Two parallel swirling/rotating jets with a distance between them are termed biswirling jets here, which have important and complicated vortex structures different from the single swirling jet due to the negligible vortex-vortex interactions. The visualization of vortex-vortex interaction between the biswirling jets is accomplished by using direct numerical simulation. The evolution of vortex structures of the biswirling jets is found rather complicated. The turbulent kinetic energy and turbulence dissipation in the central convergence region are augmented locally and rather strongly. The modulation of turbulent kinetic energy by jet-jet interaction upon different scales of vortices is dominated by the swirling levels and the distance between the jets. The turbulent kinetic energy upon intermediate and small scale vortices in bijets with not very high swirling level and at a very close distance is smaller than that in single swirling jets, whereas the opposite is true under a far distance, and so forth.