The boundary-constraint method for constructing vortex-surface fields

Abstract

We develop a boundary-constraint method for constructing the vortex-surface field (VSF) in a three-dimensional fluid velocity–vorticity field. The isosurface of the VSF is a vortex surface consisting of vortex lines, which can be used to characterize the evolution of vortical structures in a Lagrangian sense. The evolution equation with pseudo-time is solved under the VSF boundary constraint to obtain a numerical solution of the VSF. Compared with the existing two-time method, the boundary-constraint method constructs the VSF from a single velocity dataset at a given time instead of a time series of velocity fields starting from a simple condition. This improvement significantly increases the applicability of the VSF method and reduces the demanding computational cost and required velocity data size. Using the boundary-constraint method, we construct the VSFs in Taylor–Green flow and transitional channel flow. In addition, the uniqueness of the VSF solution is discussed and the convergence of the error in the calculation of VSFs is analyzed.