Friday, February 24, 2012
Nonlinear Gravity-Capillary Wave Patterns Generated by a Slow-Moving Pressure Source
James Duncan, Professor, Department of Mechanical Engineering, University of Maryland
Nonlinear wave patterns generated by an isolated steady pressure distribution moving across a water surface at speeds (Uc) below the minimum phase speed (Cmin) for linear gravity-capillary waves are explored experimentally. The pressure distribution is created by forcing air toward the water surface through a vertically oriented tube (internal diameter of 3 mm) that is mounted on a carriage that travels over the water surface. It is found that the wave patterns created are sensitive to both the air-flow rate and Uc. Several distinct regimes are found. At low values of Uc (< 0.83Cmin), the pattern is an isolated single depression that is centered on the pressure disturbance. The maximum depth of the depression increases slowly with carriage speed. At a critical value of Uc , which depends on the air-flow rate, the pattern transitions to a second stable state in which the largest depression of the surface occurs behind the pressure disturbance. The maximum depth of the surface depression increases by a factor of about two over this transition and the trailing surface pattern looks very much like a freely propagating three-dimensional gravity-capillary solitary wave (lump). In the narrow transition zone between these states, the wave pattern is unsteady and oscillates in the cross-stream direction. As Uc is increased further, the depth of the depression decreases. The values of the maximum depth of the depression plotted versus Uc fall on a single curve in this region, independent of air flow rate. At still higher carriage speeds, Uc > 0.96Cmin, a third state is found with a V-shaped surface pattern that oscillates in time, shedding lumps from its tips. The frequency of this shedding process decreases with increasing Uc. This work is being carried out in collaboration with T. Akylas and his research group at MIT who are performing numerical simulations of the flow.