Space-time rescaling symmetry in the tactic migration of micrometer-size organisms

It is observed that the Navier-Stokes rescaling invariance $\overrightarrow{\mathrm{x}}\to \lambda \overrightarrow{\mathrm{x}}$, $t\to {\lambda }^{2}t$, $\overrightarrow{\mathrm{v}}\to {\lambda }^{-1\mathrm{}}\overrightarrow{\mathrm{v}}$ shows up in the chemotaxis of motile $E$. coli and the phototaxis of $P$. uncinatum. Quantitatively accurate measurements on other motile bacteria and blue-green algae may reveal that this underlying hydrodynamic symmetry is featured commonly in the tactic migration of micrometer-size organisms in aqueous media.