Scattered waves and motions of marine vessels advancing in a seaway

► We present a frequency-domain model for motions of vessels advancing in a seaway. ► A new radiation condition accounts for the Doppler shift of the scattered waves. ► This condition applies to a range of speed, above and below the group velocity of the scattered waves. ► The forward speed requires higher resolution and larger domain for model convergence. ► Hydrodynamic coefficients and vessel response agree well with laboratory data.