  The majority of studies on multi-scale vortex motions employ a
two-dimensional geometry by using a variety of observational and numerical
data. This approach limits the understanding the nature of physical processes
responsible for vortex dynamics. Here we develop a new methodology to extract
essential information from the boundary surface of vortex tubes. 3D
high-resolution magnetoconvection MURaM numerical data has been used to analyse
photospheric intergranular velocity vortices. The Lagrangian Averaged Vorticity
Deviation (LAVD) technique was applied to define the centers of vortex
structures and their boundary surfaces based on the advection of fluid
elements. These surfaces were mapped onto a constructed envelope grid that
allows the study of the key plasma parameters as functions of space and time.
Quantities that help in understanding the dynamics of the plasma, e.g. Lorentz
force, pressure force, plasma-$\beta$ were also determined. Our results suggest
that, while density and pressure have a rather global behaviour, the other
physical quantities undergo local changes, with their magnitude and orientation
changing in space and time. At the surface, the mixing in the horizontal
direction is not efficient, leading to appearance of localized regions with
higher/colder temperatures. In addition, the analysis of the MHD Poynting flux
confirms that the majority of the energy is directed in the horizontal
direction. Our findings also indicate that the pressure and magnetic forces
that drive the dynamics of the plasma on vortex surfaces are unbalanced and
therefore the vortices do not rotate as a rigid body.
