Rossby wave instability in a Keplerian Disk

Rossby Wave Instability (RWI) is a concept related to astrophysical

accretion disc An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is typically a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other ...

s. In non-self-gravitating discs, for example around newly forming stars, the instability can be triggered by an axisymmetric bump, at some radius

r_0

, in the disc surface mass-density. It gives rise to exponentially growing non-axisymmetric perturbation in the vicinity of

r_0

consisting of

anticyclonic An anticyclone is a weather phenomenon defined as a large-scale circulation of winds around a central region of high atmospheric pressure, clockwise in the Northern Hemisphere and counterclockwise in the Southern Hemisphere as viewed from abo ...

vortices. These vortices are regions of high pressure and consequently act to trap dust particles which in turn can facilitate planetesimal growth in proto-planetary discs. The Rossby vortices in the discs around stars and

black holes A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...

may cause the observed quasi-periodic modulations of the disc's thermal emission. The theory of the Rossby wave instability in accretion discs was developed by Lovelace et al. and Li et al. for thin Keplerian discs with negligible self-gravity and earlier by Lovelace and Hohlfeld for thin disc galaxies where the self-gravity may or may not be important and where the rotation is in general non-Keplerian.

Rossby wave Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and ...

s, named after

Carl-Gustaf Arvid Rossby Carl-Gustaf Arvid Rossby ( 28 December 1898 – 19 August 1957) was a Swedish-born American meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics. He identified and characterized both the jet ...

, are important in planetary atmospheres and oceans and are also known as planetary waves. These waves have a significant role in the transport of heat from equatorial to polar regions of the Earth. They may have a role in the formation of the long-lived (

>300

yr) Great Red Spot on

Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandt ...

which is an

vortex. The Rossby waves have the notable property of having the

phase velocity The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...

opposite to the direction of motion of the atmosphere or disc in the comoving frame of the fluid. The Rossby wave instability occurs because of the local wave trapping in a disc. It is related to the Papaloizou and Pringle instability; where the wave is trapped between the inner and outer radii of a disc or torus.

References

Further reading