  Modelling the vortex structures and then translating them into the
corresponding velocity fields are two essential aspects for the vortex-based
modelling works in wall-bounded turbulence. This work develops a datadriven
method, which allows an effective reconstruction for the velocity field based
on a given vortex field. The vortex field is defined as a vector field by
combining the swirl strength and the real eigenvector of the velocity gradient
tensor. The distinctive properties for the vortex field are investigated, with
the relationship between the vortex magnitude and orientation revealed by the
differential geometry. The vortex-to-velocity reconstruction method
incorporates the vortex-vortex and vortex-velocity correlation information and
derives the inducing model functions under the framework of the linear
stochastic estimation. Fast Fourier transformation is employed to improve the
computation efficiency in implementation. The reconstruction accuracy is
accessed and compared with the widely-used Biot-Savart law. Results show that
the method can effectively recover the turbulent motions in a large scale
range, which is very promising for the turbulence modelling. The method is also
employed to investigate the inducing effects of vortices at different heights,
and some revealing results are discussed and linked to the hot research topics
in wall-bounded turbulence.
