  Recently, a non-abelian generalisation of the Navier-Stokes equation that
exhibits a manifest duality between colour and kinematics has been proposed by
Cheung and Mangan. In this paper, we offer a new perspective on the double copy
formulation of this equation, based on the homotopy algebraic picture suggested
by Borsten, Kim, Jur\v{c}o, Macrelli, Saemann, and Wolf. In the process, we
describe precisely how the double copy can be realised at the level of
perturbiner expansions. Specifically, we will show that the colour-dressed
Berends-Giele currents for the non-abelian version of the Navier-Stokes
equation can be used to construct the Berends-Giele currents for the double
copied equation by replacing the colour factors with a second copy of kinematic
numerators. We will also show a Kawai-Lewellen-Tye relation stating that the
full tree-level scattering amplitudes in the latter can be written as a product
of tree-level colour ordered partial amplitudes in the former.
