  This paper presents a measurement of fiducial and differential cross-sections
for $W^{+}W^{-}$ production in proton-proton collisions at $\sqrt{s}=13$ TeV
with the ATLAS experiment at the Large Hadron Collider using a dataset
corresponding to an integrated luminosity of 139 fb$^{-1}$. Events with exactly
one electron, one muon and no hadronic jets are studied. The fiducial region in
which the measurements are performed is inspired by searches for the
electroweak production of supersymmetric charginos decaying to two-lepton final
states. The selected events have moderate values of missing transverse momentum
and the `stransverse mass' variable $m_{\textrm{T2}}$, which is widely used in
searches for supersymmetry at the LHC. The ranges of these variables are chosen
so that the acceptance is enhanced for direct $W^{+}W^{-}$ production and
suppressed for production via top quarks, which is treated as a background. The
fiducial cross-section and particle-level differential cross-sections for six
variables are measured and compared with two theoretical SM predictions from
perturbative QCD calculations.
