The second order wave potential does not contribute to the mean wave drift force component given in Equation 5–6. However, it has been reported that in shallow water the difference frequency drift force may be increased significantly by the second order potential contribution. Therefore, the inclusion of the second order potential would be necessary for the accurate evaluation of the second order wave exciting forces in shallow water.

In Aqwa this is done by using Pinkster's approximation for long crested wave case (see [37]). The second order force component induced by the second order potential corresponding to a pair of incident waves of (, , , ) and (, , , ) is given as

(5–28)

where is the first order wave exciting force induced by a regular wave with the wave number of and unit wave amplitude, which can be directly calculated by Equation 4–8. The factor is expressed as

(5–29)

where

In Aqwa, this simplification is only applied for the long crested wave case when the full QTF matrix is required. When Newman's approximation is employed, this term is ignored.