The tailbud is the posterior leading edge of the growing vertebrate embryo and consists of motile progenitors of the axial skeleton, musculature and spinal cord. We measure the 3D cell flow field of the zebrafish tailbud and identify changes in tissue fluidity revealed by reductions in the coherence of cell motion without alteration of cell velocities. We find a directed posterior flow wherein the polarization between individual cell motion is high, reflecting ordered collective migration. At the posterior tip of the tailbud, this flow makes sharp bilateral turns facilitated by extensive cell mixing due to increased directional variability of individual cell motions. Inhibition of Wnt or Fgf signaling or cadherin 2 function reduces the coherence of the flow but has different consequences for trunk and tail extension. Modeling and additional data analyses suggest that the balance between the coherence and rate of cell flow determines whether body elongation is linear or whether congestion forms within the flow and the body axis becomes contorted.