This paper presents a study of the production of $WW$ or $WZ$ boson pairs, with one $W$ boson decaying to $e\nu$ or $\mu\nu$ and one $W$ or $Z$ boson decaying hadronically. The analysis uses 20.2 fb$^{-1}$ of $\sqrt{s}=8$ TeV $pp$ collision data, collected by the ATLAS detector at the Large Hadron Collider. Cross-sections for $WW/WZ$ production are measured in high-$p_{T}$ fiducial regions defined close to the experimental event selection. The cross-section is measured for the case where the hadronically decaying boson is reconstructed as two resolved jets, and the case where it is reconstructed as a single jet. The transverse momentum distribution of the hadronically decaying boson is used to search for new physics. Observations are consistent with the Standard Model predictions, and $95\%$ confidence intervals are calculated for parameters describing anomalous triple gauge-boson couplings.
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