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We present spatial-resolved measurements of the columnar vortex structures inrotating Rayleigh-B\'enard convection. The scaled radial profiles of theazimuthal velocity $u_{\phi}(r)$ and vertical vorticity ${\omega}(r)$ of thevortices are analyzed and compared with the predictions of the asymptotictheory. The results reveal that the asymptotic theory predicts accurately$u_{\phi}(r)$ and ${\omega}(r)$ in the geostrophic convection regime, butextension of the theory in the weak rotation regime is needed to interpret therotation-dependence of the experimental data. Our measurements of the meanvelocity, vorticity of the vortices, and the strength of the vortex shieldstructure all indicate a flow transition from weekly rotating convection togeostrophic convection. Results of the parameter values for the transition arein agreement with the scaling relationship obtained from previous heat-transfermeasurements.

Fine vortex structure and flow transition to the geostrophic regime in rotating Rayleigh-B\'enard convection