Wave drift damping is induced by nonlinear surface wave effects, which provides additional damping for the slow-drift motions, along with above mentioned nonlinear drag forces. It is employed in Aqwa time domain analysis when the first and second order wave exciting forces are included (Aqwa-Drift).

For a long crested wave case, the wave drift damping coefficients used in Aqwa are based on the work of Kim and Sclavounos [23], in which the Aranha's formulae are employed. The wave drift damping coefficient is defined in the drift matrix equation for a floating structure with small forward speed:

(7–21)

where are the drift forces and moment when floating structure has a relative speed , and is the incident wave angle relative to the structure local axis frame Gxyz.

For a deep water case, the drift damping coefficients are estimated by

(7–22)

The drifting damping coefficients due to the yaw motion are given by Aranha and Martins [3] and are based on the slender-body approximation

(7–23)

where

in which is the water-line profile of the ship with length .

For the finite depth water of d, Equation 7–22 is extended as

(7–24)

where

The drift damping coefficients due to the yaw motion for finite depth water have the same forms as those given by Equation 7–23.

For a multiple directional wave case, the mean drift force component is written as

(7–25)

As discussed by Kim et al [24], the damping coefficient in Equation 7–24 is extended as

(7–26)

where

is the total number of wave directions,

is the number of frequencies.

Other damping terms in Equation 7–24 have the similar forms as that expressed in Equation 7–25 for the multiple directional wave case.