2014A&A...562A..25C

Query : 2014A&A...562A..25C

2014A&A...562A..25C - Astronomy and Astrophysics, volume 562A, 25-25 (2014/2-1)

Elliptical instability of compressible flow in ellipsoids.

CLAUSEN N. and TILGNER A.

Abstract (from CDS):

Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability typically leads to three-dimensional turbulence. The associated turbulent dissipation together with the dissipation of the large scale mode may be important for the synchronization process in stellar and planetary binary systems. In order to determine the influence of the compressibility on the stability limits of tidal flows in stars or planets, we calculate the growth rates of perturbations in flows with elliptical streamlines within ellipsoidal boundaries of small ellipticity. In addition, the influence of the orbiting frequency of the tidal perturber ΩP and the viscosity of the fluid are taken into account. We studied the linear stability of the flow to determine the growth rates. We solved the Euler equation and the continuity equation. The viscosity was introduced heuristically in our calculations. We assumed a power law for the radial dependence of the background density. Together with the use of the anelastic approximation, this enabled us to use semi-analytical methods to solve the equations. It is found that the growth rate of a certain mode combination depends on the compressibility. However, the influence of the compressibility is negligible for the growth rate maximized over all possible modes if viscous bulk damping effects can be neglected. The growth rate maximized over all possible modes determines the stability of the flow. The stability limit for the compressible fluid confined to an ellipsoid is the same as for incompressible fluid in an unbounded domain. Depending on the ratio ΩP/ΩF, with ΩF the spin rate of the central object in the frame of the rotating tidal perturber, certain pairs of modes resonate with each other. The size of the bulk damping term depends on the modes that resonate with each other. Therefore the growth rate of the viscous flow depends on the compressibility. Estimates for the stability limit in viscous fluids are given.

Abstract Copyright: ∼

Journal keyword(s): hydrodynamics - instabilities - waves

Simbad objects: 1

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Number of rows : 1
N Identifier Otype ICRS (J2000)
RA 		ICRS (J2000)
DEC 		Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2024 		#notes
1 V* V636 Cen EB* 14 16 57.9122377992 -49 56 42.372930480   9.70 9.09     G0V 96 0

Query : 2014A&A...562A..25C

Basic data :
V* V636 Cen -- Eclipsing Binary
Origin of the objects types :

(Ref) Object type as listed in the reference "Ref"
(acronym) Object type linked to the acronym according to the original reference
() Anterior to 2007, before we can link the objet type to a reference, or given by the CDS team in some particular cases

