### Abstract

Moore's approximation method, first formulated for vortex sheets, is generalized and applied to axi-symmetric flow with swirl and with smooth initial data. The approximation preserves the forward cascade of energy but neglects any backflow of energy. It splits the Euler equations into two sets of equations: one for u_{+} = u_{+} (r,z,t) containing all non-negative wavenumbers (in z) and the second for u_{-} = u_{+}. The equations for u_{+} are exactly the Euler equations but with complex initial data. Traveling waves solutions u_{+} = u_{+}(r,z-iσt) with imaginary wave speed are found numerically for this problem. The asymptotic properties of the resulting Fourier coefficients show a singularity forming in finite time at which the velocity blows up.

Original language | English (US) |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 67 |

Issue number | 1-3 |

DOIs | |

State | Published - Aug 15 1993 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics

### Cite this

*Physica D: Nonlinear Phenomena*,

*67*(1-3), 1-18. https://doi.org/10.1016/0167-2789(93)90195-7