We propose a dynamical vortex definition (the 'λρ 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, λρ defines a vortex to be a connected region with two negative eigenvalues of the tensor SM + Sv. Here, SM is the symmetric part of the tensor product of the momentum gradient tensor ∇(ρu) and the velocity gradient tensor ∇u, with Sv denoting the symmetric part of momentum-dilatation gradient tensor ∇(vρu), and v ≡ ∇ · u, the dilatation rate scalar. The λρ definition is examined and compared with the λ2 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 λ2 and λρ structures are nearly identical, so that the λ2 method is still valid for low M compressible flows. But, the λρ definition is needed for studying vortex dynamics in highly compressible and strongly varying density flows.
- compressible flows
- multiphase and particle-laden flows
- vortex flows