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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rossby Wave Instability in Astrophysical Discs ： ウィキペディア英語版 Rossby wave instability in astrophysical discs Rossby Wave Instability (RWI) is a concept related to astrophysical 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 (\exp(m\phi), $m=1,2..$ ) 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. The Rossby vortices in the discs around stars and black holes may cause the observed quasi-periodic modulations of the disc's thermal emission. The theory of the Rossby wave instability (RWI) in accretion discs was developed by Lovelace et al.〔Lovelace, R.V.E., Li, H., Colgate, S.A., \& Nelson, A.F. 1999, "Rossby Wave Instability of Keplerian Accretion Disks", ApJ, 513, 805-810,http://arxiv.org/abs/astro-ph/9809321〕 and Li et al.〔Li, H., Finn, J.M., Lovelace, R.V.E., \& Colgate, S.A. 2000, ``Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory'', ApJ, 533, 1023-1034, http://arxiv.org/abs/astro-ph/9907279〕 for thin Keplerian discs with negligible self-gravity and earlier by Lovelace and Hohlfeld 〔Lovelace, R.V.E., \& Hohlfeld, R.G. 1978, "Negative mass instability of flat galaxies", ApJ, 221, 51-61, http://adsabs.harvard.edu/abs/1978ApJ...221...51L〕 for thin disc galaxies where the self-gravity may or may not be important and where the rotation is in general non-Keplerian. In the first case the instability can occur if there is an axisymmetric bump (as a function of radius) in the inverse potential vorticity $$ (r) = )\cdot\hat}~, at some radius $r\_0$, where $\backslash Sigma$ is the surface mass density of the disc, $\backslash approx\; r\backslash Omega(r)\backslash hat$ is the flow velocity of the disc, $\backslash Omega(r)\; \backslash approx\; (GM\_$ */r^3)^ is the angular velocity of the flow (with $M\_$ * the mass of the central star), $S$ is the specific entropy of the gas, and $\backslash gamma$ is the specific heat ratio. The approximations involve the neglect of the relatively small radial pressure force. Note that $$ is related to the inverse of the which is defined as $()\_z/\backslash Sigma$. A sketch of a bump in $(r)$ is shown in Figure 1. Rossby waves, named after Carl-Gustaf Arvid Rossby are important in planetary atmospheres and oceans and are also known as it planetary waves (see Rossby et al.;〔Rossby C.-G. and Collaborators 1939, "Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action", Journal of Marine Research, 2, 38-55, http://www.ingentaconnect.com/content/jmr/jmr/1939/00000002/00000001/art00006〕 Brekhovskikh and Goncharovv;〔Brekhovskikh, L. M., \& Goncharov, V. 1993, (Berlin : Springer), pp 246-252, http://adsabs.harvard.edu/abs/1985SSWP....1.....B〕 Chelton and Schlax;〔Chelton, D.B., and Schlax, M.G. 1996, ``Global Observations of Oceanic Rossby Waves'', Science, 272, 234-238, http://www.ocean.washington.edu/courses/oc513/Chelton.Science.1996.pdf〕 Lindzen 〔Lindzen, R.S. 1988, "Instability of plane parallel shear flow (toward a mechanistic picture of how it works", Pure Appl. Geophys., 126, 103-121, http://link.springer.com/article/10.100〕). 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 (e.g., Marcus 〔Marcus, P.S. 1993, ``Jupiter's Great Red Spot and other Vortices'', Ann. Rev. Astron. and Astrophys., 31, 523-573, http://adsabs.harvard.edu/abs/1993ARA〕). 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 (ref, 5; ref. 1). == Schrödinger-like equation for perturbation == Linearization of the Euler and continuity equations for a thin fluid disc with perturbations proportional to $f(r)\backslash exp(m\backslash phi-\backslash omega\; t)$(with azimuthal mode number $m=1,\; 2,..$ and angular frequency $\backslash omega$) leads to a Schrödinger-like equation for the enthalpy perturbation $\backslash psi=\backslash delta\; p/\backslash rho$, $$ = V_(r)~\psi~. The effective potential well $V\_\; (r)$ is closely related to $(r)$: If the height of the bump in $(r)$ is too small the potential well is shallow and there are no `bound Rossby wave states' in the well. On the other hand for a sufficiently large bump in $(r)$ the potential $V\_$ is sufficiently deep to have a bound state. The condition for there to be just one bound state allows one to solve for the imaginary part of the wave frequency, $\backslash omega\_i\; =\; \backslash Im(\backslash omega)$ which is the growth rate of the instability (ref. 1). For moderate strength bumps (with fractional amplitudes $\backslash Delta\backslash Sigma/\backslash Sigma\; \backslash lesssim\; 0.2$), the growth rates are of the order of $\backslash omega\_i\; =\; (0.1-0.2)\backslash Omega(r\_0)$. The real part of the wave frequency $\backslash omega\_r\; =\backslash Re(\backslash omega)$ is approximately $m\backslash Omega(r\_0)$. A more complete analysis (Tagger;〔Tagger, M., 2001, "On Rossby waves and vortices with differential rotation", A\&A, 380, 750-757, http://arxiv.org/abs/astro-ph/0110298〕 Tsang and Lai;〔Tsang, D., and Lai, D., 2008, "Super-reflection in fluid discs: corotation amplifier, corotation resonance, Rossby waves and overstable modes", MNRAS, 387, 446-462, http://arxiv.org/abs/0710.2313〕 Lai and Zhang 〔Lai, D., and Tsang ,D., 2009, ``Corotational instability of inertial-acoustic modes in black hole accretion discs and quasi-periodic oscillations'', MNRAS, 393, 979-991, http://arxiv.org/abs/0810.0203〕) reveals that the Rossby wave is not completely trapped in the potential well $V\_$, but leaks outward across a forbidden region at an outer Lindblad resonance (at $r\_$ indicated in Figure 1) and inward across another forbidden region at an inner Lindblad resonance (at $r\_$). Once the waves cross the forbidden regions they propagate as spiral density wave. The full expression for the effective potential for a thin homentropic ($S=$ const) disc is Figure 2 shows the effective potential for sample cases. Note that the inward propagating waves with have negative energy () whereas the outward propagating waves with $\backslash omega\_r\; >\; m\; \backslash Omega(r)$ have positive energy ($E>0$) (ref. 12). The Rossby wave instability occurs because of the local wave trapping in a disc. It is related to the Papaloizou and Pringle instability;〔Papaloizou, J. C. B., \& Pringle, J. E. 1984, "The dynamical stability of differentially rotating discs with constant specific angular momentum", MNRAS, 208, 721-750, http://adsabs.harvard.edu/abs/1984MNRAS.208..721P〕〔Papaloizou, J. C. B., \& Pringle, J. E. 1985, "The dynamical stability of differentially rotating discs. II", MNRAS, 213, 799-820, http://adsabs.harvard.edu/abs/1985MNRAS.213..799P〕) where the wave is trapped between the inner and outer radii of a disc or torus. Figure 3 shows computer simulations of the formation of a single Rossby vortex.〔Lovelace, R.V.E. and Romanova, M.M. 2013,"Rossby Wave Instability in Astrophysical Discs", 13 pages, 4 figures, http://arxiv.org/abs/1312.4572〕 More information on the Rossby wave instability in astrophysical discs can be found in Lovelace and Romanova (ref.15). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rossby wave instability in astrophysical discs」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.