Wake and wave resistance on viscous thin films

The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationar...

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Bibliographic Details
Published in:Journal of fluid mechanics 2016-04, Vol.792, p.829-849
Main Authors: Ledesma-Alonso, René, Benzaquen, Michael, Salez, Thomas, Raphaël, Elie
Format: Article
Language:English
Subjects:
Fluid mechanics
Free surfaces
Physics
Surface waves
Thin films
Viscosity
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Summary:The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationary deformation of the interface – a wake – that spatially vanishes in the far region. The shape of the wake and the way it vanishes depend on both the speed and size of the external source and the properties of the film. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail. For finite-size pressure disturbances, it increases with the speed, up to a certain transition value, above which a monotonic decrease occurs. The role of the horizontal extent of the pressure field is studied as well, revealing that for a smaller disturbance the latter transition occurs at a higher speed. Eventually, for a Dirac pressure source, the wave resistance either saturates for a one-dimensional geometry, or diverges for a two-dimensional geometry.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2016.110