact to produce the static pattern. For this to happen, they suggest, the zonal (east-west) wave number of both types of wave should be in the range 6–8, the synoptic waves should be arrested within the troposphere (so that energy does not escape to the stratosphere) and mid-latitude waveguides should trap the quasistationary components of the synoptic waves. In this case the planetary-scale waves may respond unusually strongly to orography and thermal sources and sinks because of "quasiresonance".

A 2017 study by Mann, Rahmstorf, et al. connected the phenomenon of anthropogenic Arctic amplification to planetary wave resonance and extreme weather events.

To start with, a zonal mean flow, U, can be considered to be perturbed where U is constant in time and space. Let be the total horizontal wind field, where u and v are the components of the wind in the x- and y- directions, respectively. The total wind field can be written as a mean flow, U, with a small superimposed perturbation, u′ and v′.

The perturbation is assumed to be much smaller than the mean zonal flow.

The relative vorticity and the perturbations and can be written in terms of the stream function (assuming non-divergent flow, for which the stream function completely describes the flow):

Considering a parcel of air that has no relative vorticity before perturbation (uniform U has no vorticity) but with planetary vorticity f as a function of the latitude, perturbation will lead to a slight change of latitude, so the perturbed relative vorticity must change in order to conserve potential vorticity. Also the above approximation U >> u' ensures that the perturbation flow does not advect relative vorticity.

with . Plug in the definition of stream function to obtain:

Using the method of undetermined coefficients one can consider a traveling wave solution with zonal and meridional wavenumbers k and ℓ, respectively, and frequency :

This yields the dispersion relation:

The zonal (x-direction) phase speed and group velocity of the Rossby wave are then given by

where c is the phase speed, cg is the group speed, U is the mean westerly flow, is the Rossby parameter, k is the zonal wavenumber, and ℓ is the meridional wavenumber. It is noted that the zonal phase speed of Rossby waves is always westward (traveling east to west) relative to mean flow U, but the zonal group speed of Rossby waves can be eastward or westward depending on wavenumber.
The Rossby parameter is defined as the rate of change of the Coriolis frequency along the meridional direction:

where is the latitude, ω is the angular speed of the Earth's rotation, and a is the mean radius of the Earth.

If , there will be no Rossby waves; Rossby waves owe their origin to the gradient of the tangential speed of the planetary rotation (planetary vorticity). A "cylinder" planet has no Rossby waves. It also means that at the equator of any rotating, sphere-like planet, including Earth, one will still have Rossby waves, despite the fact that , because . These are known as Equatorial Rossby waves.

• Atmospheric wave
• Equatorial wave
• Equatorial Rossby wave – mathematical treatment
• Harmonic
• Kelvin wave
• Polar vortex
• Rossby whistle