Analytic calculation of two-dimensional linear viscous gravity–capillary waves on deep water generated by a moving forcing at non-critical conditions: wave patterns and spatial decay rate

Two-dimensional (2-D) steady viscous gravity–capillary wave patterns (minimum phase speed: c min ) by a moving Gaussian forcing (speed: V ) above the surface of deep water are calculated by analytically solving a theoretically derived linear wave model equation, based on the spatial Fourier transform and Cauchy residue theorem. By considering viscous effects on the poles in the relevant complex region, the analytics results in a single expression of wave profiles for both supercritical ( V > c min ) and subcritical ( V