The effect of viscosity on the waves due to a moving oscillatory surface pressure

Abstract

It is known that when a pressure distributionp 0(x) exp (i ω t moves with a constant velocityu 0 parallel to $$\overrightarrow {o x} $$ on the surface (y=0) of an inviscid liquid, (i) the steady-state wave amplitude does not die out at large distances from the source for (ωu 0/g≠1/4, and(ii) the solution becomes singular for ωu 0/g=1/4. Here is shown that the consideration of even a slight viscosity of the liquid leads to a wave decay with distance for all (ωu 0/g), the solution remaining non-singular for (ωu 0/g=1/4. Furthermore, for a finitely distributedp 0(x), the wave amplitude is always non-zero, unlike in the case of an inviscid fluid, where no energy is transmitted for an infinite number of values of a parameter involving ω,u 0 and the length of the pressure strip.