We experimentally investigate the dynamics of surface waves excited by oscillations from a cylindrical sidewall. Particle-imaging-velocimetry measurements with fluorescent particles were used to determine the flow patterns near the sidewall of the cylindrical fluid container and to identify the locations of the evolving air–water interfaces. The high-frequency wall oscillations created four jets that originate at the cylindrical sidewall. Four vortex streets shed from the jets propagate from the sidewall to the centre of the container and subsequently excite a low-frequency gravity wave. The interaction between this gravitational surface wave and the high-frequency capillary waves was found to be responsible for creating droplet splash at the water surface. This phenomenon was first described as ‘Long-Xi’ or ‘dragon wash’ in ancient China. The physical processes for generating the droplet ejection, including the circular capillary waves, azimuthal waves, streaming jets and low-frequency gravity waves, are described in this paper.

/pdf/experimental-studies-of-surface-waves-inside-a-cylindrical-2m40yesige.pdf

Experimental studies of surface waves inside a cylindrical container

The qualitative effect of a major disturbance such as an earthquake or a hurricane or, on a lesser scale, a powerboat moving along the edge of a bay, harbor, or lake, can be observed in a partially filled wineglass. We simulate this small-scale disturbance and do a quantitative analysis to explain how a resonance can occur on the liquid surface in the wineglass. An explanation is also given why such circumstances can occur in scaled-up situations such as bays, rivers, and harbors.

A storm in a wineglass

We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek time-harmonic solutions of the linearized problem, which describes the time-evolution of the fluid due to a small initial disturbance of the surface at rest. As opposed to the zero surface tension case, where the problem reduces to a partial differential equation for the velocity potential, we obtain a coupled system for the velocity potential and the free surface displacement. We derive a new variational formulation of the coupled problem and establish the existence of solutions using the direct method from the calculus of variations. We prove a domain monotonicity result for the fundamental sloshing eigenvalue. In the limit of zero surface tension, we recover the variational formulation of the mixed Steklov--Neumann eigenvalue problem and give the first-order perturbation formula...

A Variational Characterization of Fluid Sloshing with Surface Tension

On a special case of forced capillary–gravity waves in a circular basin under Hocking’s edge condition

The experiment is carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we find the viscosity is important to achieve the low frequency water wave with the cooperation of hundreds of “finger” waves. Shadowgraphs have been taken qualitatively using laser sheet and vertical velocities of surface waves have been measured quantitatively by Polytec Scanning Vibrometer. The viscous cooperation effects are shown to be the most important mechanism for the dragon wash phenomena.

Experimental studies on dragon wash phenomena

Exact solution for forced capillary-gravity waves in a circular basin under Hocking's edge condition

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Exact solution for forced capillary-gravity waves in a circular basin under Hocking's edge condition

On a special case of forced capillary–gravity waves in a circular basin under Hocking’s edge condition