Rossby wave instability

{{Short description|Concept in astrophysics}}

{{primary sources| date=March 2020}}

File:Rossby wave instability in a Keplerian Disk.png

Rossby Wave Instability (RWI) is a concept related to astrophysical accretion discs. 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 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.{{cite journal | last1=Lyra | first1=W. | last2=Johansen | first2=J. | last3=Zsom | first3=A. | last4=Klahr | first4=H. | last5=Piskunov | first5=N. | date=April 2009 |doi= 10.1051/0004-6361/200811265|arxiv = 0901.1638 |bibcode = 2009A&A...497..869L | volume=497 |title=Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks |journal=Astronomy & Astrophysics | issue=3 |pages=869–888| s2cid=15820108 }} The Rossby vortices in the discs around stars and black holes may cause the observed quasi-periodic modulations of the disc's thermal emission.

Rossby waves, named after Carl-Gustaf Arvid Rossby, are important in planetary atmospheres and oceans and are also known as planetary waves.{{cite journal |doi=10.1357/002224039806649023 | volume=2 | title=Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action | journal=Journal of Marine Research | pages=38–55| year=1939 | last1=Rossby | first1=C.-G. | s2cid=27148455 }}{{cite book |doi=10.1007/978-3-642-96861-7_11 |chapter=Waves in Rotating Fluids |title=Mechanics of Continua and Wave Dynamics |series=Springer Series on Wave Phenomena |year=1985 |last1=Brekhovskikh |first1=Leonid |last2=Goncharov |first2=Valery |volume=1 |pages=236–261 |isbn=978-3-642-96863-1 }}{{cite journal |url=http://www.ocean.washington.edu/courses/oc513/Chelton.Science.1996.pdf |doi=10.1126/science.272.5259.234|bibcode = 1996Sci...272..234C | volume=272 |title=Global Observations of Oceanic Rossby Waves |journal=Science |pages=234–238|year=1996|last1=Chelton|first1=D. B.|last2=Schlax|first2=M. G.|issue=5259|s2cid=126953559}}{{cite journal |doi=10.1007/BF00876917|bibcode = 1988PApGe.126..103L | volume=126 | title=Instability of plane parallel shear flow (toward a mechanistic picture of how it works) |journal=Pure and Applied Geophysics |pages=103–121|year = 1988 |last1 = Lindzen |first1 = Richard S. |issue = 1 |s2cid = 128547643 }} 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 which is an anticyclonic vortex.{{cite journal |doi=10.1146/annurev.aa.31.090193.002515 | volume=31 | title=Jupiter's Great Red Spot and Other Vortices | journal=Annual Review of Astronomy and Astrophysics | pages=523–569|bibcode = 1993ARA&A..31..523M | year=1993 | last1=Marcus | first1=Philip S. }} The Rossby waves have the notable property of having the phase velocity opposite to the direction of motion of the atmosphere or disc in the comoving frame of the fluid.

The theory of the Rossby wave instability in accretion discs was developed by Lovelace et al.{{cite journal | last1=Lovelace | first1=R. V. E. | last2=Li | first2=H. | last3=Colgate | first3=S. A. | last4=Nelson | first4=A. F. | date=March 1999 |doi= 10.1086/306900|arxiv = astro-ph/9809321 |bibcode = 1999ApJ...513..805L | volume=513 |title=Rossby Wave Instability of Keplerian Accretion Disks |journal=The Astrophysical Journal | issue=2 |pages=805–810| s2cid=8914218 }} and Li et al.{{cite journal |doi=10.1086/308693|arxiv = astro-ph/9907279 |bibcode = 2000ApJ...533.1023L | volume=533 |title=Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory |journal=The Astrophysical Journal |pages=1023–1034|year = 2000 |last1 = Li |first1 = H. |last2 = Finn |first2 = J. M. |last3 = Lovelace |first3 = R. V. E. |last4 = Colgate |first4 = S. A. |issue = 2 |s2cid = 119382697 }} for thin Keplerian discs with negligible self-gravity and earlier by Lovelace and Hohlfeld{{cite journal |bibcode=1978ApJ...221...51L|doi = 10.1086/156004 | volume=221 | title=Negative mass instability of flat galaxies |journal=The Astrophysical Journal |pages=51|year = 1978 |last1 = Lovelace |first1 = R. V. E. |last2 = Hohlfeld |first2 = R. G. }} for thin disc galaxies where the self-gravity may or may not be important and where the rotation is in general non-Keplerian.

The Rossby wave instability occurs because of the local wave trapping in a disc. It is related to the Papaloizou and Pringle instability;{{cite journal |bibcode=1984MNRAS.208..721P|doi = 10.1093/mnras/208.4.721 | volume=208 | title=The dynamical stability of differentially rotating discs with constant specific angular momentum |journal=Monthly Notices of the Royal Astronomical Society |pages=721–750|year = 1984 |last1 = Papaloizou |first1 = J. C. B. |last2 = Pringle |first2 = J. E. |issue = 4 |doi-access = free }}{{cite journal|bibcode=1985MNRAS.213..799P|doi = 10.1093/mnras/213.4.799 | volume=213 | title=The dynamical stability of differentially rotating discs - II|journal=Monthly Notices of the Royal Astronomical Society|pages=799–820|year = 1985 |last1 = Papaloizou |first1 = J. C. B. |last2 = Pringle |first2 = J. E. |issue = 4 |doi-access = free }} where the wave is trapped between the inner and outer radii of a disc or torus.