# Inclusion of a Ship's Wake

If a propeller is calculated as operating behind a ship, the viscous part of the flow around the ship's hull is not included correctly. Therefore, a wake field is used in these cases. The wake field should either be taken from measurements or determined using a viscous flow solver.

To include a ship's wake field the velocity difference \(\Delta \vec{v}_{\text{viscous}}\) between the flow velocity of the potential flow \(\vec{v}\) and the velocity of the viscous flow \(\vec{v}_{\text{viscous}}\) is inserted as an additional part of the motion velocity \(\vec{v}_{\text{mot}}\) in the Neumann boundary condition. This way, the equation used for the calculation of the source strength \(\sigma\) is extended, resulting in the following equation: $$ \sigma = \frac{\partial \Phi_{\text{ind}}}{\partial n} = \left(\vec{v}_{\text{mot}} - \Delta \vec{v}_{\text{viscous}} - \vec{v}_{\text{ext}}\right) \cdot \vec{n} $$

More detailed descriptions of this approach can be found in our *pan*MARE-related publications, especially by Greve (2015) and Berger (2018).