Multi-UAV (unmanned aerial vehicle) target enclosing control is one of the key technologies for achieving cooperative tasks. It faces limitations in communication resources and task framework separation. To address this, a distributed cooperative control strategy is proposed based on dynamic time-varying formation description and event-triggering mechanism. Firstly, a formation description method based on a geometric transformation parameter set is established to uniformly describe the translation, rotation, and scaling movements of the formation, providing a foundation for time-varying formation control. Secondly, a cooperative architecture for adaptive target enclosing tasks is designed. This architecture achieves an organic combination of formation control and target enclosing in a unified framework, thereby meeting flexible transitions between multiple formation patterns such as equidistant surrounding and variable-distance enclosing. Thirdly, a distributed dynamic event-triggered cooperative enclosing controller is developed. This strategy achieves online adjustment of communication thresholds through internal dynamic variables, significantly reducing communication while strictly ensuring system performance. By constructing a Lyapunov function, the stability and Zeno free behavior of the closed-loop system are proven. The simulation results verify this strategy, showing that this strategy can significantly reduce communication frequency while ensuring enclosing accuracy and formation consistency and effectively adapt to uniform and maneuvering target scenarios.