Kelvin–Froude wake patterns of a traveling pressure disturbance

According to Kelvin, a point pressure source uniformly traveling over the surface of deep calm water leaves behind universal wake pattern confined within $39^{\circ}$ sector and consisting so-called transverse diverging wavefronts. Actual ship wakes differ in their appearance from both each other Kelvin's prediction. The difference can be attributed deviation limit for given shape disturbance quantified by Froude number $F$. We show that linear theory effect arbitrary on mimicked an effective distribution. Further, resulting patterns are qualitatively different depending whether water-piercing is present or not ("sharp" vs "smooth" disturbances). For smooth sources, we generalize stationary phase argument encompass finite size effects classify patterns. Specifically, there exist two characteristic numbers, $F_{1}$ $F_{2}>F_{1}$, such as only if $F\gtrsim F_{1}$. $F_{1}\lesssim F \lesssim F_{2}$, consists wavefronts angle may smaller than Kelvin's. An additional made found F_{2}$. If has sharp boundary, always features interference effects. constant line segment mimicking slender understood due opposing resembling (but identical to) originating at segment's ends.