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Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction ${f_{\text{G}}} = {{\bar n} \mathord{\left/ \right. } {{n_{\text{G}}}}} = {{\bar n} \mathord{\left/ \right. } {\left( {{{{I_{\text{p}}}} \mathord{\left/ \right. } {\pi {a^2}}}} \right)}}$ increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized ${\boldsymbol{E}} \times {\boldsymbol{B}}$ shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.