The total correlations in a bipartite quantum system are measured by the quantum mutual information $mathcal{I}$, which consists of quantum discord and classical correlation. However, recent results in quantum information shows that coherence, which is a part of total correlation, is more general and more fundamental than discord. The role of coherence in quantum resource theories is worthwhile to investigate. We first study the relation between quantum discord and coherence by reducing the difference between them. And then, we consider the dynamics of quantum discord, classical correlations and quantum coherence under incoherent quantum channels. We discover that coherence indicate the behavior of quantum discord (classical correlation) for times $t<bar t$, and indicate the decoherence of classical correlation (quantum discord) for times $t>bar t$. What is more, the coherence frozen and decay indicate the quantum discord and classical correlation frozen and decay respectively.
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