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In this paper, a unified dark fluid with constant adiabatic sound speed isdecomposed into cold dark matter interacting with vacuum energy. Based onMarkov chain Monte Carlo method, we constrain this model by jointing thegeometry and dynamical measurement. The geometry test includes cosmic microwavebackground radiation from \textit{Planck}, baryon acoustic oscillation, andtype Ia supernovae; the dynamic measurement is $f\sigma_8(z)$ data points whichis obtained from the growth rate via redshift-space distortion, and$\sigma_8(z)$ is the root-mean-square amplitude of the density contrast$\delta$ at the comoving $8h^{-1}$ Mpc scale. The jointed constraint shows that$\alpha$ = $ 0.000662_{- 0.000662}^{+ 0.000173}$ and $\sigma_8$ = $ 0.824_{-0.0166}^{+ 0.0128}$. The CMB and matter power spectra are both similar for thecase of $\alpha=$ mean value and that of $\alpha=0$. However, the evolutionarycurves of $f\sigma_8(z)$ are different. This means that, to some extent, thedata points of the growth rate could break the degeneracy of the dark energymodels.

Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data