 Stationary-phase wake of an impulsive capillary wave

ID: stationary-phase-wake-of-an-impulsive-capillary-wave

Along

x = V t > 0

, if

ϵ V^{2} / S^{2} ≪ 1

, the stationary wavenumber

k_{0} = 4 V^{2} / (9 S^{2})

obeys

k_{0} ϵ ≪ 1

η (x, t) \sim \frac{W ϵ S t ^{2}}{x ^{5/2}} \frac{9}{2 π} sin (\frac{4 x ^{3}}{27 S ^{2} t ^{2}} - \frac{π}{4}) .

Only the integrated initial velocity

- 2 W ϵ

survives in this long-wave far field.

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