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How strain and spin may make a star bi-polar

Published online by Cambridge University Press:  01 April 2014

Lawrence K. Forbes
Lawrence K. Forbes*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, TAS 7001, Australia
*
†Email address for correspondence: larry.forbes@utas.edu.au
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Abstract

A previous study by Forbes (ANZIAM J., vol. 53, 2011, pp. 87–121) has argued that, when a light fluid is injected from a point source into a heavier ambient fluid, the interface between them is most unstable to perturbations at the lowest spherical mode. This means that, regardless of initial conditions, the outflow from a point source eventually becomes a one-sided jet. However, two-sided (bi-polar) outflows are nevertheless often observed in astrophysics, in apparent contradiction to this prediction. While there are many possible explanations for this fact, the present paper considers the effect of a straining flow in the ambient fluid. In addition, solid-body rotation in the inner fluid is also accounted for, in a Boussinesq viscous model. It is shown analytically that there are circumstances under which straining flow alone is sufficient to convert the one-sided jet into a genuine bi-polar outflow, in linearized theory. This is confirmed in a numerical solution of a viscous model of the flow, based on a spectral solution technique that accounts for nonlinear effects. Rotation can also generate flows that are two-sided, and this is likewise revealed through an asymptotic analysis and numerical solutions of the nonlinear equations.

