Mean drift induced by free and forced dilational waves

• Published in: Physics of fluids (1994) 2003-12, Vol.15 (12), p.3703-3709
• Main Authors: Weber, Jan Erik, Christensen, Kai Haakon
• Format: Article
• Language: English
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.1621867

The mean drift velocity induced by longitudinal dilational waves in an elastic film is studied theoretically on the basis of a Lagrangian description of motion. The film is horizontal and situated at the interface between two viscous fluids. For time-damped dilational waves we let the film (i) move freely with the mean fluid velocity at the interface, and (ii) be kept fixed, i.e., having no mean motion. In the latter case the mean Lagrangian drift velocity in both fluids becomes oppositely directed to the wave propagation direction after a very short time. This is due to the fact that a fixed film initially generates a strong source of negative Eulerian second order mean momentum at the interface. This effect becomes even more pronounced when we consider forced dilational waves in a fixed film. Now a suitably arranged shear stress in the upper fluid prevents wave amplitude decay in the film. Accordingly, the negative mean Eulerian momentum at the interface becomes independent of time, and the backward drift will propagate deeper and deeper into the lower fluid. For a no-slip bottom at finite depth we may have a stationary drift solution with negative Lagrangian drift velocity everywhere in the fluid.