Other object types: 		EB* (), * (HD,CD,...), V* (V*), X (1RXS), NIR (2MASS)
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
  • ra dec : right ascension and declination (unit and frame defined according to your Output Options)
    Grey values are increasing the original precision due to the computation of frame transformations
  • (wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
  • [error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
    position angle (in degrees North celestial pole to East)
  • quality : flag of quality
    • E ≥ 10"
    • D : 1-10" (and some old data)
    • C : 0.1-1"
    • B : 0.01-0.1" + 2MASS, Tyc
    • A : VLBI, Hipparcos
  • bibcode : bibcode of the coordinates reference
ICRS coord. (ep=J2000) : 		14 16 57.9122377992 -49 56 42.372930480 (Optical) [ 0.0169 0.0257 90 ] A 2020yCat.1350....0G
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
  • ra dec : right ascension and declination (unit and frame defined according to your Output Options)
    Grey values are increasing the original precision due to the computation of frame transformations
  • (wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
  • [error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
    position angle (in degrees North celestial pole to East)
  • quality : flag of quality
    • E ≥ 10"
    • D : 1-10" (and some old data)
    • C : 0.1-1"
    • B : 0.01-0.1" + 2MASS, Tyc
    • A : VLBI, Hipparcos
  • bibcode : bibcode of the coordinates reference
FK4 coord. (ep=B1950 eq=1950) : 		14 13 40.1952698602 -49 42 48.316093137 [ 0.0169 0.0257 90 ]
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
  • ra dec : right ascension and declination (unit and frame defined according to your Output Options)
    Grey values are increasing the original precision due to the computation of frame transformations
  • (wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
  • [error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
    position angle (in degrees North celestial pole to East)
  • quality : flag of quality
    • E ≥ 10"
    • D : 1-10" (and some old data)
    • C : 0.1-1"
    • B : 0.01-0.1" + 2MASS, Tyc
    • A : VLBI, Hipparcos
  • bibcode : bibcode of the coordinates reference
Gal coord. (ep=J2000) : 		316.7419954309822 +10.6193620817911 [ 0.0169 0.0257 90 ]
Syntax of proper motions is : "pm-ra pm-dec [error ellipse] quality bibcode"
  • pm-ra : mu-ra*cos(dec) (expressed in the ICRS system in mas/yr)
  • pm-dec : mu-dec (expressed in the ICRS system in mas/yr)
  • [error ellipse] : error major axis and minor axis (in mas), orientation angle (in deg)
  • quality : flag of quality (A=best quality -> E=worst quality, {� } =unknown quality)
  • bibcode : bibcode of the proper motion reference
Proper motions mas/yr : 		-22.843 -25.096 [0.030 0.037 90] A 2020yCat.1350....0G
Syntax of radial velocity (or/and redshift) is : "value [error] (wavelength) quality bibcode"
  • value : radial velocity or/and redshift (Heliocentric frame) according to your Output Options
    (redshift may be not displayed if the data value is <0 and the database inside value is a radial velocity)
  • [error] : error of the corresponding value displayed before
  • (wavelength) : wavelength range of the measurement : Rad, mm, IR, Opt, UV, Xray, Gam or  '∼'(unknown)
  • quality : flag of quality ( A=best quality -> E=worst quality, ∼=unknown quality)
  • bibcode : bibcode of the value's origin
Radial velocity / Redshift / cz : 		V(km/s) -14.60 [0.2] / z(~) -0.000049 [0.000001] / cz -14.60 [0.20]
   A 2007A&A...475..519H
Syntax of parallax is : 'value quality [error] bibcode'
  • value : parallax value
  • quality : flag of quality (A=best quality -> E=worst quality, {� } =unknown quality)
  • [error] : mean error
  • bibcode : bibcode of the parallax reference
Parallaxes (mas): 		13.9206 [0.0314] A 2020yCat.1350....0G
Spectral type is made of 3 parts: %coding is composed of 4 parts :
  • the spectral type, which is made of a temperature class, eventually a luminosity class (roman number) and/or spectral peculiarities;
  • a quality letter: A=best quality→E=worst quality, {� } =unknown quality %
  • a quality letter: A=best quality -> E=worst quality, {� } =unknown quality
  • bibcode : bibcode of the spectral type reference
Spectral type: 		G0V C 2006A&A...460..695T
Syntax of fluxes (or magnitudes) is : "filter-name (System) flux-value [error] quality MultVarFlags bibcode"
  • filter-name : U, B, V, R, I, G, J, H, K, u, g, r, i, z
  • (System) : may be AB (default is Vega)
  • flux-value : value of flux or magnitude
  • [error] : error value
  • quality : flag of quality of the flux value ( A=best quality -> E=worst quality, {� } =unknown quality)
  • MultVarFlags : Mult is zero or one char (J) for joined photometry ; Var can be zero or two chars (V[0-4])
  • bibcode : bibcode of the flux reference
Fluxes (6) :
B 9.70 [~] D 2006A&A...460..695T
V 9.09 [~] D 2006A&A...460..695T
G 8.497600 [0.002893] C 2020yCat.1350....0G
J 7.474 [0.030] C 2003yCat.2246....0C
H 7.126 [0.027] C 2003yCat.2246....0C
K 7.060 [0.021] C 2003yCat.2246....0C
SIMBAD within arcmin
', {sourceSize:12, color:'#30a090'})); aladin.on('objectClicked', function(object) { var objName=object.data.MAIN_ID; aladin.showPopup(object.ra,object.dec,'',''+ objName+''); });" title="Show Simbad objects"> Overlay Simbad points in this preview
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The link on the acronym of the identifiers give access to the information for this acronym in the dictionary of nomenclature.
Identifiers (19) :
An access of full data is available using the icon Vizier near the identifier of the catalogue

HD 124784 GSC 08285-00847 1RXS J141658.4-495648 uvby98 100124784
CD-49 8609 HIC 69781 SAO 224812 V* V636 Cen
CPC 0 12167 HIP 69781 SV* SON 4987 Gaia DR3 6091428734401256448
CPD-49 6836 2MASS J14165790-4956423 TIC 331183881 Gaia DR2 6091428734401256448
GEN# +1.00124784 PPM 319361 TYC 8285-847-1

References (96 between 1850 and 2024) (Total 96)
Simbad bibliographic survey began in 1850 for stars (at least bright stars) and in 1983 for all other objects (outside the solar system).
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Collections of Measurements


velocities : 3    V* : 2    distance : 2    ROT : 1    Fe_H : 2    PLX : 4    PM : 4    MK : 3   

   

External archives :

Archive data at HEASARC - High-Energy Astrophysics Science Archive Research Center

Link by name to the catalogue in VizieR :

HD 124784 CD-49 8609 CPD-49 6836 GSC 08285-00847 HIC 69781
HIP 69781 2MASS J14165790-4956423 PPM 319361 1RXS J141658.4-495648 SAO 224812
TYC 8285-847-1 uvby98 100124784 V* V636 Cen Gaia DR3 6091428734401256448 Gaia DR2 6091428734401256448

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