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Richard P. Nelson, Oliver Gressel, Orkan M. Umurhan, Erratum: Linear and non-linear evolution of the vertical shear instability in accretion discs, Monthly Notices of the Royal Astronomical Society, Volume 456, Issue 1, 11 February 2016, Page 239, https://doi.org/10.1093/mnras/stv2440
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The paper Nelson, Gressel & Umurhan (2013) has been found to contain the following errors. Equation (32) in that paper should read (1)The version of this equation that appeared in the original paper omitted the term |$+ i \Omega _0 \bar{V}_z k_x g$|. One effect of including this term in the above dispersion relation is that acoustic modes can be destabilised in the presence of a radial temperature gradient in the disc. The statement in Nelson et al. (2013) suggesting that acoustic modes are stable is therefore not correct. An analysis of these unstable acoustic modes is contained in Mohandas & Pessah (2015).
\begin{eqnarray}
\omega ^4 &-& \left[ c_0^2\left(k_x^2 + k_z^2\right) + \kappa _0^2 + N_0^2\right]\omega ^2 - 2\Omega _0 \bar{V}_z c_0^2 k_x k_z + i \Omega _0 \bar{V}_z k_x g \nonumber \\
&& +\; \kappa _0^2 \left(c_0^2 k_z^2 + N_0^2\right) = 0.
\end{eqnarray}
Equation (39) of Nelson et al. (2013) contains a typographical error. It should read (2)whereas the last term in this expression was misprinted in the original paper as +σ2k2Π. The analysis of equation (2) is unaffected by this typographical error.
\begin{equation}
\frac{\mathrm{d}^2\Pi }{\mathrm{d} z^2} -\left(1 + ikq\right)z\frac{\mathrm{d}\Pi }{\mathrm{d} z} - \sigma ^2k^2 \Pi = 0,
\end{equation}
We thank Goparkumar Mohandas and Colin McNally for bringing the errors that we report in this erratum to our attention.
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© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
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