Toward vortex identification based on local pressure-minimum criterion in compressible and variable density flows

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 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 λ_ρ structures are nearly identical, so that the λ₂ 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.