A search for a high-mass Higgs boson $H$ is performed in the $H\to WW\to\ell\nu\ell\nu$ and $H\to WW\to \ell\nu{qq}$ decay channels using $pp$ collision data corresponding to an integrated luminosity of 20.3 fb$^{-1}$ collected at $\sqrt{s}=$ 8 TeV by the ATLAS detector at the Large Hadron Collider. No evidence of a high-mass Higgs boson is found. Limits on $\sigma_H\times \mathrm{BR}(H\to WW)$ as a function of the Higgs boson mass $m_H$ are determined in three different scenarios: one in which the heavy Higgs boson has a narrow width compared to the experimental resolution, one for a width increasing with the boson mass and modeled by the complex-pole scheme following the same behavior as in the Standard Model, and one for intermediate widths. The upper range of the search is $m_H=1500$ GeV for the narrow-width scenario and $m_H=1000$ GeV for the other two scenarios. The lower edge of the search range is $200$--$300$ GeV and depends on the analysis channel and search scenario. For each signal interpretation, individual and combined limits from the two $WW$ decay channels are presented. At $m_{H} = 1500$ GeV, the highest-mass point tested, $\sigma_H\times\mathrm{BR}(H\rightarrow WW)$ for a narrow-width Higgs boson is constrained to be less than 21 fb and 6.0 fb at 95% CL for the gluon fusion and vector-boson fusion production modes, respectively.

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