Modulation effects of submarine internal wake waves on free surface divergence field

Disturbances of a submarine in a stratified flow stimulate an infinite mode of internal waves with multiple dispersion relationships. The surface convergence and divergence field are then modulated by such trailing waves, affecting the spatial distribution of microscale waves and leaving traces that are easily detected by Synthetic Aperture Radar. The present modified model combines the source-caused internal waves theory with the wind-waves spectrum model and coupling wave components of the full wave systems decomposed by the Fourier series method based on the second-order multi-directional irregular waves interactions theory. The effects of maximum Brunt-Vaisala frequency amplitude and depth, internal wave modes, submarine dive depth and velocity, wind speed, and wind direction are discussed in this study. It is shown that after the appearance of mode 0, the wake waves have an appreciable effect on the modulation of the free surface wind wave field. However, this effect is not fixed to manifest as an enhancement of the free surface convergence or divergence field intensity. The free surface field has the maximum divergence intensity amplitude under the downwind sailing condition when the submarine is sailing at low speed. At high speed, the maximum divergence intensity amplitude is at an angle of 30 degrees between the sailing direction and the wind direction, while the minimum divergence intensity is downwind.