## Abstract

We propose a dynamical vortex definition (the 'λ_{ρ} definition') for flows dominated by density variation, such as compressible and multi-phase flows. Based on the search of the pressure minimum in a plane, λ_{ρ} defines a vortex to be a connected region with two negative eigenvalues of the tensor S^{M} + S^{v}. Here, S^{M} is the symmetric part of the tensor product of the momentum gradient tensor ∇(ρu) and the velocity gradient tensor ∇u, with S^{v} denoting the symmetric part of momentum-dilatation gradient tensor ∇(vρu), and v ≡ ∇ · u, the dilatation rate scalar. The λ_{ρ} definition is examined and compared with the λ_{2} definition using the analytical isentropic Euler vortex and several other flows obtained by direct numerical simulation (DNS) - e.g. liquid jet breakup in a gas, a compressible wake, a compressible turbulent channel and a hypersonic turbulent boundary layer. For low Mach number (M ≤ 5) compressible flows, the λ_{2} and λ_{ρ} structures are nearly identical, so that the λ_{2} method is still valid for low M compressible flows. But, the λ_{ρ} definition is needed for studying vortex dynamics in highly compressible and strongly varying density flows.

Original language | English |
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Pages (from-to) | 5-17 |

Number of pages | 13 |

Journal | Journal of Fluid Mechanics |

Volume | 850 |

DOIs | |

Publication status | Published - 10 Sept 2018 |

Externally published | Yes |

## Keywords

- compressible flows
- multiphase and particle-laden flows
- vortex flows