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

We propose a dynamical vortex definition (the 'lambda(rho) 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, lambda(rho) 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 del (rho u) and the velocity gradient tensor del u, with S-v denoting the symmetric part of momentum-dilatation gradient tensor del(v rho u), and v equivalent to del.u, the dilatation rate scalar. The lambda(rho) definition is examined and compared with the lambda(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 less than or similar to 5) compressible flows, the lambda(2) and lambda(rho) structures are nearly identical, so that the lambda(2) method is still valid for low M compressible flows. But, the lambda(rho) definition is needed for studying vortex dynamics in highly compressible and strongly varying density flows.