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Erschienen in:
2013 | CompoundObjectErratum | Buchkapitel
Erratum to: Lighthill’s Theory of Aerodynamic Noise
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Excerpt
Equation 3.2 should appear as follows:
$$\frac{\partial (\rho {u}_{i})} {\partial t} +{ \sum \limits_{j}}\frac{\partial (\rho {u}_{i}{u}_{j})} {\partial {x}_{j}} ={ \sum \limits_{j}}\frac{\partial {\tau }_{ij}} {\partial {x}_{j}} + {F}_{i}{\mbox{, Nm}}^{-3},$$
(3.2)
$$\begin{array}{rcl} {\tau }_{ij}& =& \left (-p -\frac{2} {3}\mu \sum \frac{\partial {u}_{j}} {\partial {x}_{j}}\right ){\delta }_{ij} + \mu \left (\frac{\partial {u}_{i}} {\partial {x}_{j}} + \frac{\partial {u}_{j}} {\partial {x}_{i}} \right ) =- p{\delta }_{ij} - {\tau }_{ij}^{{_\ast}}, \\ {\delta }_{ij}& =& \mbox{ Kronecker delta: }{\delta }_{ii} = 1,{\delta }_{ij} = 0, \\ {\tau }_{ij}^{{_\ast}}& =& \left (\frac{2} {3}\mu \sum \frac{\partial {u}_{j}} {\partial {x}_{j}}\right ){\delta }_{ij} - \mu \left (\frac{\partial {u}_{i}} {\partial {x}_{j}} + \frac{\partial {u}_{j}} {\partial {x}_{i}} \right ). \end{array}$$
(3.3)