Abstract. We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibbon, who observed that the vorticity vector ω aligns with the intermediate eigenvector of the strain-matrix S, we study this problem in the context of both the three-dimensional Euler and Navier-Stokes equations using the variables α =ξ · Sξ and χ =ξ × Sξ whereξ = ω/ω. This introduces the dynamic angle φ(x, t) = arctan( χ α ), which lies between ω and Sω. For the Euler equations a closed set of differential equations for α and χ is derived in terms of the Hessian matrix of the pressure P = {p ,ij }. For the Navier-Stokes equations, the Burgers vortex and shear-layer solutions turn out to be the Lagrangian fixed-point solutions of the equivalent (α, χ) equations with a corresponding angle φ = 0. Under certain assumptions for more general flows it is shown that there is an attracting fixed point of the (α, χ) equations which corresponds to positive vortex stretching and for which the cosine of the corresponding angle is close to unity. This indicates that near alignment is an attracting state of the system and is consistent with the formation of Burgers-like structures.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.