JFM classification

Interfacial Flows (free surface): Fingering instability Mathematical Foundations: General fluid mechanics Mathematical Foundations: Mathematical Foundations
Type
Papers
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , pp. 332 - 367
Copyright
© 2014 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A.(Eds.) 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Anathpindika, S. 2009 Supersonic cloud collision. I. Astron. Astrophys. 504, 437–450.CrossRefGoogle Scholar
Baker, G., Caflisch, R. E. & Siegel, M. 1993 Singularity formation during Rayleigh–Taylor instability. J. Fluid Mech. 252, 51–78.CrossRefGoogle Scholar
Baker, G. R. & Pham, L. D. 2006 A comparison of blob methods for vortex sheet roll-up. J. Fluid Mech. 547, 297–316.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Braine, J., Lisenfeld, U., Duc, P.-A., Brinks, E., Charmandaris, V. & Leon, S. 2004 Colliding molecular clouds in head-on galaxy collisions. Astron. Astrophys. 418, 419–428.CrossRefGoogle Scholar
Chambers, K. & Forbes, L. K. 2012 The cylindrical magnetic Rayleigh–Taylor instability for viscous fluids. Phys. Plasmas 19, 102111.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Cowley, S. J., Baker, G. R. & Tanveer, S. 1999 On the formation of Moore curvature singularities in vortex sheets. J. Fluid Mech. 378, 233–267.CrossRefGoogle Scholar
Cui, A. Q. & Street, R. L. 2004 Large-eddy simulation of coastal upwelling flow. Environ. Fluid Mech. 4, 197–223.CrossRefGoogle Scholar
Dgani, R. & Soker, N. 1998 Instabilities in moving planetary nebulae. Astrophys. J. 495, 337–345.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
Epstein, R. 2004 On the Bell–Plesset effects: the effects of uniform compression and geometrical convergence on the classical Rayleigh–Taylor instability. Phys. Plasmas 11, 5114–5124.CrossRefGoogle Scholar
Farrow, D. E. & Hocking, G. C. 2006 A numerical model for withdrawal from a two-layer fluid. J. Fluid Mech. 549, 141–157.CrossRefGoogle Scholar
Forbes, L. K. 2009 The Rayleigh–Taylor instability for inviscid and viscous fluids. J. Engng Maths 65, 273–290.CrossRefGoogle Scholar
Forbes, L. K. 2011a A cylindrical Rayleigh–Taylor instability: radial outflow from pipes or stars. J. Engng Maths 70, 205–224.CrossRefGoogle Scholar
Forbes, L. K. 2011b Rayleigh–Taylor instabilities in axi-symmetric outflow from a point source. ANZIAM J. 53, 87–121.CrossRefGoogle Scholar
Forbes, L. K. & Brideson, M. A. 2013 Exact solutions for interfacial outflows with straining. ANZIAM J. (in press).Google Scholar
Gómez, L., Rodríguez, L. F. & Loinard, L. 2013 A one-sided knot ejection at the core of the HH 111 outflow. Rev. Mex. Astron. Astrofís. 49, 79–85.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 2000 Tables of Integrals, Series and Products, 6th edn. Academic Press.Google Scholar
Huarte-Espinosa, M., Frank, A., Balick, B., Blackman, E. G., de Marco, O., Kastner, J. H. & Sahai, R. 2012 From bipolar to elliptical: simulating the morphological evolution of planetary nebulae. Mon. Not. R. Astron. Soc. 424, 2055–2068.CrossRefGoogle Scholar
Inogamov, N. A. 1999 The Role of Rayleigh–Taylor and Richtmyer–Meshkov Instabilities in Astrophysics: An Introduction, Astrophysics and Space Physics Reviews, vol. 10, pp. 1–335. Harwood Academic.Google Scholar
Inoue, T. & Fukui, Y. 2013 Formation of massive molecular cloud cores by cloud–cloud collision. Astrophys. J. Lett. 774, L31.CrossRefGoogle Scholar
Klein, R. I. & Woods, D. T. 1998 Bending mode instabilities and fragmentation in interstellar cloud collisions: a mechanism for complex structure. Astrophys. J. 497, 777–799.CrossRefGoogle Scholar
Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292–313.CrossRefGoogle Scholar
Kreyszig, E. 2011 Advanced Engineering Mathematics, 10th edn. Wiley.Google Scholar
Lovelace, R. V. E., Romanova, M. M., Ustyugova, G. V. & Koldoba, A. V. 2010 One-sided outflows/jets from rotating stars with complex magnetic fields. Mon. Not. R. Astron. Soc. 408, 2083–2091.CrossRefGoogle Scholar
Mac Low, M.-M. & Klessen, R. S. 2004 Control of star formation by supersonic turbulence. Rev. Mod. Phys. 76, 125–194.CrossRefGoogle Scholar
Mac Low, M.-M. & McCray, R. 1988 Superbubbles in disk galaxies. Astrophys. J. 324, 776–785.CrossRefGoogle Scholar
Matsuoka, C. & Nishihara, K. 2006 Analytical and numerical study on a vortex sheet in incompressible Richtmyer–Meshkov instability in cylindrical geometry. Phys. Rev. E 74, 066303.CrossRefGoogle Scholar
McClure-Griffiths, N. M., Dickey, J. M., Gaensler, B. M. & Green, A. J. 2003 Loops, drips, and walls in the galactic chimney GSH 277+00+36. Astrophys. J. 594, 833–843.CrossRefGoogle Scholar
Mikaelian, K. O. 2005 Rayleigh–Taylor and Richtmyer–Meshkov instabilities and mixing in stratified cylindrical shells. Phys. Fluids 17, 094105.CrossRefGoogle Scholar
Moore, D. W. 1979 The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. R. Soc. Lond. A 365, 105–119.Google Scholar
Nordhaus, J., Brandt, T. D., Burrows, A. & Almgren, A. 2012 The hydrodynamic origin of neutron star kicks. Mon. Not. R. Astron. Soc. 423, 1805–1812.CrossRefGoogle Scholar
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. Appl. Phys. Lett. 25, 96–98.Google Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177.Google Scholar
Reipurth, B. & Bally, J. 2001 Herbig–Haro flows: probes of early stellar evolution. Annu. Rev. Astron. Astrophys. 39, 403–455.CrossRefGoogle Scholar
Reipurth, B., Yu, K. C., Rodríguez, L. F., Heathcote, S. & Bally, J. 1999 Multiplicity of the HH 111 jet source: Hubble Space Telescope NICMOS images and VLA maps. Astron. Astrophys. 352, L83–L86.Google Scholar
Resnick, R. & Halliday, D. 1966 Physics. Wiley.Google Scholar
Romanova, M. M., Ustyugova, G. V., Koldoba, A. V. & Lovelace, R. V. E. 2013 Warps, bending and density waves excited by rotating magnetized stars: results of global 3D MHD simulations. Mon. Not. R. Astron. Soc. 430, 699–724.CrossRefGoogle Scholar
Schmitt, R. W. 1995 The salt finger experiments of Jevons (1857) and Rayleigh (1880). J. Phys. Oceanogr. 25, 8–17.2.0.CO;2>CrossRefGoogle Scholar
Shariff, K. 2009 Fluid mechanics in disks around young stars. Annu. Rev. Fluid Mech. 41, 283–315.CrossRefGoogle Scholar
Sharp, D. H. 1984 An overview of Rayleigh–Taylor instability. Physica D 12, 3–18.CrossRefGoogle Scholar
Stahler, S. W. & Palla, F. 2004 The Formation of Stars. Wiley.CrossRefGoogle Scholar
Taylor, Sir G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, I. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
Tryggvason, G., Dahm, W. J. A. & Sbeih, K. 1991 Fine structure of vortex sheet rollup by viscous and inviscid simulation. J. Fluids Engng 113, 31–36.CrossRefGoogle Scholar
von Winckel, G.2004 lgwt.m. Available at: MATLAB file exchange website. http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=4540&objectType=file.Google Scholar
Ye, W.-H., Wang, L.-F. & He, X.-T. 2010 Jet-like long spike in nonlinear evolution of ablative Rayleigh–Taylor instability. Chin. Phys. Lett. 12, 125203.Google Scholar
Zinnecker, H. & Yorke, H. W. 2007 Toward understanding massive star formation. Annu. Rev. Astron. Astrophys. 45, 481–563.CrossRefGoogle Scholar