Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-04T05:51:19.650Z Has data issue: false hasContentIssue false
  • English
  • Français

A general theory of curved vortices with circular cross-section and variable core area

Published online by Cambridge University Press:  26 April 2006

J. S. Marshall
J. S. Marshall
Affiliation:
Department of Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A theory is derived for general motions of an inviscid vortex with circular crosssection and variable core area using a directed filament model of the vortex. The theory reduces in special cases to any of several previous vortex theories in the literature, but it is better suited than previous theories for handling nonlinear areavarying waves on the vortex core. Jump conditions across points of discontinuity and a variational form of the theory are also given. The theory is applied to obtain new solutions for several fundamental problems in vortex dynamics related to axisymmetric solitary waves on a vortex core, axisymmetric and helical vortex breakdowns and the buckling of a columnar vortex under compression.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 229 , August 1991 , pp. 311 - 338
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ashurst, W. T. & McMurtry, P. A. 1989 Flame generation of vorticity: vortex dipoles from monopoles. Combust. Sci. Tech. 66, 17–37.Google Scholar
Beale, J. T. & Majda, A. 1981 Rates of convergence for viscous splitting of the Navier-Stokes equations. Math. Comput. 37, 243–259.Google Scholar
Bray, K. N. C. 1980 Turbulent flow with premixed reactants. In Turbulent Reacting Flows (ed. P. A. Libby & F. A. Williams). Topics in Applied Physics, vol. 44. Springer.
Cheer, A. Y. 1979 A study of incompressible two-dimensional vortex flow past a circular cylinder. Lawrence Berkeley Lab. Rep. LBL-9950.Google Scholar
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 785–796.Google Scholar
Chorin, A. J. 1978 Vortex sheet approximation of boundary layers. J. Comput. Phys 27, 428–442.Google Scholar
Chorin, A. J. 1980 Flame advection and propagation algorithms. J. Comput. Phys. 35, 1–11.Google Scholar
Chorin, A. J. & Mardsden, J. E. 1979 A Mathematical Introduction to Fluid Mechanics. Springer.
Clements, R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.Google Scholar
Dahlquist, G., Bjørk, Å. & Anderson, N. 1974 Numerical Methods. Prenctice-Hall.
Dorny, C. N. 1975 A Vector Space Approach to Models and Optimization. Wiley-Interscience.
Ganji, A. T. & Sawyer, R. F. 1980 Turbulence, combustion, pollutant and stability of a premixed step combuster. NASA Contractor Rep. 3230.Google Scholar
Ghoniem, A. F., Chorin, A. J. & Oppenheim, A. K. 1982 Numerical modelling of turbulent flow in a combustion tunnel.. Phil. Trans. R. Soc. Lond. A 304, 303–325.Google Scholar
Hald, O. H. 1979 Convergence of vortex methods for Euler's equations II. SIAM J. Numer. Anal. 16, 726–755.Google Scholar
Hald, O. H. 1985 Convergence of vortex methods for Euler's equations III. Rep. PAM-270. Center for Pure and Applied Mathematics, U. C. Berkeley.Google Scholar
Henhici, P. 1974 Applied and Computational Complex Analysis, vol. 1. John Wiley & Sons.
Ho, C. M. 1986 An alternative look at the unsteady separation phenomenon. In Recent Advances in Aerodynamics (ed. A. Krothapalli). Springer.
Keller, J. O., Vaneveld, L., Korschelt, D., Ghoniem, A. F., Daily, J. W. & Oppenheim, A. K. 1981 Mechanism of instabilities in turbulent combustion leading to flashback. AIAA 19th Aerospace Sciences Meeting, AIAA -81–0107.Google Scholar
Law, C. K. 1988 Dynamics of stretched flames. 22nd Symp. (Intl) on Combustion, pp. 1381–1402. The Combustion Institute.
Lie, S. & Engel, F. 1880 Theorie der Transformation Gruppen. Leipzig: Teubner.
Majda, A. J. & Beale, J. T. 1982 The design and numerical analysis of vortex methods In Transonic, Shock and Multidimensional Flows. Academic.
Milne-Thompson, L. M. 1968 Theoretical Hydrodynamics, 5th edn. Macmillan.
Noh, W. F. & Woodward, P. 1976 SLIC (Simple Line Interface Calculation). Proc. 5th Intl Conf, on Fluid Dynamics (ed. A. Vooren & P. Zandbergen), pp. 330–339. Springer.
Pitz, R. W. & Daily, J. W. 1983 Experimental study of combustion in a turbulent free shear layer formed at a rearward-facing step. AIAA J. 21, 1565–1570.Google Scholar
Plee, S. L. & Mellor, A. M. 1978 Review of flashback reported in prevaporizing/premixing combustors. Combust. Flame 32, 193–203.Google Scholar
Sand, I. Os. 1987 On the unsteady reacting and non-reacting flow in a channel with cavity. Dr. Scient. thesis, University of Bergen, Norway.
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn. McGraw-Hill.
Sethian, J. 1984 Turbulent combustion in open and closed vessels. J. Comput. Phys. 54, 425–456.Google Scholar
Trefethen, L. N. 1979 Numerical computation of the Schwarz-Christoffel transformation. STAN-79–710.Google Scholar
Vaneveld, L., Hom, K. & Oppenheim, A. K. 1982 Secondary effects in combustion instabilities leading to flashback. AIAA 20th Aerospace Sciences Meeting. AIAA-82–0037.Google Scholar
Williams, J. C. 1977 Incompressible boundary-layer separation. Ann. Rev. Fluid Mech. 9, 113–144.Google Scholar