Abstract
The effect of fluid compressibility on the evolution of the pressure distribution and free surface elevation, following the initiation of a horizontal motion of a vertical wavemaker, is analysed. This effect is significant even in a liquid (like water) when the time scale of the motion is very short (e.g. impulsive motions).
In the leading order the present problem is analogous to that of supersonic flow about a thin wing, thus the solution is represented by means of an appropriate ‘supersonic source’ distribution. Closed-form results are obtained for the case of impulsive motion (i.e. a “step function” velocity). The pressure field corresponds to systems of ‘double rarefaction’ and ‘double compression’ waves traversing the fluid domain intermittently. Following the passage of a rarefaction (compression) wave, the free surface becomes locally concave (convex). The resulting free surface profile consists of an elongating wavetrain in front of a ‘jet’ riding up the vertical wall.
On the compressible time-scale the pressure and velocity fields approach a steady long-time limit. This limit corresponds to the ‘short-time’ incompressible flow prevailing after the attenuation of the pressure waves. The spatial nonuniformity of the asymptotic expansion in the neighbourhood of the waterline is briefly discussed.
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Frankel, I. Compressible flow induced by the transient motion of a wavemaker. Z. angew. Math. Phys. 41, 628–655 (1990). https://doi.org/10.1007/BF00946098
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DOI: https://doi.org/10.1007/BF00946098