  New measurements of rapidity-even dipolar flow, v$^{even}_{1}$, are presented
for several transverse momenta, $p_T$, and centrality intervals in Au+Au
collisions at $\sqrt{s_{NN}}~=~200,~39$ and $19.6$ GeV, U+U collisions at
$\sqrt{s_{NN}}~=~193$ GeV, and Cu+Au, Cu+Cu, d+Au and p+Au collisions at
$\sqrt{s_{NN}}~=~200$~GeV. The v$^{even}_{1}$ shows characteristic dependencies
on $p_{T}$, centrality, collision system and $\sqrt{s_{_{NN}}}$, consistent
with the expectation from a hydrodynamic-like expansion to the dipolar
fluctuation in the initial state. These measurements could serve as constraints
to distinguish between different initial-state models, and aid a more reliable
extraction of the specific viscosity $\eta/s$.
