A characterization of the standard Reeb flow

Among the topological conjugacy classes of the continuous flows $\{{\varphi }^t\}$ whose orbit foliations are the planar Reeb foliation, there is one class called the standard Reeb flow. We show that $\{{\varphi }^t\}$ is conjugate to the standard Reeb flow if and only if $\{{\varphi }^t\}$ is conjugate to $\{{\varphi }^{\lambda t}\}$ for any $\lambda >0$.