Stirred mixing is one of the important unit operations in the chemical, petroleum, pharmaceutical and food industries. The mixing of liquids is achieved by a rotating shear flow field formed by a periodic jet flow from the impeller. In this work, we investigated the flow structure in a square stirred tank without baffles and with a Rushton impeller (RT) using particle image velocimetry (PIV) technique. The instantaneous flow fields were obtained as a function of various rotations per minute (rpm) for the impeller (N=120, 150, 180, 210 and 240 rpm), while phase-resolved velocity information was obtained for N=150 rpm. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were applied to analyze the velocity fields, flow structure and dynamic information in the absence of impeller area. As demonstrated by the results, there is a wide range of spatial and temporal scales throughout the process. The high energy parts exist in two kinds of structures except for the average fluid flow. The instability phenomenon results from the cyclic shear flow and the trailing vortices structure caused by the periodic jet near the blade passage frequency. As the Reynolds number is on the rise, the periodic flow increases, the random turbulence is reduced, and the flow tends to the ultimate stable state. The square section acts like baffles to change the direction of the fluid circumferential velocity while increasing the radial and tangential flow, which is conducive to mixing. This study provides a basis for understanding the flow structure and unsteady characteristics in a square stirred mixing tank.